{"pdfData":[[{"bbox":[86,125,143,138],"type":"text","angle":0,"index":0,"text":"进位计数制","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":0,"id":"171a7ac6-f45b-4915-92bf-5381579b034a","page_size":[595,841],"block_position":"0-0"},{"bbox":[86,141,246,154],"type":"text","angle":0,"index":1,"text":"基数 R：允许使用的基本数码个数","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":0,"id":"f712a7e8-c30b-4bca-a1d7-fbbc5354d789","page_size":[595,841],"block_position":"0-1"},{"bbox":[87,157,299,169],"type":"text","angle":0,"index":2,"text":" 权 Wi：权也称位权，第 i 位上的数码的权重","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":0,"id":"1b128072-3910-463e-925d-ee9d680d3f7d","page_size":[595,841],"block_position":"0-2"},{"bbox":[87,172,244,185],"type":"text","angle":0,"index":3,"text":"值，即权与数码所处的位置 i 有关","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":0,"id":"98321c62-772d-45cd-a5e7-b830c7bd4615","page_size":[595,841],"block_position":"0-3"},{"bbox":[88,189,132,200],"type":"text","angle":0,"index":4,"text":"$\\mathbf { \\nabla } \\cdot \\mathbf { \\vec { w } } \\mathbf { \\vec { i } } = \\mathbf { \\vec { R } }$","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":0,"id":"8aa0a517-940a-40f5-9f21-f29df4df16b6","page_size":[595,841],"block_position":"0-4"},{"bbox":[113,210,386,229],"type":"title","angle":0,"index":5,"text":"# 假设任意数值N用R进制数来表示：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":0,"id":"ac6c07c8-d8df-40a3-b138-9cc544ff2db6","page_size":[595,841],"block_position":"0-5"},{"bbox":[86,236,424,301],"type":"text","angle":0,"index":6,"text":"N= (Dm-1Dm-2...D。.D.1D-2...D-k） R权重 Di：基本符号， $\\mathsf { D } _ { \\mathsf { i } } \\in [ \\mathsf { 0 } ,$ R-1],i=-k,-k+1, .….，m-1；小数点在D和D之间","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":0,"id":"a7f89e84-6f2f-435d-a7bd-f43af14f7190","page_size":[595,841],"block_position":"0-6"},{"bbox":[113,306,352,325],"type":"title","angle":0,"index":7,"text":"# 数值N的实际值为：加权求和","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":0,"id":"7941e577-6a62-4b42-9ccf-1bcb6050233d","page_size":[595,841],"block_position":"0-7"},{"bbox":[86,327,408,394],"type":"text","angle":0,"index":8,"text":"进1 m-1六进制？ 十进制 8N=∑(Di×R')","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":0,"id":"9f719d1b-92f8-4557-b898-5498831685a9","page_size":[595,841],"block_position":"0-8"},{"bbox":[117,407,450,427],"type":"title","angle":0,"index":9,"text":"# X 何谓十进制、二进制、八进制、十六进制？","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":0,"id":"b7889b47-3641-4981-bafb-2d160817e054","page_size":[595,841],"block_position":"0-9"},{"bbox":[110,429,413,564],"index":10,"angle":0,"type":"table_body","img_path":"/","id":"1393657b-e678-437e-af8f-6dba57f18282","color":{"line":"rgba(103, 194, 63, 1)","fill":"rgba(103, 194, 63, 1)"},"table_body":"
进制基数R权Wi数码符号
十进制R=1010i0~9
二进制R=22i0、1
八进制R=88i0~7
十六进制R=1616i0~9、A~F
","page_idx":0,"page_size":[595,841],"block_position":"0-10"},{"bbox":[87,592,164,605],"type":"title","angle":0,"index":11,"text":"# 二进制 八进制","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":0,"id":"97844ba1-a582-4f43-9034-43f828e4d477","page_size":[595,841],"block_position":"0-11"},{"bbox":[86,608,433,636],"type":"text","angle":0,"index":12,"text":" 以小数点为中心分别向两边分组，每三位一组，写出对应的八进制数字（不够位数则在两边加0补足3位 ）","id":"f95bc0c6-3bbf-4313-b7c1-aa8a6b5d2ea3","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":0,"page_size":[595,841],"block_position":"0-12"},{"bbox":[88,640,187,652],"type":"text","angle":0,"index":13,"text":" 二进制 十六进制","id":"0402b5a9-7afb-46c3-a24f-f022faa044eb","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":0,"page_size":[595,841],"block_position":"0-13"},{"bbox":[87,655,433,683],"type":"text","angle":0,"index":14,"text":" 以小数点为中心分别向两边分组，每四位一组，写出对应的十六进制符号（不够位数则在两边加0补足4位 ）","id":"b24e5aea-5883-47fa-aa8c-d2c58e1d9029","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":0,"page_size":[595,841],"block_position":"0-14"},{"bbox":[88,687,176,699],"type":"text","angle":0,"index":15,"text":" 八进制 二进制","id":"09222da1-4e61-4cf3-823e-5eb2d6058dc1","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":0,"page_size":[595,841],"block_position":"0-15"},{"bbox":[86,702,453,729],"type":"text","angle":0,"index":16,"text":" 将每位八进制数展开为3位二进制数，整数的最高位0和小数的最低位0可以略去","id":"0a3a06cb-38a7-4133-889f-963b2ce016e5","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":0,"page_size":[595,841],"block_position":"0-16"},{"bbox":[88,733,186,745],"type":"text","angle":0,"index":17,"text":" 十六进制 二进制","id":"7680e6c6-a294-43a1-a8fb-e40214d769ba","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":0,"page_size":[595,841],"block_position":"0-17"},{"bbox":[87,749,453,761],"type":"text","angle":0,"index":18,"text":" 将每位十六进制数展开为4位二进制数，整数的最高位0和小数的最低位0可","id":"257f45b1-3cef-4aaa-9ec8-08563414973b","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":0,"page_size":[595,841],"block_position":"0-18"}],[{"bbox":[88,79,121,90],"type":"title","angle":0,"index":0,"text":"# 以略去","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":1,"id":"5f6714f8-9ef9-4623-8233-0455a1c4dcde","page_size":[595,841],"block_position":"1-0"},{"bbox":[86,110,305,122],"type":"text","angle":0,"index":1,"text":"如何在计算机内使用二进制来表示十进制数据？","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"id":"e258d3d8-d60a-4640-bceb-373ee0ead3eb","page_size":[595,841],"block_position":"1-1"},{"bbox":[88,125,164,137],"type":"text","angle":0,"index":2,"text":"十进制数的编码","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"id":"4080dc23-f4a4-48ed-a678-2bcd5a1ad73e","page_size":[595,841],"block_position":"1-2"},{"bbox":[88,142,271,154],"type":"text","angle":0,"index":3,"text":"BCD（Binary Coded Decimal）码：","id":"67ee6122-c670-4d00-8c01-9cc5a5f3b3ac","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-3"},{"bbox":[88,157,259,169],"type":"text","angle":0,"index":4,"text":" 使用二进制来编码十进制数字 $\\pmb { 0 } \\sim \\pmb { 9 }$","id":"b6b70f56-7a5a-405f-b8d7-87749df37359","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-4"},{"bbox":[88,173,145,185],"type":"text","angle":0,"index":5,"text":"编码方法：","id":"2890ce23-0b3e-4c7a-b722-277c4770b968","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-5"},{"bbox":[88,188,317,200],"type":"text","angle":0,"index":6,"text":" 一般使用 4 位二进制编码来表示 1 位十进制数字","id":"d35415a4-be37-448c-8e72-8d7dc571807f","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-6"},{"bbox":[88,204,291,216],"type":"text","angle":0,"index":7,"text":" 在 16 个编码中选用 10 个来表示数字 $\\pmb { 0 } \\sim \\pmb { 9 }$","id":"58f0f5ef-ab35-4a54-8a08-844672415325","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-7"},{"bbox":[88,219,238,231],"type":"text","angle":0,"index":8,"text":" 不同的选择构成不同的 BCD 码","id":"5b003b84-1be6-4b25-bafa-e3a74917b825","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-8"},{"bbox":[88,235,124,247],"type":"text","angle":0,"index":9,"text":"分类：","id":"832db182-fd2d-407c-89ca-bf4ce51c0ef6","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-9"},{"bbox":[87,250,433,278],"type":"text","angle":0,"index":10,"text":" 有权码：编码的每一位都有固定的权值，加权求和的值即是表示的十进制数字。如 8421 码、2421 码、5211 码、4311 码、84 -2-1 码等","id":"a04cfd83-e1de-4c0c-96bb-1788dbb482e0","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-10"},{"bbox":[88,281,412,309],"type":"text","angle":0,"index":11,"text":" 无权码：编码的每一位并没有固定的权，主要包括格雷码、余 3 码等十进制数串的表示方法","id":"a264c739-543c-48db-85d6-82b3cea0963a","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-11"},{"bbox":[87,312,405,325],"type":"text","angle":0,"index":13,"text":"数值数据：用于表示数的大小，其值确定，可与数轴上确切的点对应","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"id":"4ee9f9e3-189f-4c84-9228-875fd9be76ab","page_size":[595,841],"block_position":"1-12"},{"bbox":[88,328,427,341],"type":"text","angle":0,"index":14,"text":" 非数值数据：没有值大小的概念，表示字符、汉字、图像、声音等信息","id":"463b3d9c-06e4-4909-b623-79dfe3a380b5","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-13"},{"bbox":[88,343,417,356],"type":"text","angle":0,"index":15,"text":" 计算机中如何表示数值数据？数值数据的格式要素，必须要考虑三点","id":"d7c25fa5-51dd-4826-af73-11d76f8093d6","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-14"},{"bbox":[88,359,198,372],"type":"text","angle":0,"index":17,"text":" 第一，符号如何表示？","id":"5aecab98-9fb0-450d-9f04-97763e76c64f","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-15"},{"bbox":[88,375,208,387],"type":"text","angle":0,"index":18,"text":" 第二，小数点如何表示？","id":"d20f0e1a-775b-4f30-bbf3-f74f2428a5ff","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-16"},{"bbox":[88,391,302,403],"type":"text","angle":0,"index":19,"text":" 第三，二进制数字如何排列来表示某个数值？","id":"f3e4817e-7b58-43bb-ae8f-feccfa71b3b5","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-17"},{"bbox":[88,407,326,418],"type":"text","angle":0,"index":20,"text":" 机器数：数值数据在计算机中的二进制表示形式。","id":"cbd8824e-e3ba-4114-a649-804e0924d97a","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-18"},{"bbox":[88,422,304,433],"type":"text","angle":0,"index":21,"text":" 机器数的符号位必须被数值化为二进制 0 和 1","id":"101d70af-6b8e-4a7f-99b6-24af168016a0","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-19"},{"bbox":[88,438,287,449],"type":"text","angle":0,"index":22,"text":" 机器数的小数点用隐含规定的方式来表达","id":"3dc89ebf-6088-4303-9e48-bdfa0facd24d","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-20"},{"bbox":[88,454,265,465],"type":"text","angle":0,"index":23,"text":" 表示的数值范围受计算机字长的限制","id":"06469610-5c6e-4ca7-a289-3b9156c2b0ce","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-21"},{"bbox":[88,469,395,481],"type":"text","angle":0,"index":24,"text":" 编码方法：不同的排列方式，常见的有原码、反码、补码、移码。","id":"4588f54f-af13-49d4-a266-4d7ade6d9cb2","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-22"},{"bbox":[88,484,260,496],"type":"text","angle":0,"index":25,"text":" 真值：机器数真正表示的数值数据","id":"77151774-a1bf-4077-b586-7538a509d062","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-23"},{"bbox":[88,500,251,528],"type":"text","angle":0,"index":26,"text":" 书写： $+ /$ －符号 数值（二进制或十进制）","id":"49443895-f6cc-4fcd-b9de-62c25e456a6d","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-24"},{"bbox":[87,546,262,559],"type":"text","angle":0,"index":28,"text":"计算机中参与运算的数值数据有两种：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"id":"0dbc566b-1065-4ab6-afa0-ae80168c70a0","page_size":[595,841],"block_position":"1-25"},{"bbox":[87,562,437,590],"type":"text","angle":0,"index":29,"text":" 无符号数据（Unsigned ）：所有的二进制数据位数均用来表示数值本身，没有正负之分","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"id":"b0b27e77-28be-47f4-a538-b3e9e46639ff","page_size":[595,841],"block_position":"1-26"},{"bbox":[88,593,405,606],"type":"text","angle":0,"index":30,"text":" 带符号数据（Signed）：则其二进制数据位，包括符号位和数值位","id":"e94cfaca-bc21-470c-b176-dfe6651cb84d","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-27"},{"bbox":[88,609,386,621],"type":"text","angle":0,"index":31,"text":" 当机器字长相同时，无符号数和有符号数的表示范围是不同的","id":"d8cc4fc6-d592-4c71-acc7-f9ea61ba08ad","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-28"},{"bbox":[88,624,241,636],"type":"text","angle":0,"index":32,"text":"计算机中：小数点的表示方法？","id":"1c0ae2b5-0385-4e6c-9ef7-7725d3cc7927","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-29"},{"bbox":[88,640,286,652],"type":"text","angle":0,"index":33,"text":" 计算机中没有专用的部件用来表示小数点","id":"aaade793-8555-4f25-9b3c-4bd6d166d2af","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-30"},{"bbox":[88,655,286,667],"type":"text","angle":0,"index":34,"text":" 机器数中，小数点及其位置是隐含规定的","id":"0bbf8179-20fd-45ab-8352-bfab8c971e49","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-31"},{"bbox":[88,671,234,683],"type":"text","angle":0,"index":35,"text":" 有两种隐含方式：定点和浮点","id":"d54c6391-22ef-43e8-ae8d-067e96857794","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-32"},{"bbox":[86,687,414,699],"type":"text","angle":0,"index":37,"text":"定点机器数（Fixed Point）：小数点的位置是固定不变的，两种位置：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"id":"dd8fbf86-b715-4447-9cae-30be4567e8a7","page_size":[595,841],"block_position":"1-33"},{"bbox":[88,703,276,730],"type":"text","angle":0,"index":38,"text":" 定点小数：纯小数，隐含固定在符号位Xs（最高位）之后，整数位是符号位","id":"408f5fad-efc6-464b-a5a0-1f9d2ba62236","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-34"},{"bbox":[88,734,265,761],"type":"text","angle":0,"index":39,"text":" 定点整数：纯整数，小数点隐含固定在最低位之后，最高位为符号位Xs","id":"f30a0a89-454b-4e57-aafc-6cb7d9a82649","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":1,"page_size":[595,841],"block_position":"1-35"}],[{"bbox":[93,105,282,244],"index":0,"angle":0,"type":"image","img_path":"/c7b139b89222151266e017727943407c6624042609160e115030648370c50579.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.3176470588235294,"page_idx":2,"id":"e86b7703-35b7-4d5f-bcc0-9ef349191b84","page_size":[595,841],"block_position":"2-0"},{"bbox":[86,280,332,295],"type":"text","angle":0,"index":1,"text":"浮点机器数：将实数数值大小表示成科学计数法形式","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":2,"id":"53384b30-a7a4-4639-81bb-d981f979eee0","page_size":[595,841],"block_position":"2-1"},{"bbox":[87,296,214,309],"type":"text","angle":0,"index":2,"text":" 浮点数 N 由三部分构成：","id":"8ab5be1d-d204-461a-a939-d694d040b2df","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":2,"page_size":[595,841],"block_position":"2-2"},{"bbox":[87,312,315,325],"type":"text","angle":0,"index":3,"text":" 阶码的底 R：隐含表示，一般约定为 2、8 或 16","id":"f38bd8a7-5778-4198-b05b-3de5c60cc63b","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":2,"page_size":[595,841],"block_position":"2-3"},{"bbox":[87,328,226,340],"type":"text","angle":0,"index":4,"text":" 尾数M：系数，为定点小数","id":"086e066f-e4f5-4904-9587-b53be9f9876f","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":2,"page_size":[595,841],"block_position":"2-4"},{"bbox":[87,343,240,356],"type":"text","angle":0,"index":5,"text":" 阶码 E：R 的指数，为定点整数","id":"b4ab1a20-4dd4-4f78-adfa-85c03f44b635","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":2,"page_size":[595,841],"block_position":"2-5"},{"bbox":[86,359,458,388],"type":"text","angle":0,"index":6,"text":" 对尾数所表示的定点小数，进行按比例放大（阶码为正数）或者按比例缩小（阶码为负数），数据真值的小数点位置是浮动的——位置由阶码规定","id":"56efbdda-2a7e-4173-9eb1-9085dd2ff48d","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":2,"page_size":[595,841],"block_position":"2-6"},{"bbox":[116,423,595,528],"index":8,"angle":0,"type":"image","img_path":"/1daf5d1e2f93f95400319c82fbc9d2ae791ee6d59e6b25c4acc80a7508d40b5d.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.8050420168067227,"page_idx":2,"id":"7fd58f22-a299-4c25-b197-1c6740066329","page_size":[595,841],"block_position":"2-7"},{"bbox":[87,561,449,575],"type":"text","angle":0,"index":9,"text":" 负精度-δ：机器数在数轴上最靠近原点0的负数，计算机能表示的最大负数","id":"75c9db67-db43-4fbb-acaf-b549040c3599","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":2,"page_size":[595,841],"block_position":"2-8"},{"bbox":[86,577,446,606],"type":"text","angle":0,"index":10,"text":" 正精度δ：机器数在数轴上最靠近原点0的正数，计算机能表示的最小正数绝对值称为精度δ或分辨率，代表了机器数所能表示的绝对值最小的非零值","id":"e35af294-056a-455c-acf0-d9eb62cd3abd","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":2,"page_size":[595,841],"block_position":"2-9"},{"bbox":[87,608,406,622],"type":"text","angle":0,"index":11,"text":" 机器数的表示范围：[最小数，最大负数]、0、[最小正数，最大数]","id":"359bbb53-1d1a-4c5a-937b-bccd002afe7c","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":2,"page_size":[595,841],"block_position":"2-10"},{"bbox":[87,624,370,637],"type":"text","angle":0,"index":12,"text":" 最大数和和最小数：取决于机器数的编码方式、位数和格式","id":"741e174a-37a1-454d-bac0-158d93f18b42","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":2,"page_size":[595,841],"block_position":"2-11"},{"bbox":[93,645,316,714],"index":14,"angle":0,"type":"image","img_path":"/b6134e5eaca7a911410e0badcaa00f52a9436d482092a19623417c4bb70ff044.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.37478991596638656,"page_idx":2,"id":"b1e7d68e-4b59-41a9-9851-8da9f55d5b34","page_size":[595,841],"block_position":"2-12"},{"bbox":[86,733,418,746],"type":"text","angle":0,"index":15,"text":"下溢：位于最大负数和最小正数之间的数据（除 0 外），机器无法表示。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":2,"id":"ebd9f2f0-77dd-4b4e-8e5f-fa183d797a33","page_size":[595,841],"block_position":"2-13"},{"bbox":[87,749,259,761],"type":"text","angle":0,"index":16,"text":" 处理：计算机直接将其视为机器零。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":2,"id":"7b93c4dd-1b1b-4bd5-83e4-606012828cf0","page_size":[595,841],"block_position":"2-14"}],[{"bbox":[86,79,459,107],"type":"text","angle":0,"index":0,"text":" 上溢：当一个数据大于最大（正）数，或者小于最小（负）数时，机器也无法表示，称为上溢，上溢又称溢出。","id":"95d42820-5f2b-4aba-81eb-2f9703bb20c6","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":3,"page_size":[595,841],"block_position":"3-0"},{"bbox":[87,110,280,122],"type":"text","angle":0,"index":1,"text":" 处理：计算机置溢出标志位，或者报警。","id":"e6744db7-4fed-4d2e-99e5-b82d0e0c9777","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":3,"page_size":[595,841],"block_position":"3-1"},{"bbox":[88,126,142,137],"type":"title","angle":0,"index":3,"text":"# 原码表示法","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":3,"id":"66bcbd30-ccbc-4be2-94c8-5c9259b78a1c","page_size":[595,841],"block_position":"3-2"},{"bbox":[86,150,264,163],"type":"title","angle":0,"index":4,"text":"# 数学定义：真值与编码之间的数学关系","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":3,"id":"bfd3f077-7731-45e1-b83f-678970674091","page_size":[595,841],"block_position":"3-3"},{"bbox":[120,164,324,259],"index":5,"angle":0,"type":"image","img_path":"/1671e19ddf9f093cf00cf7c15db5550fd45f081c57f5b8e26a12151e29b38513.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.34285714285714286,"page_idx":3,"id":"3ed35f37-4e0e-4bf0-b9b4-dd7fa60140ea","page_size":[595,841],"block_position":"3-4"},{"bbox":[107,301,130,327],"type":"title","angle":0,"index":6,"text":"# 翻数","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":3,"id":"ffb4b6e5-6c9e-43fb-9e3d-0651961e5d36","page_size":[595,841],"block_position":"3-5"},{"bbox":[137,294,248,331],"index":7,"angle":0,"type":"image","img_path":"/c815c6dc8826c731955012e56a7cb6cd015ca599083efa4e0ef91814247f3469.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.2,"page_idx":3,"id":"576430db-ac6f-42f7-b0c7-2c0641d02412","page_size":[595,841],"block_position":"3-6"},{"bbox":[280,301,302,327],"type":"title","angle":0,"index":8,"text":"# 业数","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":3,"id":"904b13a3-c9fc-4d55-8747-088e6f1da42b","page_size":[595,841],"block_position":"3-7"},{"bbox":[307,295,415,333],"index":9,"angle":0,"type":"image","img_path":"/26ff03a141ea9e96a1420fe0eb7111445ecdcbf59b2601a1c00de37b3c4ddc8c.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.2,"page_idx":3,"id":"c446efd5-ffe0-47d3-abb4-151e5d317de8","page_size":[595,841],"block_position":"3-8"},{"bbox":[97,342,290,354],"type":"text","angle":0,"index":10,"text":"：-（--u）X--","id":"ab47a832-24c1-4eb7-b76f-1b58564882f4","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":3,"page_size":[595,841],"block_position":"3-9"},{"bbox":[97,359,275,372],"type":"text","angle":0,"index":11,"text":"//：-（Su-」）XSu","id":"85e4aadf-c63c-4f75-b921-225e040f7b69","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":3,"page_size":[595,841],"block_position":"3-10"},{"bbox":[86,375,404,387],"type":"text","angle":0,"index":14,"text":"、（5）淌围： $\\nleftarrow$ ","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":3,"id":"b34fe3f9-f832-4182-8503-5197900473b3","page_size":[595,841],"block_position":"3-11"},{"bbox":[87,391,381,403],"type":"text","angle":0,"index":15,"text":" 使用原码进行加减乘除运算：规则类似于真值的加减乘除运算","id":"eb0a4b58-dd5f-4b59-a52f-424b99416c83","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":3,"page_size":[595,841],"block_position":"3-12"},{"bbox":[88,407,350,418],"type":"text","angle":0,"index":16,"text":" 符号位单独处理，不能参加运算，参加运算的是绝对值","id":"59e25ee6-b1c8-47d5-b8cc-92d55bc4c38e","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":3,"page_size":[595,841],"block_position":"3-13"},{"bbox":[88,422,144,433],"type":"text","angle":0,"index":17,"text":" 加减运算：","id":"3f6f4737-65b8-40be-a583-ea5de5dc5471","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":3,"page_size":[595,841],"block_position":"3-14"},{"bbox":[88,437,297,449],"type":"text","angle":0,"index":18,"text":"• 根据符号位决定进行的是绝对值的加还是减","id":"17928473-35ea-41d7-a7e9-34f00a51dd8d","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":3,"page_size":[595,841],"block_position":"3-15"},{"bbox":[88,453,202,465],"type":"text","angle":0,"index":19,"text":"• 进行绝对值的加减运算","id":"a0fdbeac-626a-4992-8a2b-5b6626715a5e","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":3,"page_size":[595,841],"block_position":"3-16"},{"bbox":[88,468,317,481],"type":"text","angle":0,"index":20,"text":"• 根据绝对值的大小决定结果（和或者差）的符号","id":"96adc388-9138-478d-94dc-1e9ed762f507","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":3,"page_size":[595,841],"block_position":"3-17"},{"bbox":[86,530,300,543],"type":"text","angle":0,"index":22,"text":"表示方法：最高位为符号位，其他位为数值位","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":3,"id":"135e6b51-aa06-4937-8df4-d4c3a7b510f8","page_size":[595,841],"block_position":"3-18"},{"bbox":[87,546,225,559],"type":"text","angle":0,"index":23,"text":" 符号位：0－正数，1－负数","id":"c3dec733-3cf0-4ab9-80c3-8d1072e83032","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":3,"page_size":[595,841],"block_position":"3-19"},{"bbox":[88,562,202,574],"type":"text","angle":0,"index":24,"text":" 数值位：与绝对值相同","id":"9de30d96-d2c5-41bd-bcde-ea45aa412617","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":3,"page_size":[595,841],"block_position":"3-20"},{"bbox":[93,592,224,644],"type":"title","angle":0,"index":26,"text":"# “”和””只用于助记，在计算机中并无专用部件来表示","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":3,"id":"cf2849e5-b900-4ea3-858b-7888c7e97a0f","page_size":[595,841],"block_position":"3-21"},{"bbox":[87,655,157,667],"type":"title","angle":0,"index":27,"text":"# 对于定点整数：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":3,"id":"15c96a93-0273-4441-a4ce-2a6735f0a34b","page_size":[595,841],"block_position":"3-22"},{"bbox":[87,671,314,683],"type":"text","angle":0,"index":28,"text":" 若 ${ \\bf X } = + { \\bf X } 1 { \\bf X } 2$ ……Xn，则[X]原= 0,X1X2 ……Xn","id":"cd9ce53e-39ee-4528-9ced-d3fb4590218f","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":3,"page_size":[595,841],"block_position":"3-23"},{"bbox":[88,687,321,699],"type":"text","angle":0,"index":29,"text":" 若 $\\mathbf { \\lambda } \\mathbf { x } ( = \\mathbf { - }$ X1X2 ……Xn，则[X]原 $\\varXi$ 1,X1X2 ……Xn 。","id":"14a3b230-dfa0-4c6a-bde4-8f842434054f","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":3,"page_size":[595,841],"block_position":"3-24"},{"bbox":[88,702,170,714],"type":"text","angle":0,"index":31,"text":" 对于定点小数：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":3,"id":"277c3684-f8c5-4c43-afc5-a1e0b21c9d08","page_size":[595,841],"block_position":"3-25"},{"bbox":[87,718,323,730],"type":"text","angle":0,"index":32,"text":" 若 X=+0.X1X2 ……Xn，则[X]原 $\\backslash =$ 0.X1X2 ……Xn","id":"f14c7434-73ab-4c9b-abae-c93f442f362f","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":3,"page_size":[595,841],"block_position":"3-26"},{"bbox":[88,734,323,746],"type":"text","angle":0,"index":33,"text":" 若 $\\mathbf { \\lambda } \\mathbf { x } ( = \\mathbf { - }$ 0.X1X2 ……Xn，则[X]原 $\\varXi$ 1.X1X2 ……Xn","id":"26c1b155-1256-48d3-8ec9-2f91db4882d8","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":3,"page_size":[595,841],"block_position":"3-27"}],[{"bbox":[87,79,112,92],"type":"title","angle":0,"index":0,"text":"# 补码","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":4,"id":"4019a323-f062-4b18-add5-6cc2d528b979","page_size":[595,841],"block_position":"4-0"},{"bbox":[106,113,399,196],"index":1,"angle":0,"type":"image","img_path":"/811671a79ae1be5c45f4f715ff2f2fb25f3fcc69b175fff61442343d1a530415.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.492436974789916,"page_idx":4,"id":"1c6961bc-79e3-4999-9016-16bf38af4ce7","page_size":[595,841],"block_position":"4-1"},{"bbox":[86,218,321,232],"type":"text","angle":0,"index":2,"text":"2、表示方法：最高位为符号位，其他位为数值位。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":4,"id":"2f7a4df1-e4e1-42a2-a064-472fcd82fa51","page_size":[595,841],"block_position":"4-2"},{"bbox":[87,235,230,248],"type":"text","angle":0,"index":3,"text":" 符号位：0－正数，1－负数。","id":"7828b98c-ae9b-4c35-9688-1bab853eef1d","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":4,"page_size":[595,841],"block_position":"4-3"},{"bbox":[87,250,424,263],"type":"text","angle":0,"index":4,"text":" 数值位：正数时，与绝对值相同；负数时，为绝对值取反后，末位加 1。","id":"3d4a0afb-775a-4635-87cb-15fc0bf83313","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":4,"page_size":[595,841],"block_position":"4-4"},{"bbox":[98,269,263,336],"index":6,"angle":0,"type":"image","img_path":"/ffe44f4fd0268aa31595488035281a89922feca95c9661470ec0bbee0d1405be.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.2773109243697479,"page_idx":4,"id":"90b30254-6a3a-493d-8db7-50b67faf2b11","page_size":[595,841],"block_position":"4-5"},{"bbox":[113,347,230,366],"type":"title","angle":0,"index":7,"text":"# 真值=加权求和","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":4,"id":"c8970997-6c0f-4a9a-b420-3f09cc14f0bb","page_size":[595,841],"block_position":"4-6"},{"bbox":[89,380,169,394],"type":"text","angle":0,"index":8,"text":"对于定点整数:","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":4,"id":"a1182bbb-7d0c-4ee6-8aa5-979774c2a520","page_size":[595,841],"block_position":"4-7"},{"bbox":[104,401,323,416],"type":"text","angle":0,"index":9,"text":"■ 若X=+XX..X， 则[X]补= 0.,X.X..Xn","id":"964e5d84-5ea4-4714-9f10-0e7e667d0333","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":4,"page_size":[595,841],"block_position":"4-8"},{"bbox":[104,423,348,439],"type":"text","angle":0,"index":10,"text":"$\\not \\equiv \\emptyset \\mathbb { X } = - \\mathbb { X } _ { 1 } \\mathbb { X } _ { 2 } . . . . . . \\mathbb { X } _ { n } , \\mathbb { M } \\subseteq \\mathbb { X } _ { 1 } = \\ 1 , \\overline { { X _ { 1 } } } \\overline { { X _ { 2 } } } . . . . . . . \\ \\overline { { X _ { n } } } \\ + \\ 1$","id":"c391c35d-e911-48cd-b01e-231cf3d6db04","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":4,"page_size":[595,841],"block_position":"4-9"},{"bbox":[89,446,169,459],"type":"text","angle":0,"index":12,"text":"对于定点小数：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":4,"id":"9fe6fde1-7ebd-4b5c-bb2f-5c86ebf66d4f","page_size":[595,841],"block_position":"4-10"},{"bbox":[104,467,339,481],"type":"text","angle":0,"index":13,"text":"$\\begin{array} { r } { \\dot { \\Xi } \\mathsf { X } = + 0 . \\mathsf { X } _ { 1 } \\mathsf { X } _ { 2 } . . . . . . . \\mathsf { X } _ { \\mathrm { n } } \\ , \\perp \\sharp [ \\mathsf { X } ] _ { \\sharp \\flat } = 0 . \\mathsf { X } _ { 1 } \\mathsf { X } _ { 2 } . . . . . . . \\mathsf { X } _ { \\mathrm { n } } } \\end{array}$ ${ \\bf \\omega } = + { \\bf 0 }$","id":"cafe7026-98a9-4d2e-b89c-5aeed8cc7b18","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":4,"page_size":[595,841],"block_position":"4-11"},{"bbox":[104,489,412,505],"type":"text","angle":0,"index":14,"text":"■ 若X=-0. $\\mathbf { X } _ { 1 } \\mathbf { X } _ { 2 } . . . . . . \\mathbf { X } _ { n }$ ，则 $[ \\mathsf { X } ] _ { * \\mathsf { h } } = 1 .$ . X X... X +.....1.","id":"0044d0f1-83a9-4899-b6b1-01e14bfc89ea","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":4,"page_size":[595,841],"block_position":"4-12"},{"bbox":[86,530,421,559],"type":"text","angle":0,"index":16,"text":"0的表示：0 的补码表示形式是唯一的，即分别按照正数和负数表示均一致，为全零。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":4,"id":"38023dfc-bcfc-4e97-834b-f53ba76ec25a","page_size":[595,841],"block_position":"4-13"},{"bbox":[87,562,236,575],"type":"text","angle":0,"index":17,"text":" $[ + 0 ]$ 补＝ 00…0 [-0]补 $= 0 0 . . . 0$","id":"8f8ed188-7ece-44a6-b43c-f05a8c535e85","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":4,"page_size":[595,841],"block_position":"4-14"},{"bbox":[87,577,427,590],"type":"text","angle":0,"index":18,"text":" （2）表示范围：对于 $\\mathsf { n } + \\mathsf { 1 }$ 位补码机器数 X，它所能表示的数据范围为：","id":"1ad57fca-8687-40a5-b666-a5f24b7a4347","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":4,"page_size":[595,841],"block_position":"4-15"},{"bbox":[88,593,232,605],"type":"text","angle":0,"index":19,"text":" 定点整数： $- 2 \\mathsf { n } { \\mathsf { \\leq } } \\mathsf { X } \\leq 2 \\mathsf { n } - 1$","id":"646c5a97-57b2-45ba-84c4-744a436aae92","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":4,"page_size":[595,841],"block_position":"4-16"},{"bbox":[88,609,237,621],"type":"text","angle":0,"index":20,"text":" 定点小数： $- 1 \\leq x \\leq 1 - 2 - \\mathsf { n }$","id":"31a2b1b7-81d2-4724-8c8f-db7cd3bc1d77","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":4,"page_size":[595,841],"block_position":"4-17"},{"bbox":[93,624,159,636],"type":"title","angle":0,"index":22,"text":"# （3）补码运算","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":4,"id":"ca9bca95-c171-4c49-a713-d1a80a6085d0","page_size":[595,841],"block_position":"4-18"},{"bbox":[87,640,265,652],"type":"text","angle":0,"index":23,"text":" 补码的符号位同数值位一起参加运算","id":"54d09af5-c389-4016-9aaa-0e475d6bc87b","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":4,"page_size":[595,841],"block_position":"4-19"},{"bbox":[88,655,202,667],"type":"text","angle":0,"index":24,"text":" 可以将减法转化为加法","id":"6116f0b3-fec5-40f1-8ad5-c454c08dd147","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":4,"page_size":[595,841],"block_position":"4-20"},{"bbox":[88,671,192,683],"type":"text","angle":0,"index":25,"text":" 简化了运算器的结构","id":"a688c0fc-527a-4b6b-bc5b-837f71fe027f","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":4,"page_size":[595,841],"block_position":"4-21"},{"bbox":[87,687,305,715],"type":"text","angle":0,"index":27,"text":" 计算机中的整型数据（int）均用补码来表示反码","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":4,"id":"d7d44e0b-f1d6-4a20-817b-d540d8595baa","page_size":[595,841],"block_position":"4-22"}],[{"bbox":[93,90,124,125],"type":"title","angle":0,"index":0,"text":"# 定点整数","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":5,"id":"8130f426-5af2-4133-99d8-42dd63534beb","page_size":[595,841],"block_position":"5-0"},{"bbox":[132,84,318,137],"type":"interline_equation","angle":0,"index":1,"text":"$$\n[ \\mathbf {X} ] _ {\\text {反}} = \\left\\{ \\begin{array}{l l} \\mathbf {X} & \\mathbf {X} \\geq 0 \\\\ 2 ^ {n + 1} - 1 + \\mathbf {X} & \\mathbf {X} \\leq 0 \\end{array} \\right.\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":5,"id":"fff15f36-7d5f-4a55-bc16-60fa47cae6ed","page_size":[595,841],"block_position":"5-1"},{"bbox":[172,142,293,162],"type":"interline_equation","angle":0,"index":2,"text":"$$\n(\\mod (2 ^ {n + 1} - 1))\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":5,"id":"0e4fb34c-6654-429e-a853-d11947b1fb0b","page_size":[595,841],"block_position":"5-2"},{"bbox":[359,95,390,128],"type":"title","angle":0,"index":3,"text":"# 定点小数","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":5,"id":"62ca3ec5-94ab-4ab4-aa7c-c51a8b719735","page_size":[595,841],"block_position":"5-3"},{"bbox":[399,85,580,137],"type":"interline_equation","angle":0,"index":4,"text":"$$\n[ \\mathrm {X} ] _ {\\text {反}} = \\left\\{ \\begin{array}{l l} \\mathrm {X} & \\mathrm {X} \\geq 0 \\\\ 2 - 2 ^ {- n} + \\mathrm {X} & \\mathrm {X} \\leq 0 \\end{array} \\right.\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":5,"id":"5569c07d-b353-4cb3-ab1f-e5b7685b8e59","page_size":[595,841],"block_position":"5-4"},{"bbox":[439,141,547,160],"type":"text","angle":0,"index":5,"text":"（ mod (2-2-n) )","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":5,"id":"105e8cc9-e7ee-4d87-baf6-f83af0cfdc4d","page_size":[595,841],"block_position":"5-5"},{"bbox":[86,172,314,185],"type":"text","angle":0,"index":6,"text":"、表示方法：最高位为符号位，其他位为数值位。","id":"62412574-694f-4491-9ffd-d2b114b4d7b3","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":5,"page_size":[595,841],"block_position":"5-6"},{"bbox":[87,188,229,200],"type":"text","angle":0,"index":7,"text":" 符号位：0－正数，1－负数。","id":"f005ab19-40da-48a3-9eff-4973a354c384","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":5,"page_size":[595,841],"block_position":"5-7"},{"bbox":[87,203,359,217],"type":"text","angle":0,"index":8,"text":" 数值位：正数时，与绝对值相同；负数时，为绝对值取反","id":"a5562014-faab-492b-b58e-aa38070ce469","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":5,"page_size":[595,841],"block_position":"5-8"},{"bbox":[91,231,263,238],"type":"text","angle":0,"index":10,"text":"双值位，正数时，与绝对值怕问，贝数的，为绝对值取汉","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":5,"id":"4cab2395-6a7d-4694-90bd-25cb4ecf0393","page_size":[595,841],"block_position":"5-9"},{"bbox":[96,242,146,253],"type":"text","angle":0,"index":11,"text":"对于定点整数：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":5,"id":"b397ce9b-68dd-4a62-96f0-7a074a3c8fb5","page_size":[595,841],"block_position":"5-10"},{"bbox":[158,240,297,251],"type":"text","angle":0,"index":12,"text":"·若 $\\mathsf { X } = + \\mathsf { X } _ { 1 } \\mathsf { X } _ { 2 } . . . . . . \\mathsf { X } _ { n } ,$ $\\mathbb { M } [ \\mathbf { X } ] _ { E } = 0 , \\mathbf { X } _ { 1 } \\mathbf { X } _ { 2 } . . . . . . . \\mathbf { X } _ { n }$","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":5,"id":"f4e54a49-c156-435f-922c-e8e221297e3a","page_size":[595,841],"block_position":"5-11"},{"bbox":[158,252,306,261],"type":"text","angle":0,"index":13,"text":"·若 $\\scriptstyle ( = - \\textsf { X } _ { 1 } , \\textsf { X } _ { 2 } , \\ldots , \\textsf { X } _ { n }$ ，则[X]反=1,xx... Xn","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":5,"id":"5897bbab-0694-4159-b0b1-0aadfb477520","page_size":[595,841],"block_position":"5-12"},{"bbox":[96,271,146,280],"type":"text","angle":0,"index":14,"text":"对于定点小数：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":5,"id":"3a8a84c5-7612-415a-b60b-91f9b833539a","page_size":[595,841],"block_position":"5-13"},{"bbox":[158,269,303,280],"type":"text","angle":0,"index":15,"text":"·若 $\\mathsf { \\pmb { \\Lambda } } = + \\mathbf { 0 } . \\mathsf { \\pmb { X } } _ { 1 } \\mathsf { \\pmb { X } } _ { 2 } . . . . . . . \\mathsf { \\pmb { X } } _ { n }$ $\\mathbb { R } ^ { | | \\mathbf { \\boldsymbol { X } } | } \\mathbb { R } ^ { = } \\mathbf { 0 } . \\mathbf { \\boldsymbol { X } } _ { 1 } \\mathbf { \\boldsymbol { X } } _ { 2 } . . . . . . . \\mathbf { \\boldsymbol { X } _ { n } }$","id":"a874159a-2f72-4708-ac98-916711c2f5aa","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":5,"page_size":[595,841],"block_position":"5-14"},{"bbox":[158,280,316,295],"type":"text","angle":0,"index":16,"text":"若X=-0.Xx，则1. $\\boldsymbol { \\mathfrak { A } } \\boldsymbol { \\mathfrak { A } } [ \\mathbf { X } ] _ { E } = \\mathbf { 1 } .$","id":"69b97709-c432-46f4-8447-48721c501d72","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":5,"page_size":[595,841],"block_position":"5-15"},{"bbox":[86,303,233,313],"type":"text","angle":0,"index":18,"text":"（1）0的表示：0的反码表示有两种形式","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":5,"id":"ce262fb3-9272-4047-9ec0-2bda7aac80c5","page_size":[595,841],"block_position":"5-16"},{"bbox":[97,317,158,326],"type":"interline_equation","angle":0,"index":19,"text":"$$\n\\begin{array}{r l} {[ + 0 ] _ {\\text {反}} = 0 0 \\dots 0} \\end{array}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":5,"id":"0fbd21e9-612d-4b1b-b554-9a8447dcaf1b","page_size":[595,841],"block_position":"5-17"},{"bbox":[201,317,252,327],"type":"interline_equation","angle":0,"index":20,"text":"$$\n[ - 0 ] _ {\\text {反}} = 1 1 \\dots 1\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":5,"id":"3c199a72-26ab-49b5-9551-31f28f194974","page_size":[595,841],"block_position":"5-18"},{"bbox":[86,328,329,338],"type":"text","angle":0,"index":21,"text":"（2）表示范围：对于n $^ +$ 1位反码机器数×，它所能表示的数据范围为：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":5,"id":"a0035d27-fd5c-456e-abe6-459e2d4c261a","page_size":[595,841],"block_position":"5-19"},{"bbox":[96,341,227,351],"type":"text","angle":0,"index":22,"text":"定点整数：-(2n-1）≤X≤2n-1","id":"dac1174e-b1d3-42fd-9567-9189afb26652","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":5,"page_size":[595,841],"block_position":"5-20"},{"bbox":[96,354,238,364],"type":"text","angle":0,"index":23,"text":"·定点小数:-（1-2-n）≤X≤1-2-n","id":"afe007a5-c40e-49fe-b798-529c4180b842","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":5,"page_size":[595,841],"block_position":"5-21"},{"bbox":[86,375,111,386],"type":"text","angle":0,"index":25,"text":"移码","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":5,"id":"62e4027c-2167-4678-a1c4-07de279282b0","page_size":[595,841],"block_position":"5-22"},{"bbox":[112,394,143,428],"type":"title","angle":0,"index":26,"text":"# 定点整数","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":5,"id":"bf6f9861-4dce-40e2-8c8b-42d77cda3b47","page_size":[595,841],"block_position":"5-23"},{"bbox":[161,398,317,428],"type":"interline_equation","angle":0,"index":27,"text":"$$\n[ \\mathrm {X} ] _ {\\text {移}} = 2 ^ {\\mathrm {n}} + \\mathrm {X}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":5,"id":"0d1e9019-aaa4-4eed-a721-f9b4cd93b8db","page_size":[595,841],"block_position":"5-24"},{"bbox":[199,440,287,460],"type":"interline_equation","angle":0,"index":28,"text":"$$\n(\\mod 2 ^ {n + 1})\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":5,"id":"548b84ae-e65a-4c42-81ef-8e4c2c4c2aff","page_size":[595,841],"block_position":"5-25"},{"bbox":[86,468,321,481],"type":"text","angle":0,"index":29,"text":"2、表示方法：最高位为符号位，其他位为数值位。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":5,"id":"578502ff-794d-4da6-b250-ca0d5ff0aeae","page_size":[595,841],"block_position":"5-26"},{"bbox":[87,484,230,497],"type":"text","angle":0,"index":30,"text":" 符号位：1－正数，0－负数。","id":"ffa07804-7b23-4875-8f19-34b495c2a6ea","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":5,"page_size":[595,841],"block_position":"5-27"},{"bbox":[87,499,424,513],"type":"text","angle":0,"index":31,"text":" 数值位：正数时，与绝对值相同；负数时，为绝对值取反后，末位加 1。","id":"f88249b3-e9bf-4061-aacf-bcd09d925649","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":5,"page_size":[595,841],"block_position":"5-28"},{"bbox":[86,528,581,539],"type":"text","angle":0,"index":33,"text":"值位，正效的，与绝对值怕问，贝双的，为绝对值耿反旧，不位加","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":5,"id":"2806949f-02ce-426a-a43e-4aee40d031da","page_size":[595,841],"block_position":"5-29"},{"bbox":[94,596,221,614],"type":"title","angle":0,"index":34,"text":"# 对于定点整数：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":5,"id":"e35e991f-2a7e-4fd2-8625-056c7667e91d","page_size":[595,841],"block_position":"5-30"},{"bbox":[443,560,543,600],"type":"text","angle":0,"index":35,"text":"移码=补码的符号位取反","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":5,"id":"32ba3f63-47c2-487f-b4cb-4787d8f81abb","page_size":[595,841],"block_position":"5-31"},{"bbox":[117,629,483,653],"type":"text","angle":0,"index":36,"text":"·若 $\\mathfrak { c } { = } { + } \\mathfrak { X } _ { 1 } \\mathfrak { X } _ { 2 } { \\dots } { \\dots } \\mathfrak { X } _ { n }$ ，则 $[ \\mathsf { X } ] _ { \\mp \\mathcal { B } } = \\mathsf { 1 } , \\mathsf { X } _ { 1 } \\mathsf { X } _ { 2 } . . . . . . \\mathsf { X } _ { \\mathsf { n } }$","id":"ea0edb8f-9d7b-4f08-af64-2c5b1589f2b7","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":5,"page_size":[595,841],"block_position":"5-32"},{"bbox":[118,665,536,690],"type":"text","angle":0,"index":37,"text":"·若 $\\mathbf { \\ddot { X } } = - \\mathbf { \\nabla } \\mathbf { X } _ { 1 } \\mathbf { X } _ { 2 } \\ldots \\ldots \\mathbf { X } _ { n }$ ，则 $[ \\mathbf { X } ] _ { \\mathcal { F B } } = \\mathbf { 0 } ,$ ,xX Xx.. Xn +1.","id":"dc0d4c8a-bc06-4a45-8f3f-f9de876bf62d","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":5,"page_size":[595,841],"block_position":"5-33"},{"bbox":[93,702,294,715],"type":"text","angle":0,"index":39,"text":"（1） 0的表示：0 的移码表示形式是唯一的","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":5,"id":"397cf0e1-dada-41b4-a48f-02867293f11b","page_size":[595,841],"block_position":"5-34"},{"bbox":[88,718,236,730],"type":"text","angle":0,"index":40,"text":" $[ + 0 ]$ 移＝ 10…0 [-0]移＝ 10…0","id":"c6b3e35e-190e-4f0d-82a3-8f4c757ee9b2","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":5,"page_size":[595,841],"block_position":"5-35"},{"bbox":[87,733,428,746],"type":"text","angle":0,"index":41,"text":" （2）表示范围：对于 $\\mathsf { n } + \\mathsf { 1 }$ 位移码机器数 X，它所能表示的数据范围为：","id":"dc9dc6d4-e774-4492-bb08-9ba4b954b9c0","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":5,"page_size":[595,841],"block_position":"5-36"},{"bbox":[88,749,232,761],"type":"text","angle":0,"index":42,"text":" 定点整数： $- 2 \\mathsf { n } { \\mathsf { \\leq } } \\mathsf { X } \\leq 2 \\mathsf { n } - 1$","id":"834d50a7-5b80-4cec-a132-431bf686a5a5","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":5,"page_size":[595,841],"block_position":"5-37"}],[{"bbox":[104,82,138,111],"index":0,"angle":0,"type":"image","img_path":"/17570bda25ff10b972ee9301e89e66c4e3e561a977bba5dfa96f0a63acf2709d.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.2,"page_idx":6,"id":"82e4464b-c6b1-4870-8dca-471197070366","page_size":[595,841],"block_position":"6-0"},{"bbox":[158,81,295,98],"type":"title","angle":0,"index":1,"text":"# 四种定点机器数的对比","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":6,"id":"cd5562e6-c796-442f-bdef-57680b7d5cce","page_size":[595,841],"block_position":"6-1"},{"bbox":[329,84,406,99],"type":"title","angle":0,"index":2,"text":"# 1、表示方法","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":6,"id":"8d440689-e7bd-46f0-a024-2f54965f5aa4","page_size":[595,841],"block_position":"6-2"},{"bbox":[129,141,180,156],"type":"title","angle":0,"index":3,"text":"# 定点整数","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":6,"id":"0a6b8bd7-cb45-42cb-8db6-058075a9b7a3","page_size":[595,841],"block_position":"6-3"},{"bbox":[182,103,493,196],"index":4,"angle":0,"type":"table_body","img_path":"/","id":"00c2dfcb-c930-41cb-bfaf-b5f94a08e9bc","color":{"line":"rgba(103, 194, 63, 1)","fill":"rgba(103, 194, 63, 1)"},"table_body":"
真值X=+ X1X2......XnX=- X1X2......Xn
原码[X]原=0 X1X2......Xn[X]原=1 X1X2......Xn
反码[X]反=0 X1X2......Xn[X]反=1 X1X2......Xn
补码[X]补=0 X1X2......Xn[X]补=1 X1X2......Xn+1
移码[X]移=1 X1X2......Xn[X]移=0 X1X2......Xn+1
","page_idx":6,"page_size":[595,841],"block_position":"6-4"},{"bbox":[120,236,146,264],"type":"title","angle":0,"index":5,"text":"# 定点小数","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":6,"id":"312c07c7-8e98-4f78-888a-26b9eed1913f","page_size":[595,841],"block_position":"6-5"},{"bbox":[152,200,495,301],"index":6,"angle":0,"type":"table_body","img_path":"/","id":"b3eef30a-04bd-451f-83d0-8558a0df547f","color":{"line":"rgba(103, 194, 63, 1)","fill":"rgba(103, 194, 63, 1)"},"table_body":"
真值X=+0.X1X2......XnX=-0.X1X2......Xn
原码[X]原=0.X1X2......Xn[X]原=1.X1X2......Xn
反码[X]反=0.X1X2......Xn[X]反=1.X1X2......Xn
补码[X]补=0.X1X2......Xn[X]补=1. X1 X2...... Xn + 0.00......1
移码[X]移=1.X1X2......Xn[X]移=0. X1 X2...... Xn + 0.00......1
","page_idx":6,"page_size":[595,841],"block_position":"6-6"},{"bbox":[88,333,577,522],"index":7,"angle":0,"type":"table_body","img_path":"/","id":"6cf01096-dfe8-44c0-a720-05ed7f07dd5f","color":{"line":"rgba(103, 194, 63, 1)","fill":"rgba(103, 194, 63, 1)"},"table_body":"
真值X=+0X=-0
原码[X]原=0 00......0[X]原=1 00......0
反码[X]反=0 00......0[X]反=1 11......1
补码[X]补=0 00......0
移码[X]移=1 00......0
","page_idx":6,"page_size":[595,841],"block_position":"6-7"},{"bbox":[169,548,236,562],"index":8,"angle":0,"type":"table_caption","text":"n+1位机器数","id":"f9e7bafe-035a-4c80-b9bd-bd709c3f8da2","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":6,"page_size":[595,841],"block_position":"6-8"},{"bbox":[92,569,307,665],"index":9,"angle":0,"type":"table_body","img_path":"/","id":"6a058ff0-87f6-488c-b31b-1f207b34fd48","color":{"line":"rgba(103, 194, 63, 1)","fill":"rgba(103, 194, 63, 1)"},"table_body":"
定点整数定点小数
原码- (2n-1) ≤X ≤ 2n-1- (1-2-n) ≤X≤1-2-n
反码- (2n-1) ≤X ≤ 2n-1- (1-2-n) ≤X≤1-2-n
补码-2n≤X ≤ 2n-1-1≤X ≤ 1-2-n
移码-2n≤X ≤ 2n-1-1≤X ≤ 1-2-n
","page_idx":6,"page_size":[595,841],"block_position":"6-9"}],[{"bbox":[92,87,198,144],"type":"interline_equation","angle":0,"index":1,"text":"$$\n\\begin{array}{l} \\because [ X ] _ {\\text {原}} = X _ {S}, X _ {1} X _ {2} \\dots X _ {n} \\\\ \\cdot X _ {S} = 0: X = + X _ {1} X _ {2} \\dots X _ {n} \\\\ X _ {S} = 1: X = - X _ {1} X _ {2} \\dots X _ {n} \\\\ \\end{array}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":7,"id":"abdc6517-76fa-4293-922e-dea9b54110de","page_size":[595,841],"block_position":"7-0"},{"bbox":[251,87,368,145],"type":"interline_equation","angle":0,"index":3,"text":"$$\n\\begin{array}{l} \\because [ X ] _ {\\text {反}} = X _ {S}, X _ {1} X _ {2} \\dots X _ {n} \\\\ = X _ {S} = 0: X = + X _ {1} X _ {2} \\dots X _ {n} \\\\ \\cdot \\mathbf {x} _ {s} = 1: X = - \\overline {{X _ {1}}} \\overline {{X _ {2}}} \\dots \\overline {{X _ {n}}} \\\\ \\end{array}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":7,"id":"c85477a3-fa85-4ff3-8336-96e8ea262835","page_size":[595,841],"block_position":"7-1"},{"bbox":[92,164,158,178],"type":"text","angle":0,"index":4,"text":"[X]补→真值？","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":7,"id":"74ad871a-fa5a-420d-9931-c0d50d49ae06","page_size":[595,841],"block_position":"7-2"},{"bbox":[92,180,230,222],"type":"interline_equation","angle":0,"index":5,"text":"$$\n\\begin{array}{l} \\because [ X ] _ {\\text {补}} = X _ {S}, X _ {1} X _ {2} \\dots X _ {n} \\\\ \\cdot X _ {S} = 0: X = + X _ {1} X _ {2} \\dots X _ {n} \\\\ \\cdot X _ {S} = 1: X = - \\left(\\overline {{X _ {1}}} \\overline {{X _ {2}}} \\dots \\overline {{X _ {n}}} + 1\\right) \\\\ \\end{array}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":7,"id":"eb0b8455-afe1-4ccb-9a72-12c91cf9f695","page_size":[595,841],"block_position":"7-3"},{"bbox":[251,165,318,179],"type":"text","angle":0,"index":6,"text":"[X]移→真值？","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":7,"id":"23fe4961-dcb5-4ab1-99b8-d72033a50725","page_size":[595,841],"block_position":"7-4"},{"bbox":[251,182,389,223],"type":"interline_equation","angle":0,"index":7,"text":"$$\n\\begin{array}{l} \\because [ X ] _ {\\text {移}} = X _ {S}, X _ {1} X _ {2} \\dots X _ {n} \\\\ = X _ {S} = 1: X = + X _ {1} X _ {2} \\dots X _ {n} \\\\ \\cdot \\mathbf {X} _ {s} = \\mathbf {0}: X = - (\\overline {{X _ {1}}} \\overline {{X _ {2}}} \\dots \\overline {{X _ {n}}} + 1) \\\\ \\end{array}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":7,"id":"1764115a-1624-467d-b514-469c4a413b6a","page_size":[595,841],"block_position":"7-5"},{"bbox":[88,234,143,247],"type":"title","angle":0,"index":8,"text":"# 浮点数格式","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":7,"id":"1975045e-0384-450f-9336-0c75465ab44c","page_size":[595,841],"block_position":"7-6"},{"bbox":[89,254,158,266],"type":"text","angle":0,"index":9,"text":"浮点数N的构成：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":7,"id":"37f8b0a2-838e-4bc8-9122-cdfcc5f5c629","page_size":[595,841],"block_position":"7-7"},{"bbox":[204,253,270,264],"type":"interline_equation","angle":0,"index":10,"text":"$$\nN = M \\times R ^ {E}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":7,"id":"f41735c7-7928-45fe-9ac4-9242d31bbcb3","page_size":[595,841],"block_position":"7-8"},{"bbox":[89,269,342,280],"type":"text","angle":0,"index":11,"text":"阶码E（Exponent）、尾数M（Mantissa）和阶码的底R（Radix)","id":"6ac8ea68-36c6-42a1-b37c-53e0434e26c9","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":7,"page_size":[595,841],"block_position":"7-9"},{"bbox":[89,282,296,293],"type":"text","angle":0,"index":12,"text":"阶码的底R：是一个常数，隐含规定，一般为2、8或16","id":"ca3fd726-e23e-4d14-9111-05dddaa3243d","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":7,"page_size":[595,841],"block_position":"7-10"},{"bbox":[94,301,121,324],"type":"text","angle":0,"index":14,"text":"为什么将数符放置在首位？","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":7,"id":"a5050e6b-e287-495f-927f-3dc275147c90","page_size":[595,841],"block_position":"7-11"},{"bbox":[93,338,126,360],"type":"text","angle":0,"index":15,"text":"将数符放置在首位，方便比较大小","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":7,"id":"b03d0d81-2c48-48a7-b03a-d96fc6cbf96e","page_size":[595,841],"block_position":"7-12"},{"bbox":[166,301,345,337],"index":16,"angle":0,"type":"image","img_path":"/f318b4e4d2f9ec985b58f83758be6fd1d10255482e3dcd00bc9b8f495c476389.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.30084033613445377,"page_idx":7,"id":"122ceed3-3317-4391-81be-48d60be5870a","page_size":[595,841],"block_position":"7-13"},{"bbox":[158,341,228,351],"type":"text","angle":0,"index":17,"text":"浮点数格式要素：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":7,"id":"9c5ca997-a5b9-4efd-8ac0-5dcdb7a05bf4","page_size":[595,841],"block_position":"7-14"},{"bbox":[170,353,315,363],"type":"text","angle":0,"index":18,"text":"$\\textcircled{1}$ 位数：阶码位数 $^ +$ 尾数位数→总位数","id":"b98a7f53-da17-4dd8-8230-b0269ea4d4c2","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":7,"page_size":[595,841],"block_position":"7-15"},{"bbox":[170,364,317,375],"type":"text","angle":0,"index":19,"text":"$\\textcircled{2}$ 编码：阶码和尾数采用的机器数编码","id":"3de5a688-f707-4aa0-902d-d6cb960e72e8","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":7,"page_size":[595,841],"block_position":"7-16"},{"bbox":[170,376,293,386],"type":"text","angle":0,"index":20,"text":"$\\textcircled{3}$ 排列顺序：数符是否在最高位","id":"7a7b931d-6c4d-487f-9556-dd0f1c2e9443","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":7,"page_size":[595,841],"block_position":"7-17"},{"bbox":[170,388,309,398],"type":"text","angle":0,"index":21,"text":"$\\textcircled{4}$ 其他特殊的编码规则：譬如隐藏位","id":"aa2b9bf3-fb24-4a94-b497-500cdd4e1926","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":7,"page_size":[595,841],"block_position":"7-18"},{"bbox":[98,421,189,433],"type":"title","angle":0,"index":23,"text":"# 尾数M：定点小数","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":7,"id":"fb67cce8-3c51-4af0-8a6e-6266f910963f","page_size":[595,841],"block_position":"7-19"},{"bbox":[314,420,427,432],"type":"interline_equation","angle":0,"index":24,"text":"$$\n0. 1 0 1 1 1 0 \\times 2 ^ {- 2} = 0. 0 0 1 0 1 1 1\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":7,"id":"858a7411-c8ac-49a6-8a54-39ee88ccc84c","page_size":[595,841],"block_position":"7-20"},{"bbox":[335,437,414,453],"type":"interline_equation","angle":0,"index":25,"text":"$$\nN = M \\times R ^ {E}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":7,"id":"c6081617-5529-4795-8244-8f8a716ac9e8","page_size":[595,841],"block_position":"7-21"},{"bbox":[111,439,293,449],"type":"text","angle":0,"index":26,"text":"尾数的位数：决定了浮点数有效数值的精度","id":"a85f842c-ec22-4e28-bace-70023697393d","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":7,"page_size":[595,841],"block_position":"7-22"},{"bbox":[111,454,284,465],"type":"text","angle":0,"index":27,"text":"·尾数的符号：数符，代表了浮点数的正负","id":"b0dfe0c5-7b6d-43d5-9eb3-ccf5c1aacb4e","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":7,"page_size":[595,841],"block_position":"7-23"},{"bbox":[111,470,275,481],"type":"text","angle":0,"index":28,"text":"·尾数的编码：一般采用原码和补码表示","id":"74cb106b-76ce-4068-ac26-575566490964","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":7,"page_size":[595,841],"block_position":"7-24"},{"bbox":[98,487,184,499],"type":"title","angle":0,"index":30,"text":"# 阶码E：定点整数","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":7,"id":"8a96663c-247a-47c1-abbe-def64e057223","page_size":[595,841],"block_position":"7-25"},{"bbox":[111,504,296,515],"type":"text","angle":0,"index":31,"text":"·阶码的位数：多少决定了浮点数的表示范围","id":"67cc5d98-c1bf-441d-bbc3-6834e0bf7b16","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":7,"page_size":[595,841],"block_position":"7-26"},{"bbox":[111,520,436,532],"type":"text","angle":0,"index":32,"text":"·阶码的数值：大小决定了数据实际小数点位置与尾数的小数点位置之间的偏移量","id":"317c213a-2284-4487-a320-bac9a5e11abb","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":7,"page_size":[595,841],"block_position":"7-27"},{"bbox":[111,536,436,548],"type":"text","angle":0,"index":33,"text":"·阶码的符号：阶符，决定了实际小数点位置在尾数的小数点位置的左边还是右边","id":"2b731640-936a-452a-a147-414a4bc2adac","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":7,"page_size":[595,841],"block_position":"7-28"},{"bbox":[111,553,275,564],"type":"text","angle":0,"index":34,"text":"·阶码的编码：一般采用移码和补码表示","id":"25cc9507-46c5-4e4b-9b24-766cd76f5ee7","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":7,"page_size":[595,841],"block_position":"7-29"},{"bbox":[98,570,301,581],"type":"title","angle":0,"index":36,"text":"# 阶码的底R：一般为2、8或16，且隐含规定","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":7,"id":"0e01a6c8-b160-49e2-b9fd-7ce152e9e899","page_size":[595,841],"block_position":"7-30"},{"bbox":[270,592,285,601],"index":37,"angle":0,"type":"image","img_path":"/6a0fe239362570bed9f3912109c3557d492e9c9e6cb11a12f124138b78f42013.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.2,"page_idx":7,"id":"82c5650f-8c91-41ca-8949-c305167f1a96","page_size":[595,841],"block_position":"7-31"}],[{"bbox":[92,93,196,108],"type":"title","angle":0,"index":0,"text":"# 非规格化浮点数：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":8,"id":"4edbfcca-7174-4a7c-a082-d37e43f7cc05","page_size":[595,841],"block_position":"8-0"},{"bbox":[108,114,310,146],"type":"text","angle":0,"index":1,"text":"规格化操作：修改阶码和左右移尾数的方法来使其变为规格化浮点数","id":"397571e4-cfed-45ae-b982-97ee473eddcc","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"page_size":[595,841],"block_position":"8-1"},{"bbox":[108,151,289,166],"type":"text","angle":0,"index":2,"text":"右规：尾数进行右移实现的规格化","id":"f930e15d-ec1c-46af-a133-1543d861d150","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"page_size":[595,841],"block_position":"8-2"},{"bbox":[109,171,289,185],"type":"text","angle":0,"index":3,"text":"左规：尾数进行左移实现的规格化","id":"70824c65-94d2-4b6a-b51c-e7660e4132fe","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"page_size":[595,841],"block_position":"8-3"},{"bbox":[313,93,480,108],"type":"title","angle":0,"index":5,"text":"# 什么情况下要做规格化操作？","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":8,"id":"0d1b1f26-48c2-45c1-8e42-9240efb13e9e","page_size":[595,841],"block_position":"8-4"},{"bbox":[330,114,518,129],"type":"text","angle":0,"index":6,"text":"尾数有前导零：即 $\\textless 1 / 2$ ，需要左规","id":"c8ed897b-3b40-42b2-83cd-133067609315","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"page_size":[595,841],"block_position":"8-5"},{"bbox":[330,134,502,148],"type":"text","angle":0,"index":7,"text":"尾数运算溢出：即≥1，需要右规","id":"929399fa-92d4-4515-825b-fdcfb8ea76db","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"page_size":[595,841],"block_position":"8-6"},{"bbox":[313,160,514,176],"type":"title","angle":0,"index":9,"text":"# 使用规格化浮点数表示数据的优点：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":8,"id":"f29d04f0-d2e4-42f2-88a3-3d1a8cb6c50c","page_size":[595,841],"block_position":"8-7"},{"bbox":[330,182,454,196],"type":"text","angle":0,"index":10,"text":"提高了浮点数据的精度","id":"dcdf7eba-b327-4c83-841c-cbec3834373a","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"page_size":[595,841],"block_position":"8-8"},{"bbox":[330,201,509,216],"type":"text","angle":0,"index":11,"text":"使程序能够更方便地交换浮点数据","id":"fe96d444-6fcb-450f-b1e6-f83832e83816","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"page_size":[595,841],"block_position":"8-9"},{"bbox":[330,222,488,236],"type":"text","angle":0,"index":12,"text":"可以使浮点数的运算更为简化","id":"268a295d-fa88-47b0-ad59-6e05350e7b7c","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"page_size":[595,841],"block_position":"8-10"},{"bbox":[91,231,317,247],"type":"title","angle":0,"index":14,"text":"# （自定义格式）规格化浮点数表示方法：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":8,"id":"41f05655-a723-4f6b-869e-f12686b02ea3","page_size":[595,841],"block_position":"8-11"},{"bbox":[114,251,251,265],"type":"text","angle":0,"index":15,"text":"（1）写出数据的二进制真值","id":"9a035f24-f049-4293-9145-873dda9d7179","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"page_size":[595,841],"block_position":"8-12"},{"bbox":[114,269,453,284],"type":"text","angle":0,"index":16,"text":"(2）转换为M×2的形式，其中M为没有前导零的定点小数，E为整数","id":"d6d582fb-b6b3-4275-8728-d5ad12a17d50","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"page_size":[595,841],"block_position":"8-13"},{"bbox":[114,288,323,303],"type":"text","angle":0,"index":17,"text":"（3）按照格式写出M和E的规定机器数编码","id":"d3fbc412-16d0-42f4-90c0-9bf2da59e9bb","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"page_size":[595,841],"block_position":"8-14"},{"bbox":[115,306,257,322],"type":"text","angle":0,"index":18,"text":"（4）按照格式要求排列E和M","id":"d589ca2a-04f1-407b-bd5f-748abe85a7ed","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"page_size":[595,841],"block_position":"8-15"},{"bbox":[86,343,451,372],"type":"text","angle":0,"index":20,"text":"浮点数的运算过程中，尾数发生溢出（超出尾数所能表示的范围），进行右规。右规一次即可。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"id":"0d56b010-0af3-401e-bb3d-2ac87cd72399","page_size":[595,841],"block_position":"8-16"},{"bbox":[87,375,258,387],"type":"text","angle":0,"index":21,"text":"阶码发生溢出时，浮点数被判为溢出","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"id":"96a4857f-2afc-4fe8-b7d2-0e77823a9c54","page_size":[595,841],"block_position":"8-17"},{"bbox":[503,306,527,326],"index":22,"angle":0,"type":"image","img_path":"/a61299ff3ee52a556a1dcdca353af19b9a90d7dae7b2db0fa0bfe27f716b35b7.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.2,"page_idx":8,"id":"79e8a269-a907-42f5-a6fe-85dd305bdbcb","page_size":[595,841],"block_position":"8-18"},{"bbox":[88,424,189,443],"type":"title","angle":0,"index":23,"text":"# 1. 一些小结论","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":8,"id":"b3f7d1e8-af1f-416f-b60d-3dcde9dc862a","page_size":[595,841],"block_position":"8-19"},{"bbox":[86,511,290,524],"type":"text","angle":0,"index":24,"text":"由于补码表示的最大值和最小值是非对称的","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"id":"80f601f3-63fd-4dee-bc75-e982ff632358","page_size":[595,841],"block_position":"8-20"},{"bbox":[87,526,403,540],"type":"text","angle":0,"index":25,"text":"即最大值的绝对值(0111)的原码比最小值的绝对值的(1000)原码要小","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"id":"8ddae842-2775-4eb1-88fb-6ba846c69c62","page_size":[595,841],"block_position":"8-21"},{"bbox":[87,542,354,555],"type":"text","angle":0,"index":26,"text":"对于 n 位定点整数的机器数则为（ $( n + 1$ ）位（算上符号位）","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"id":"fe03edb9-60bc-495d-bc76-8974ac16a342","page_size":[595,841],"block_position":"8-22"},{"bbox":[87,558,184,571],"type":"text","angle":0,"index":27,"text":"对于一个负数X来说","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"id":"c661f36a-e5bd-4317-b6c3-67b76558b415","page_size":[595,841],"block_position":"8-23"},{"bbox":[87,574,167,587],"type":"text","angle":0,"index":28,"text":"[X]原+[X]补 $\\cdot = 2 \\wedge _ { \\mathsf { n } }$","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"id":"aaeadc39-ceee-488f-828b-e429cbe95d45","page_size":[595,841],"block_position":"8-24"},{"bbox":[87,588,453,602],"type":"text","angle":0,"index":29,"text":"Eg.[-2]原 $= 1 0 1 0$ ；[-2]补 $\\mathord { \\left. \\kern - delimiterspace \\right.} 1 1 0 $ ，相加为 1000（当成原码并去掉符号位，就是 8）","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"id":"fa3c8233-2fe0-426e-82cb-d50267d6c23a","page_size":[595,841],"block_position":"8-25"},{"bbox":[98,604,248,618],"type":"text","angle":0,"index":30,"text":"负数的补码就是其绝对值的补数","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"id":"5b6d72da-9d29-4fad-9227-e7b12ff477c5","page_size":[595,841],"block_position":"8-26"},{"bbox":[86,620,420,634],"type":"text","angle":0,"index":31,"text":"X的绝对值 $+ [ x ]$ 补但是[x]补当成原码去掉符号位，为10000即 $^ { 2 \\wedge }$ （ $( n + 1 )$ ）","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"id":"ffa3e73f-13b8-43b7-9dc5-e6fb3b1c7a88","page_size":[595,841],"block_position":"8-27"},{"bbox":[87,635,295,649],"type":"text","angle":0,"index":32,"text":"还是上个例子。[-2]补 $= 1 1 1 0 = 1 4$ ， $2 + 1 4 = 1 6$ ；","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"id":"fa8560c6-4953-4374-a340-ab4e7093db56","page_size":[595,841],"block_position":"8-28"},{"bbox":[87,651,304,664],"type":"text","angle":0,"index":33,"text":"所以，有符号数和无符号数之间的转换规则是：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"id":"0791d915-da1a-496c-beae-ee81b75e7b06","page_size":[595,841],"block_position":"8-29"},{"bbox":[87,667,288,680],"type":"text","angle":0,"index":34,"text":"位模式不变，但是解释这些位的方式改变了","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"id":"85e02692-cc7e-4e85-97b5-de53d26509b4","page_size":[595,841],"block_position":"8-30"},{"bbox":[87,682,163,695],"type":"text","angle":0,"index":35,"text":"数值数据的表示","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"id":"481a8e6b-6440-41fb-ace9-f817b5975ad9","page_size":[595,841],"block_position":"8-31"},{"bbox":[87,698,143,711],"type":"text","angle":0,"index":36,"text":"进位计数制","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"id":"e679d4c1-04bb-438a-b4ac-582a9682d8ed","page_size":[595,841],"block_position":"8-32"},{"bbox":[87,714,184,727],"type":"text","angle":0,"index":37,"text":"不同数制之间的转换","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"id":"153ce6c7-b1a7-4f99-af07-a6846178d5ca","page_size":[595,841],"block_position":"8-33"},{"bbox":[87,729,152,742],"type":"text","angle":0,"index":38,"text":"十进制的编码","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"id":"8268d322-23e9-41f2-8ab8-2f522e0db589","page_size":[595,841],"block_position":"8-34"},{"bbox":[87,745,121,757],"type":"text","angle":0,"index":39,"text":"机器数","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":8,"id":"a2eabe5a-6c8f-4a50-9c81-8b4d01485d2d","page_size":[595,841],"block_position":"8-35"}],[{"bbox":[87,79,377,91],"type":"text","angle":0,"index":0,"text":"数值数据在计算机中的表示形式称为机器数。机器数的特点是：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":9,"id":"49d4b8fd-b013-4a89-b004-533f23986da8","page_size":[595,841],"block_position":"9-0"},{"bbox":[88,94,324,103],"type":"text","angle":0,"index":1,"text":"$^ \\ast$ 机器数：数值数据在计算机中的二进制表示形式。真值：机器数真正表示的数值数据","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":9,"id":"321bafd0-e0b0-49c3-8dae-ce261316ab67","page_size":[595,841],"block_position":"9-1"},{"bbox":[96,105,323,113],"type":"text","angle":0,"index":2,"text":"·机器数的符号位必须被数值化为二进制0和1书写：+/-符号数值（二进制或","id":"1c6af52d-7ff0-47d5-9347-9ded698f97a8","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":9,"page_size":[595,841],"block_position":"9-2"},{"bbox":[96,115,235,123],"type":"text","angle":0,"index":3,"text":"·机器数的小数点用隐含规定的方式来表达","id":"171ac909-841a-45c8-ba25-2cb665fc3f3a","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":9,"page_size":[595,841],"block_position":"9-3"},{"bbox":[96,126,207,135],"type":"text","angle":0,"index":4,"text":"·表示的数值范围受计算机字长的限制","id":"e0cc1902-df17-40dd-9115-2ed167c7a1ea","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":9,"page_size":[595,841],"block_position":"9-4"},{"bbox":[96,137,285,145],"type":"text","angle":0,"index":5,"text":"·编码方法：不同的排列方式，常见的有原码、反码、补码、移码。","id":"75c7ee9c-94b8-4713-a894-b1089aae0c15","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":9,"page_size":[595,841],"block_position":"9-5"},{"bbox":[309,142,320,154],"index":7,"angle":0,"type":"image","img_path":"/c47a7a94827b3662a134a37286e20304c8e0e73f91dd09676afa6229802037f6.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.2,"page_idx":9,"id":"2d68469b-5f17-4d01-b11a-f30681194246","page_size":[595,841],"block_position":"9-6"},{"bbox":[87,174,250,193],"type":"title","angle":0,"index":8,"text":"# 定点机器数的表示方法","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":9,"id":"1d1892f9-19bd-4d7f-bf81-94db82b3026c","page_size":[595,841],"block_position":"9-7"},{"bbox":[87,231,195,243],"type":"text","angle":0,"index":9,"text":"一个字节由 8 个位组成","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":9,"id":"fe2cf76a-0962-4d0d-a2ae-dfe05e96bd80","page_size":[595,841],"block_position":"9-8"},{"bbox":[87,246,331,259],"type":"text","angle":0,"index":10,"text":"我们把这种按照一位一位表示数据的方式称为位模式","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":9,"id":"46ad78a9-bd03-4ad4-b872-b27102af65c0","page_size":[595,841],"block_position":"9-9"},{"bbox":[87,262,174,275],"type":"text","angle":0,"index":11,"text":"对于无符号数编码","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":9,"id":"642a8adf-f6d8-49df-9acc-5924ee045ed7","page_size":[595,841],"block_position":"9-10"},{"bbox":[87,277,272,290],"type":"text","angle":0,"index":12,"text":"在机器中的解释，采用原码表示法（？）","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":9,"id":"1289fd24-4057-4a33-a7dc-c9a55477f1db","page_size":[595,841],"block_position":"9-11"},{"bbox":[88,290,461,422],"index":13,"angle":0,"type":"image","img_path":"/29519d3b05891aec898580f89a8b7d69cdc6b6f2666f40bc361510a60e4b8e61.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.626890756302521,"page_idx":9,"id":"a6791686-157e-434d-a5ef-2c5ab90a8f27","page_size":[595,841],"block_position":"9-12"},{"bbox":[87,433,237,445],"type":"text","angle":0,"index":14,"text":"对于有符号数的编码，采用补码","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":9,"id":"a77c9971-2af7-45b4-9792-6023978a7b3a","page_size":[595,841],"block_position":"9-13"}],[{"bbox":[88,75,481,282],"index":0,"angle":0,"type":"image","img_path":"/3bb2c65a3b93dd5f3ba70445f8e1ac6b1845d70eca6912b30ec7b60296858a1a.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.6605042016806723,"page_idx":10,"id":"0a243266-df2e-41b7-9e4e-44ef215acbd5","page_size":[595,841],"block_position":"10-0"},{"bbox":[86,296,379,310],"type":"text","angle":0,"index":1,"text":"对于相同的位模式，无符号数和有符号数的数值关系如图所示：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":10,"id":"95fcdc6a-ffc5-4bca-864d-af21896d0bbb","page_size":[595,841],"block_position":"10-1"},{"bbox":[93,312,383,326],"type":"text","angle":0,"index":2,"text":"（这里的 B2U/B2T 是位向量到无符号数和有符号数的函数映射）","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":10,"id":"718111c1-0b59-4838-852e-8f1fc21a4735","page_size":[595,841],"block_position":"10-2"},{"bbox":[87,328,217,341],"type":"text","angle":0,"index":3,"text":"最高位理解成负权重-2^w-1","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":10,"id":"0ad23dce-e0e2-4883-9890-922ed92ac850","page_size":[595,841],"block_position":"10-3"},{"bbox":[88,350,208,364],"type":"interline_equation","angle":0,"index":4,"text":"$$\nB 2 U _ {w} = x _ {w - 1} \\cdot 2 ^ {w} + B 2 T _ {w}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":10,"id":"f66fe186-70b2-4246-8d19-4897e6c15dcf","page_size":[595,841],"block_position":"10-4"},{"bbox":[86,375,303,387],"type":"text","angle":0,"index":5,"text":"用 T2U 来表示有符号数到无符号数的函数映射","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":10,"id":"0e4007dd-f27c-4e09-b49d-532c48f7998b","page_size":[595,841],"block_position":"10-5"},{"bbox":[87,394,370,428],"type":"text","angle":0,"index":6,"text":"$T 2 U _ { w } ( x ) = \\left\\{ \\begin{array} { c } { { x + 2 ^ { w } , x < 0 } } \\\\ { { x , x > 0 } } \\end{array} \\right.$ $T 2 U _ { w } \\left( x \\right) = \\left( x + 2 ^ { w } \\right)$","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":10,"id":"782f6954-d64c-44f8-b771-e98424e83bc7","page_size":[595,841],"block_position":"10-6"},{"bbox":[88,437,238,470],"type":"interline_equation","angle":0,"index":7,"text":"$$\nU 2 T _ {w} (u) = \\left\\{ \\begin{array}{l} x, u \\leq T M \\max _ {u} \\\\ x - 2 ^ {w}, u > T M a x _ {u} \\end{array} \\right.\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":10,"id":"f8262ebe-bdc8-46d0-8fbb-b37cc403d792","page_size":[595,841],"block_position":"10-7"},{"bbox":[86,484,265,497],"type":"text","angle":0,"index":8,"text":"W位(包含了符号位！)补码表示的数值","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":10,"id":"afaaff51-18c4-452a-aa53-98c8200b10e6","page_size":[595,841],"block_position":"10-8"},{"bbox":[88,504,213,536],"type":"interline_equation","angle":0,"index":9,"text":"$$\n\\omega = - x _ {\\omega - 1} 2 ^ {\\omega - 1} + \\sum_ {i = 0} ^ {\\omega - 2} x _ {i} 2 ^ {i}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":10,"id":"44b158ec-79a1-47c7-be04-2432dcf9c91d","page_size":[595,841],"block_position":"10-9"},{"bbox":[86,546,379,560],"type":"text","angle":0,"index":10,"text":"也就是说，把第一位作为负数- $. 2 \\land \\mathfrak { n }$ 来处理；正数为 0,负数为 1；","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":10,"id":"138daa04-62b1-49c2-a2ed-a5c5d9ca94c5","page_size":[595,841],"block_position":"10-10"},{"bbox":[86,561,493,605],"type":"text","angle":0,"index":11,"text":"你可能已经发现，二进制数的“互补数”编码规则和补码的定义非常的像，其实不是像，而是它们本来就是等价的。也就是“对应正数的互补数”等于“对应正数按位取反再加1”。下面尝试证明。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":10,"id":"bcedfdd9-60d3-49b8-bec3-11d53d5fdf85","page_size":[595,841],"block_position":"10-11"},{"bbox":[86,608,494,637],"type":"text","angle":0,"index":12,"text":"原命题精确描述为：相对于 w 位的二进制数，整数 $\\mathsf { b } \\in ( 0 , ]$ ，即 $\\mathsf { b } \\in ( 0 , ]$ ，等式 $- b = - b + 1$成立。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":10,"id":"7dff6ad2-6a3f-4e30-9d98-3a12cc5d9044","page_size":[595,841],"block_position":"10-12"},{"bbox":[86,640,453,652],"type":"text","angle":0,"index":13,"text":"原码、补码、反码、移码的直接二进制值（机器数的形式值）各自有什么作用？","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":10,"id":"c9c10909-9b68-4e30-b97f-fe17d866240a","page_size":[595,841],"block_position":"10-13"},{"bbox":[86,655,502,683],"type":"text","angle":0,"index":14,"text":"反码、补码的真值为负数的时候机器数形式值（符号位作为 ${ 2 } \\Lambda _ { \\mathsf { n } }$ 而不是正负号）减去对应的 $2 \\sim ( \\mathsf { n } + 1 )$ 或者是 $_ { 2 ^ { \\wedge } }$ （n+1） $+ 1$ 就是这个机器数的真值。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":10,"id":"f011205d-d127-45d6-8854-80ec4a38bbdf","page_size":[595,841],"block_position":"10-14"},{"bbox":[86,687,245,700],"type":"text","angle":0,"index":15,"text":"移码是无论正负直接减去 $2 \\sim ( \\mathsf { n } + 1 )$","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":10,"id":"73ae7410-7ed9-4aaa-8ad3-d8735bed004f","page_size":[595,841],"block_position":"10-15"},{"bbox":[87,702,195,715],"type":"text","angle":0,"index":16,"text":"而原码没有类似的结果","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":10,"id":"51ba411b-76ba-4066-9e2b-f21572cb5faa","page_size":[595,841],"block_position":"10-16"}],[{"bbox":[88,82,483,259],"index":0,"angle":0,"type":"image","img_path":"/78e6ebe0fa6d18716eca1d48f88e453ca73f8c16ae9fe3c381407ee46ef7c2df.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.6638655462184874,"page_idx":11,"id":"3621499f-3937-4135-ac51-c14379db2cf9","page_size":[595,841],"block_position":"11-0"},{"bbox":[88,265,274,280],"type":"text","angle":0,"index":1,"text":"有符号数最高位为 0（正数），其余为 1","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":11,"id":"290653a8-aa9a-441e-8f3b-b9cba57107b6","page_size":[595,841],"block_position":"11-1"},{"bbox":[88,301,477,477],"index":2,"angle":0,"type":"image","img_path":"/e3ecdb1331e495f2deeb4e6668c8da5f41e4d66251fb5eee1929cfca02758dec.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.653781512605042,"page_idx":11,"id":"c7a8c0b6-53da-4606-ab1d-a31e9a2cb67c","page_size":[595,841],"block_position":"11-2"},{"bbox":[88,483,312,497],"type":"text","angle":0,"index":3,"text":"有符号数的-1和无符号数的最大值一样编码表示","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":11,"id":"c795eff3-35a7-40bc-8f8c-6fafff986e7c","page_size":[595,841],"block_position":"11-3"},{"bbox":[88,499,525,684],"index":4,"angle":0,"type":"image","img_path":"/d7ebf2a15fdae3ac42d3466cc5c4d421de2dfae73da3be0f75e1620b2f98e562.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.7344537815126051,"page_idx":11,"id":"15e82768-4638-4675-9c44-dcdf82340490","page_size":[595,841],"block_position":"11-4"}],[{"bbox":[86,84,243,103],"type":"title","angle":0,"index":0,"text":"# 2．真值与补码的转换","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":12,"id":"fa4a3ac6-573e-45d1-9b79-aab9ea7ab746","page_size":[595,841],"block_position":"12-0"},{"bbox":[86,140,142,153],"type":"title","angle":0,"index":1,"text":"# 真值->补码","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":12,"id":"0584a9c0-006c-4e20-8b4d-0c0ff0dc7b13","page_size":[595,841],"block_position":"12-1"},{"bbox":[86,156,235,168],"type":"text","angle":0,"index":2,"text":"正数的补码：去掉 $^ +$ 号前面加 0。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":12,"id":"646aede7-1355-4981-a421-9d88b8cff9ff","page_size":[595,841],"block_position":"12-2"},{"bbox":[86,171,440,184],"type":"text","angle":0,"index":3,"text":"负数的补码：1、去掉 - 号前面加 1，从右到左找到第一个 1，左边全部取反。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":12,"id":"607e80ec-2fe5-46e4-956f-1669a10a446a","page_size":[595,841],"block_position":"12-3"},{"bbox":[86,186,469,199],"type":"text","angle":0,"index":4,"text":"2、负数的补码是将原码的符号位保持不变,其余各位取反，然后加1,就得到其补码;","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":12,"id":"f2b89358-64cb-4419-ba71-774fc1a50b09","page_size":[595,841],"block_position":"12-4"},{"bbox":[86,202,294,215],"type":"text","angle":0,"index":5,"text":"计算一个负数的补码时，通常遵循以下步骤：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":12,"id":"cf17348e-d559-4a4d-855c-c62cf0778f4d","page_size":[595,841],"block_position":"12-5"},{"bbox":[105,217,486,231],"type":"text","angle":0,"index":6,"text":"1. 取绝对值的二进制表示：求出绝对值（即对应正数），求出数值的二进制形式。","id":"73cbe593-d420-4200-826d-e32f9879694a","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":12,"page_size":[595,841],"block_position":"12-6"},{"bbox":[105,233,386,246],"type":"text","angle":0,"index":7,"text":"2. 取反：将二进制数的每一位取反，即 0 变为 1，1 变为 $0 _ { \\circ }$","id":"5ed5f0cc-321a-49ad-bc85-2d912a7a4a1d","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":12,"page_size":[595,841],"block_position":"12-7"},{"bbox":[105,249,377,262],"type":"text","angle":0,"index":8,"text":"3. 加 1：在取反结果的基础上加 1，得到最终的补码表示。","id":"4119c879-0ff7-4a61-9be6-ef183bb9aa7b","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":12,"page_size":[595,841],"block_position":"12-8"},{"bbox":[86,264,454,277],"type":"text","angle":0,"index":10,"text":"也就是说，符号位参与了运算。在第 2 步实际上已经将“符号位为 1“表示成 0-1","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":12,"id":"53f1ff4e-31df-4ef7-b15c-6bbb5ddb4584","page_size":[595,841],"block_position":"12-9"},{"bbox":[86,280,504,308],"type":"text","angle":0,"index":11,"text":"实际上，这个符号位啊，你无论是先不管符号位取反再上符号位为 1，还是一起从绝对值取反（从0变成1—），不都是符号位为1吗？但参与 $+ 1$ 运算是必须的。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":12,"id":"d362122d-ee5a-457d-a1d2-1934f3f54e5d","page_size":[595,841],"block_position":"12-10"},{"bbox":[86,312,142,324],"type":"title","angle":0,"index":12,"text":"# 补码- $\\cdot >$ 真值","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":12,"id":"8cf0d563-18a8-485e-87e9-61929b73589c","page_size":[595,841],"block_position":"12-11"},{"bbox":[86,327,289,339],"type":"text","angle":0,"index":13,"text":"符号位 0 的补码的真值：去掉 0 前面加 $^ +$ 号。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":12,"id":"263ff48f-a359-47b1-88d3-9baa07c4e984","page_size":[595,841],"block_position":"12-12"},{"bbox":[86,343,200,355],"type":"text","angle":0,"index":14,"text":"符号位1的补码的真值：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":12,"id":"de232b51-e060-4f8d-854c-8441659e41d0","page_size":[595,841],"block_position":"12-13"},{"bbox":[89,358,379,370],"type":"text","angle":0,"index":15,"text":"1、去掉 1 前面加-号，从右到左找到第一个 1，左边全部取反。","id":"b377aa86-18da-4411-afa8-9aafc244a6c3","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":12,"page_size":[595,841],"block_position":"12-14"},{"bbox":[87,373,258,386],"type":"text","angle":0,"index":16,"text":"2、负数的原码就是它的补码的补码。","id":"b046921a-e691-4eac-93b3-d1253b9849af","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":12,"page_size":[595,841],"block_position":"12-15"},{"bbox":[86,389,496,417],"type":"text","angle":0,"index":17,"text":"3、如果补码的符号位为“1”，表示是一个负数，那么补码减1,再将符号位保持不变其余各位取反","id":"36660d38-cf58-4ad7-b622-a469d4d75adc","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":12,"page_size":[595,841],"block_position":"12-16"},{"bbox":[105,470,404,489],"type":"title","angle":0,"index":19,"text":"# 3.对于 $( X + 2 \\land ( \\mathbf { n } + 1 ) )$ mod (2^(n+1))的解释","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":12,"id":"29a0cca2-31e1-436d-ae3e-012fd73a07a6","page_size":[595,841],"block_position":"12-17"},{"bbox":[86,540,489,570],"type":"text","angle":0,"index":20,"text":"对某两个整数a，b，若它们除以正整数 $\\mathsf { m }$ 所得的余数相等，则称a，b对于模m同余，也就是严格来说，存在整数k使得","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":12,"id":"aef2873e-f292-4981-ae5c-f574417ab830","page_size":[595,841],"block_position":"12-18"},{"bbox":[86,572,334,585],"type":"text","angle":0,"index":21,"text":"$a - b = k m$ ，则称 a,b 对于除数 $\\mathsf { m }$ 是同余的。一般记做","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":12,"id":"2c1ca4ec-0aa8-4dff-88d5-1be339f9e6cb","page_size":[595,841],"block_position":"12-19"},{"bbox":[87,588,151,601],"type":"interline_equation","angle":0,"index":22,"text":"$$\na \\equiv b (\\bmod m)\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":12,"id":"6a0d5d20-5286-481f-b00f-e17cea002ce5","page_size":[595,841],"block_position":"12-20"},{"bbox":[86,603,454,616],"type":"text","angle":0,"index":23,"text":"在模运算中，一个数与它除以“模”后得到的余数是等价的，如 A、B、M 满足","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":12,"id":"c7238bda-9f05-427c-8c1a-174286b3ca4f","page_size":[595,841],"block_position":"12-21"},{"bbox":[86,618,502,663],"type":"text","angle":0,"index":24,"text":"$\\mathsf { A } { = } \\mathsf { B } { + } \\mathsf { K } { \\times } \\mathsf { M } ( \\mathsf { K }$ 为整数)，则记为 $\\mathsf { A } \\equiv \\mathsf { B } ( \\mathsf { m o d } \\mathsf { M } )$ )，即 A、B各除以 M后的余数相同。在补码运算中，[A]补-[B]补=[A]补 $+ \\mathsf { M }$ -[B]补，而 M-[B]补 $=$ [-B]补，因此补码可以借助加法运算来实现减法运算。从模运算的角度，补码的表示利用了以下规律：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":12,"id":"2df1f589-85d9-433d-ae10-c4c0ea59617a","page_size":[595,841],"block_position":"12-22"},{"bbox":[86,666,502,694],"type":"text","angle":0,"index":25,"text":"模运算的同余性质：对于任意整数 a 和模数 $\\mathsf { m }$ ，有 $\\mathsf { a } \\equiv \\mathsf { a } + \\mathsf { k m } ( \\mathsf { m o d } \\mathsf { m } )$ ，其中 k为整数。这意味着在模 $\\mathsf { m }$ 的运算中，数值是循环的，超过 $\\mathsf { m }$ 会回到起点。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":12,"id":"95d5c019-3c60-4914-8613-996981ebd277","page_size":[595,841],"block_position":"12-23"},{"bbox":[86,697,376,709],"type":"text","angle":0,"index":26,"text":"为何常见写法是 $^ { 6 6 } x + 2 \\wedge _ { \\mathsf { n } + 1 }$ mod $\\mathsf { \\pm } \\mathsf { \\Lambda } \\mathsf { n } \\mathsf { \\pm } ^ { \\prime }$ 1”而不是 $\\pmb { \\times }$ mod $^ { 2 n + 1 }$","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":12,"id":"c397593b-6b94-4699-8871-24f89dac90bf","page_size":[595,841],"block_position":"12-24"},{"bbox":[86,712,324,725],"type":"text","angle":0,"index":27,"text":"数论上， $^ { * } \\times$ 与 $\\mathsf { x } + 2 \\wedge \\{ \\mathsf { n } + 1 \\} \\times ^ { \\prime \\prime }$ 在模 $2 \\cdot \\{ \\mathsf { n } + 1 \\}$ 下等价；","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":12,"id":"75067381-f3ca-47c4-9902-74e1d29abbf2","page_size":[595,841],"block_position":"12-25"},{"bbox":[86,728,501,756],"type":"text","angle":0,"index":28,"text":"但在说明“补码如何把负数映射到二进制的高半区”时，显式地加上 $2 \\times \\{ \\mathsf { n } + 1 \\}$ 更能直观反映“负数被搬到了高位 $\\ O = \\uparrow$ 的区间”这个事实。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":12,"id":"bbe7ec08-b9b8-4ae7-8bf5-15b902c05874","page_size":[595,841],"block_position":"12-26"}],[{"bbox":[86,79,359,92],"type":"text","angle":0,"index":0,"text":" 非负数直接写成“它自己” (因为落在小半区间 $[ 0 , 2 \\land \\mathsf { n } ) ]$ )；","id":"adc7a7ab-97bb-4f41-9d2b-c3942d2b1533","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":13,"page_size":[595,841],"block_position":"13-0"},{"bbox":[86,95,421,108],"type":"text","angle":0,"index":1,"text":" 负数写成 $^ { \\mathfrak { a } } \\mathsf { X } + 2 ^ { \\wedge } \\{ \\mathsf { n } + 1 \\} ^ { \\prime \\prime }$ (因为这样就落在大半区间 $[ 2 \\land \\neg , 2 \\land \\{ \\mathsf { n } + 1 \\} - 1 ] ) _ { \\circ }$","id":"47aefb8d-72b1-4d4f-9730-bac6a16fe1cf","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":13,"page_size":[595,841],"block_position":"13-1"},{"bbox":[86,110,473,122],"type":"text","angle":0,"index":3,"text":"在计算机系统中， $\\mathsf { n }$ 位定点整数（包括符号位）补码的取值范围是 $- 2 \\land \\mathsf { n }$ 到 $2 \\ n _ { \\mathsf { n } } - 1$ 。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":13,"id":"f7bedaae-2a7d-4075-8c75-c6fe39b73e06","page_size":[595,841],"block_position":"13-2"},{"bbox":[86,125,502,154],"type":"text","angle":0,"index":4,"text":"这意味着总共有 $2 \\cdot \\{ \\mathsf { n } + 1 \\}$ 个不同的数值可以表示。因此，模数 $2 \\cdot \\{ \\mathsf { n } + 1 \\}$ 对应于这些数值的总数量。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":13,"id":"a3c9a37b-41ad-4e5d-a8cc-06f5f9692fc5","page_size":[595,841],"block_position":"13-3"},{"bbox":[86,157,497,185],"type":"text","angle":0,"index":5,"text":"负数的表示：在模 $2 \\cdot \\{ \\mathsf { n } + 1 \\}$ 的系统中，负数 X 可以表示为 $2 \\wedge \\{ \\mathsf { n } + 1 \\} + \\mathsf { X } ,$ ,因为 X 为负数，会落在 $2 \\land ( \\mathsf { n } )$ 到 $2 \\cdot \\{ \\mathsf { n } + 1 \\} - 1$ 的范围内，符合无符号数的表示范围。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":13,"id":"874b9419-2068-4944-aec4-01ec20d62d40","page_size":[595,841],"block_position":"13-4"},{"bbox":[86,188,483,201],"type":"text","angle":0,"index":6,"text":"因为模为 $2 \\cdot ( n + 1 ) , k = 1$ $k = 1$ ，那么就可以将- $2 ^ { \\wedge } \\mathsf { n } - 2 ^ { \\wedge } \\mathsf { n } - 1$ 统一成 $( X { + } 2 ^ { \\wedge } ( \\mathsf { n } { + } 1 ) )$ ) mod $( 2 \\land ( \\mathsf { n } + 1 ) )$","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":13,"id":"0e326804-8307-45d0-8d9a-bf6fe96f384b","page_size":[595,841],"block_position":"13-5"},{"bbox":[86,203,498,232],"type":"text","angle":0,"index":7,"text":"减法（加上一个负数）的运算用加法代替了，我们说的补码（反码）实际上是数对于一个模的同余数。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":13,"id":"46e6dabd-ffbe-42bd-afc1-2d669a979166","page_size":[595,841],"block_position":"13-6"},{"bbox":[86,234,495,263],"type":"text","angle":0,"index":8,"text":"（这里的取模运算，请让我们抛弃符号数，eg.-2 mod $8 { = } 6$ , $[ 6 ] { = } 1 1 0$ ,而 [-2]补 $\\mathord { = } 1 1 1 0$ ，当成原码，去掉符号位）","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":13,"id":"c374d215-0f63-441a-9f4b-4119ee6aa328","page_size":[595,841],"block_position":"13-7"},{"bbox":[86,265,495,294],"type":"text","angle":0,"index":9,"text":"规定：把0当成正数，也即 $+ 0$ ，这样0的编码就变成：0，0000000。那8位二进制表示的正数范围仍然是： $+ 0 -- + 1 2 7 _ { \\mathrm { { ( } } }$ 。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":13,"id":"94100fec-14d7-459b-a8ea-6af775f94060","page_size":[595,841],"block_position":"13-8"},{"bbox":[86,296,492,341],"type":"text","angle":0,"index":10,"text":"但是，对于负数就必须要做调整，也即-0必须要让位---1，0000000这个编码不能表示-0。我们可以把负数整体向后“挪动1位”：只要将8位二进制表示的负数范围从：-127—— -0变成：-128 —— -1，就能成功解决问题。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":13,"id":"bde031ee-3b9a-41ad-a32d-ed9358f893ba","page_size":[595,841],"block_position":"13-9"},{"bbox":[86,343,498,371],"type":"text","angle":0,"index":11,"text":"-0 的补数是 $2 5 6 - 0 = 2 5 6 = 0 \\times 1 0 0$ ，由于是“8 位二进制数”，所以-0 的补数是 $0 \\times 0 0$ ；‘我们知道“- $\\cdot 1 = 0 - 1 \\prime$ ，所以","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":13,"id":"afd79aa1-bcbc-41f1-abfa-dd24433f7859","page_size":[595,841],"block_position":"13-10"},{"bbox":[86,375,498,403],"type":"text","angle":0,"index":12,"text":"-1 的补数是 $2 5 6 - 1 = 2 5 5 = 0 \\times 1 =$ ；这就好比是\"0-1\"不够减，\"借 256\"得到的（这里借的是模数值）。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":13,"id":"4732c82c-b410-4dbd-9e2b-fc6aa76f599c","page_size":[595,841],"block_position":"13-11"},{"bbox":[86,406,217,418],"type":"text","angle":0,"index":13,"text":"同理，可以-2~-127的补数；","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":13,"id":"e6711684-d079-456e-b0e2-b59b7c208c19","page_size":[595,841],"block_position":"13-12"},{"bbox":[86,422,293,434],"type":"text","angle":0,"index":14,"text":"注意：这里的补数，就是计算机所讲的补码。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":13,"id":"82779037-6b72-4357-9d9c-f1399d8d5e2d","page_size":[595,841],"block_position":"13-13"},{"bbox":[86,438,255,450],"type":"text","angle":0,"index":15,"text":"-127 的补数是 $2 5 6 - 1 2 7 = 1 2 9 = 0 \\times 8 1$","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":13,"id":"d7a2e4d2-329b-425e-b0cf-c825503fa7db","page_size":[595,841],"block_position":"13-14"},{"bbox":[86,454,248,465],"type":"text","angle":0,"index":16,"text":"-1~-127 的补码范围： $0 { \\times } \\mathsf { F F } { \\sim } 0 { \\times } 8 1$","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":13,"id":"cc66ea98-ff4e-4bfb-b898-cd8c79664b04","page_size":[595,841],"block_position":"13-15"},{"bbox":[86,469,170,481],"type":"text","angle":0,"index":17,"text":"负数-128的补码：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":13,"id":"2226d375-a100-40c8-a997-f22319a484a7","page_size":[595,841],"block_position":"13-16"},{"bbox":[86,484,314,497],"type":"text","angle":0,"index":18,"text":"我们知道“- $\\cdot 1 2 8 = 0 - 1 2 8 ^ { \\prime \\prime }$ ，“ $- 1 2 8 = - 1 + - 1 2 7 ^ { \\prime \\prime }$ 所以","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":13,"id":"ef6e0f09-b52e-44da-93f1-0c93fcf92e52","page_size":[595,841],"block_position":"13-17"},{"bbox":[86,499,505,528],"type":"text","angle":0,"index":19,"text":"-128 的补数是 $2 5 6 - 1 2 8 = 1 2 8 = 0 \\times 8 0$ ；所以-128 的补码为 0x80，但是-128 没有原码和反码。所以人为地规定 10000000 表示-128","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":13,"id":"1cd35ca6-66d6-4765-b61d-86f21065489b","page_size":[595,841],"block_position":"13-18"},{"bbox":[87,531,115,543],"type":"text","angle":0,"index":20,"text":"总结：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":13,"id":"f55e5bac-5037-477f-b630-61cedc9c07b2","page_size":[595,841],"block_position":"13-19"},{"bbox":[86,546,279,559],"type":"text","angle":0,"index":21,"text":"补码补码，就是补上去一个模对应的补数","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":13,"id":"82077102-266c-40c4-9609-7f38c1726241","page_size":[595,841],"block_position":"13-20"},{"bbox":[87,580,122,597],"type":"title","angle":0,"index":22,"text":"# 小结","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":13,"id":"c2cc596d-9e7a-4250-9ae1-18e5704c3eed","page_size":[595,841],"block_position":"13-21"},{"bbox":[86,636,325,649],"type":"text","angle":0,"index":23,"text":"在一个区间长度为 M 内，统一正负数的常用方法是","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":13,"id":"b52417fc-7224-4e79-9ed5-f1763d2ccb1c","page_size":[595,841],"block_position":"13-22"},{"bbox":[86,651,181,663],"type":"interline_equation","angle":0,"index":24,"text":"$$\nX ^ {\\prime} = (X + M) \\mod M\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":13,"id":"eb4e44f4-899c-4572-87c5-ded88415516b","page_size":[595,841],"block_position":"13-23"},{"bbox":[86,666,502,710],"type":"text","angle":0,"index":25,"text":"其中 M 就是模数。如果你换成一个非 M 的倍数 N，则只有在 $\\Nu \\equiv 0$ (mod M)的情况下才能达到同样效果。因此，负数加上的部分必须是 M 的倍数，通常取最小正倍数 M 来实现统一。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":13,"id":"2ecdc43c-1599-4ac4-908d-80a283b743f6","page_size":[595,841],"block_position":"13-24"},{"bbox":[86,714,497,742],"type":"text","angle":0,"index":26,"text":"可以这么理解：如果一个区间（或集合）恰好包含 $\\mathsf { m }$ 个整数，并且这 $\\mathsf { m }$ 个整数构成了一个模 $\\mathsf { m }$ 的完全剩余系，那么对任意整数 X，用","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":13,"id":"adfc8132-97b4-47ad-9c6b-2e46f3a1a18d","page_size":[595,841],"block_position":"13-25"},{"bbox":[87,745,133,756],"type":"interline_equation","angle":0,"index":27,"text":"$$\nX \\bmod m\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":13,"id":"3dc19cd9-69cb-4502-b372-b9fdcf626e28","page_size":[595,841],"block_position":"13-26"}],[{"bbox":[86,79,501,107],"type":"text","angle":0,"index":0,"text":"总能得到落在这个集合中的唯一代表。换句话说，只要这个集合包含的元素个数为 m（而且互不同余），那么无论 X是正数还是负数，都有","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":14,"id":"7b36fe5e-b42f-4590-a0a4-919f7aa33f65","page_size":[595,841],"block_position":"14-0"},{"bbox":[87,111,148,121],"type":"interline_equation","angle":0,"index":1,"text":"$$\nX \\equiv X \\bmod m\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":14,"id":"9a9c17ca-62b0-43f4-b9b3-a285b35bc182","page_size":[595,841],"block_position":"14-1"},{"bbox":[86,125,301,138],"type":"text","angle":0,"index":2,"text":"而且 Xmodm 就是该模 m 意义下的标准表示。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":14,"id":"730b96c9-56a7-46e4-9936-0df85cecb84b","page_size":[595,841],"block_position":"14-2"},{"bbox":[87,147,255,165],"type":"title","angle":0,"index":3,"text":"# 为什么定点小数的模 2？","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":14,"id":"cfd6a2e5-2308-480e-896b-2393eae0fd8f","page_size":[595,841],"block_position":"14-3"},{"bbox":[86,172,508,232],"type":"text","angle":0,"index":4,"text":"至于模数为 2 的说法，这是因为补码表示中，数值的表示是循环的。例如，-1 和 $1 - 2 \\land ( - \\mathsf { n } )$之间的差值正好是 $2 - 2 \\land ( - \\mathsf { n } )$ ，但由于补码的循环特性，这个差值在模 2 的意义下是等价的。$- 2 \\land ( - \\mathsf { n } )$ 并没有被省略，而是补码表示的范围已经包含了从 -1 到 $1 - 2 \\land ( - \\mathsf { n } )$ 的所有可能值。补码的模数为 2 是因为补码表示中，数值的表示是循环的，且循环周期为 2。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":14,"id":"fd73d276-046f-41a9-94b5-2276a142d44d","page_size":[595,841],"block_position":"14-4"},{"bbox":[87,269,187,287],"type":"title","angle":0,"index":5,"text":"# 关于数的扩展","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":14,"id":"1a9db406-70b4-411c-8610-2aad79e7dcab","page_size":[595,841],"block_position":"14-5"},{"bbox":[86,324,242,337],"type":"text","angle":0,"index":6,"text":"基本上是这样的。对两类数来说：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":14,"id":"f42ef65c-1298-47de-84f6-07d15cd9970c","page_size":[595,841],"block_position":"14-6"},{"bbox":[105,339,236,352],"type":"text","angle":0,"index":7,"text":"高位扩展（符号扩展）：","id":"64ee88a8-b199-426c-a80e-0802d59b158f","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":14,"page_size":[595,841],"block_position":"14-7"},{"bbox":[105,355,236,368],"type":"text","angle":0,"index":8,"text":"低位扩展（增加精度）：","id":"5a5b6269-78ec-4d95-a29f-46e8d283f716","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":14,"page_size":[595,841],"block_position":"14-8"},{"bbox":[87,386,189,399],"type":"title","angle":0,"index":10,"text":"# 定点整数的符号扩展：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":14,"id":"79e7ab13-0928-4cd0-ae2c-e9ec7ae9236a","page_size":[595,841],"block_position":"14-9"},{"bbox":[86,402,218,415],"type":"text","angle":0,"index":11,"text":"对于无符号数，称为零扩展","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":14,"id":"0dd1a311-3888-4d6b-9387-8acbc45da375","page_size":[595,841],"block_position":"14-10"},{"bbox":[86,417,238,430],"type":"text","angle":0,"index":12,"text":"对于有符号数，称为符号位扩展","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":14,"id":"a6caa07c-825d-4693-8475-db985d6945b8","page_size":[595,841],"block_position":"14-11"},{"bbox":[86,433,494,461],"type":"text","angle":0,"index":13,"text":"在原符号位和数值位中间添加新位，正数都添0，负数原码添0，负数反、补码、移码添1。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":14,"id":"cb6e942e-48d5-4f9d-ab33-92370d36dfd2","page_size":[595,841],"block_position":"14-12"},{"bbox":[88,467,276,518],"type":"interline_equation","angle":0,"index":14,"text":"$$\n\\begin{array}{l} B 2 T _ {w} \\left(\\left[ x _ {w - 1}, x _ {w - 2}, \\dots , x _ {0} \\right]\\right) (1) \\\\ B 2 T _ {w + k} \\left(\\left[ x _ {w - 1}, \\dots , x _ {w - 1}, x _ {w - 1}, \\dots , x _ {0} \\right]\\right) (2) \\\\ B 2 T _ {w + 1} - B 2 T _ {w} = 0 \\\\ \\end{array}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":14,"id":"528d51f1-9cbf-49d9-a3ac-4568c2e12708","page_size":[595,841],"block_position":"14-13"},{"bbox":[87,527,189,539],"type":"title","angle":0,"index":15,"text":"# 定点小数的符号扩展：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":14,"id":"43e42c5f-652d-4810-9ec1-a0e853c89068","page_size":[595,841],"block_position":"14-14"},{"bbox":[86,542,494,570],"type":"text","angle":0,"index":16,"text":"在原符号位和数值位后面添加新位，正数都添0，负数原、补码、移码添0，负数反码添1。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":14,"id":"a64f762b-7cc8-4635-89fe-0664c49ed6c3","page_size":[595,841],"block_position":"14-15"},{"bbox":[87,573,132,586],"type":"title","angle":0,"index":17,"text":"# 低位截断","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":14,"id":"8a98a656-88b0-4590-9320-039ee1f3ab8f","page_size":[595,841],"block_position":"14-16"},{"bbox":[86,589,326,602],"type":"text","angle":0,"index":18,"text":"将 int 类型强制转换为 short 类型，高 16 位被丢弃","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":14,"id":"597bf7ca-ee6c-418a-bc66-8802ad359840","page_size":[595,841],"block_position":"14-17"},{"bbox":[86,604,503,633],"type":"text","angle":0,"index":19,"text":"将一个 $\\pmb { \\mathsf { W } }$ 位的无符号数，截断成k位的方法是，丢弃最高的w-k位。截断操作可以对应于取模运算。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":14,"id":"9756f3cc-079f-44d9-b1cb-9e7e55547c7f","page_size":[595,841],"block_position":"14-18"},{"bbox":[88,642,371,656],"type":"interline_equation","angle":0,"index":20,"text":"$$\nB 2 U _ {w} \\left(\\left[ x _ {w - 1}, x _ {w - 2}, \\dots , x _ {0} \\right]\\right) \\mod 2 ^ {k} = B 2 U _ {k} \\left(\\left[ x _ {k - 1}, x _ {k - 2}, \\dots , x _ {0} \\right]\\right)\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":14,"id":"2c86f5b3-695a-4b06-9538-951d2554f4a8","page_size":[595,841],"block_position":"14-19"},{"bbox":[87,666,154,679],"type":"title","angle":0,"index":21,"text":"# 截断有符号数","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":14,"id":"029ea83e-248b-47ab-9876-821c9f384bf4","page_size":[595,841],"block_position":"14-20"},{"bbox":[86,682,311,695],"type":"text","angle":0,"index":22,"text":"先转换成无符号数，再截断，再转换成有符号数","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":14,"id":"2f330fda-b15f-4fee-ab1b-9015d5d96b15","page_size":[595,841],"block_position":"14-21"},{"bbox":[87,698,101,710],"type":"text","angle":0,"index":23,"text":"即","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":14,"id":"af87dc26-c6d9-4aeb-b3fd-ab94f44400ad","page_size":[595,841],"block_position":"14-22"},{"bbox":[179,717,357,739],"type":"interline_equation","angle":0,"index":24,"text":"$$\nT ^ {2} U _ {w} (x) = \\left\\{ \\begin{array}{c} x + 2 ^ {w}, x < 0 \\\\ x, x > 0 \\end{array} \\right., \\text {即} T 2 U _ {w} (x) = (x + 2 ^ {w}) \\mod 2 ^ {w}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":14,"id":"92310cea-fef7-4f17-8f77-e31430453077","page_size":[595,841],"block_position":"14-23"},{"bbox":[88,742,449,754],"type":"interline_equation","angle":0,"index":25,"text":"$$\nB 2 T _ {k} \\left(\\left[ x _ {k - 1}, \\dots , x _ {0} \\right]\\right) = U 2 T _ {w} \\left(\\left[ B 2 T _ {w} \\left(\\left[ x _ {w - 1}, x _ {w - 2}, \\dots , x _ {0} \\right]\\right) + 2 ^ {w} \\right] \\mod 2 ^ {w} \\right] \\mod 2 ^ {k}) = U 2 T _ {w} \\left(B 2 U _ {w} \\left(\\left[ x _ {w - 1}, x _ {w - 2}, \\dots , x _ {0} \\right]\\right) \\mod 2 ^ {k}\\right)\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":14,"id":"814b2e4a-8c68-4d78-84dc-51383868f7bf","page_size":[595,841],"block_position":"14-24"}],[{"bbox":[86,143,196,164],"type":"title","angle":0,"index":0,"text":"# 4、其他运算符","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":15,"id":"b36d55e9-dd19-4966-93d3-91664efbf5ce","page_size":[595,841],"block_position":"15-0"},{"bbox":[86,205,242,225],"type":"title","angle":0,"index":1,"text":"# 布尔运算（位级运算）","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":15,"id":"8d7dcc1c-ec4f-412f-a3c4-e2a5ab10c58c","page_size":[595,841],"block_position":"15-1"},{"bbox":[86,260,236,274],"type":"text","angle":0,"index":2,"text":"~/NOT 非（取反）（单目运算）","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":15,"id":"90b35947-14de-42ed-92f3-5385c758836b","page_size":[595,841],"block_position":"15-2"},{"bbox":[88,276,137,289],"type":"text","angle":0,"index":3,"text":"&/AND 与","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":15,"id":"1dfa5584-9bd5-4c59-bffb-74aa6e518907","page_size":[595,841],"block_position":"15-3"},{"bbox":[89,291,129,305],"type":"text","angle":0,"index":4,"text":"|/OR 或","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":15,"id":"471bed01-b9ec-4d59-a4df-1ef091b4e8be","page_size":[595,841],"block_position":"15-4"},{"bbox":[88,307,195,320],"type":"text","angle":0,"index":5,"text":"^/EXCLUSIVE-OR 异或","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":15,"id":"ca06165c-134f-4b8b-927d-c16d6a68f815","page_size":[595,841],"block_position":"15-5"},{"bbox":[88,322,147,336],"type":"text","angle":0,"index":6,"text":"取反的时候：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":15,"id":"438c1ca9-4c7c-463c-a95d-ddb8eac406d3","page_size":[595,841],"block_position":"15-6"},{"bbox":[88,338,348,352],"type":"text","angle":0,"index":7,"text":"因此，可以总结出~按位取反的计算结论是： $\\sim \\mathsf { n } = - ( \\mathsf { n } + 1 )$","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":15,"id":"110a90a8-532c-482f-99a3-eeda7cb3eb78","page_size":[595,841],"block_position":"15-7"},{"bbox":[88,354,259,367],"type":"text","angle":0,"index":8,"text":"例如本例中， $\\mathord { \\sim } 5 = - ( 5 + 1 )$ ，即 $\\mathord { \\sim } 5 = - 6$","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":15,"id":"082c1724-3f09-44ed-86eb-f080ee9429c8","page_size":[595,841],"block_position":"15-8"},{"bbox":[87,388,154,407],"type":"title","angle":0,"index":9,"text":"# 逻辑运算","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":15,"id":"0e1bbf8d-107a-49c3-9f5a-e290e4cac8e5","page_size":[595,841],"block_position":"15-9"},{"bbox":[86,444,275,457],"type":"text","angle":0,"index":10,"text":"所有非零参数为 true，参数 0 表示 false","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":15,"id":"20be3bee-6d94-436d-b4b0-219c1de268ad","page_size":[595,841],"block_position":"15-10"},{"bbox":[88,459,267,472],"type":"text","angle":0,"index":11,"text":"结果只有两个，true与false 惰性运算","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":15,"id":"49e0a2e1-a163-488f-8d4b-791e7f717fd2","page_size":[595,841],"block_position":"15-11"},{"bbox":[89,475,120,487],"type":"text","angle":0,"index":12,"text":"|| OR","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":15,"id":"f76c5f0f-7873-4e9d-a6f6-bd4c7d598830","page_size":[595,841],"block_position":"15-12"},{"bbox":[88,491,130,502],"type":"text","angle":0,"index":13,"text":"&& AND","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":15,"id":"fc8fa020-d795-45a2-ab20-edaeffe3a085","page_size":[595,841],"block_position":"15-13"},{"bbox":[88,507,117,518],"type":"text","angle":0,"index":14,"text":"! NOT","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":15,"id":"b7bb43fe-aa22-4654-bf8c-793fad2559c5","page_size":[595,841],"block_position":"15-14"},{"bbox":[86,539,154,559],"type":"title","angle":0,"index":15,"text":"# 移位运算","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":15,"id":"7cc7cf5b-5393-429e-a63a-7a5750989980","page_size":[595,841],"block_position":"15-15"},{"bbox":[86,595,506,624],"type":"text","angle":0,"index":16,"text":"逻辑移位。将移位的数据视为无符号数据，移位的结果知识数据位置发生了变化。移出的数据位一般置入CF标志位(进位、借位 标志)","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":15,"id":"e83b45c2-3ccc-44aa-afc7-aea3618b112e","page_size":[595,841],"block_position":"15-16"},{"bbox":[86,626,504,640],"type":"text","angle":0,"index":17,"text":"算术移位，对象是有符号数，算术移位的结果在绝对值上进行放大缩小；符号位保持不变。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":15,"id":"adb4e6ed-d459-48b6-b8d5-903521dbd5b6","page_size":[595,841],"block_position":"15-17"},{"bbox":[88,642,314,655],"type":"text","angle":0,"index":18,"text":"计算机的算术移位指令大多采用补码的 移位规则","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":15,"id":"453b163f-d1c8-4bf2-96fc-41e09785dc72","page_size":[595,841],"block_position":"15-18"},{"bbox":[86,657,509,687],"type":"text","angle":0,"index":19,"text":"循环移位，左移时最高位移入最低位，右移时最高位移入最低为，若和CF标志位一起循环，则称为大循环，否则小循环","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":15,"id":"d176e0e5-a7da-4a17-a5d4-5d2f808baf71","page_size":[595,841],"block_position":"15-19"},{"bbox":[86,689,267,702],"type":"text","angle":0,"index":20,"text":"左移相当于乘以2，右移相当于除以二","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":15,"id":"dd753a25-27f2-4967-84d4-9d8ac82c12fc","page_size":[595,841],"block_position":"15-20"},{"bbox":[86,704,506,750],"type":"text","angle":0,"index":21,"text":"CF: 进位/借位标志。最近的操作使最高位产生了进位。可用来检査无符号操作的溢出。 加法运算时 $\\textstyle \\sum = 1$ ,则CF置1表示进位；减法运算时 $C { = } 0 , C F$ 置1表示借位。CF只对无符号数运算有意义。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":15,"id":"edca1e9e-3c5d-40e5-a886-f8c356e8153a","page_size":[595,841],"block_position":"15-21"}],[{"bbox":[86,79,364,90],"type":"text","angle":0,"index":0,"text":"ZF: 零标志。最近的操作得出的结果为 0（全零）则 ZF 置 1。","id":"47133cf5-b68c-457a-a820-fcee8c9cf3c8","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":16,"page_size":[595,841],"block_position":"16-0"},{"bbox":[86,95,503,121],"type":"text","angle":0,"index":1,"text":"SF: 符号标志。记录运算结果的符号，它与运算结果的最高位相同。采用补码表示，运算结果为正数置0，负数置1。","id":"40a331ba-a156-4bde-9e9d-cbbbc9317c75","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":16,"page_size":[595,841],"block_position":"16-1"},{"bbox":[86,125,503,153],"type":"text","angle":0,"index":2,"text":"OF: 溢出标志。最近的操作导致一个补码溢出——正溢出或负溢出。有符号数有意义。有溢出则置1，否则置0；","id":"6ee3da09-d92b-4539-9329-b1815e3f5f4e","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":16,"page_size":[595,841],"block_position":"16-2"},{"bbox":[86,157,345,169],"type":"text","angle":0,"index":3,"text":"PF:奇偶标志位。操作数 1 的个数为偶数置 1，否则置 0；","id":"0472b97c-1fed-40d6-b616-41bd08fb62a2","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":16,"page_size":[595,841],"block_position":"16-3"},{"bbox":[87,193,119,208],"type":"title","angle":0,"index":5,"text":"# 左移","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":16,"id":"ef213d24-c660-42f5-83b0-1439d567c821","page_size":[595,841],"block_position":"16-4"},{"bbox":[86,243,235,255],"type":"text","angle":0,"index":6,"text":"逻辑左移，高位移出，低位补0","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":16,"id":"eeff0870-7f34-4da2-8c0d-fa5a93fd368e","page_size":[595,841],"block_position":"16-5"},{"bbox":[86,259,205,270],"type":"text","angle":0,"index":7,"text":"左移不区分算术还是逻辑","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":16,"id":"7fd070d8-e388-40fb-8bb3-6a80fb56099d","page_size":[595,841],"block_position":"16-6"},{"bbox":[86,275,354,286],"type":"text","angle":0,"index":8,"text":"对于原码的算术左移，符号位不变，高位移出，低位补 0；","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":16,"id":"7e187730-ba33-4605-91ca-a4db6269ee2b","page_size":[595,841],"block_position":"16-7"},{"bbox":[87,290,282,301],"type":"text","angle":0,"index":9,"text":"当左移移出的数据位为“1”时，发生溢出。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":16,"id":"1dac2f10-fa42-43af-8516-d302a147b10c","page_size":[595,841],"block_position":"16-8"},{"bbox":[86,306,497,349],"type":"text","angle":0,"index":10,"text":"对于补码的算数左移。符号位不变，高位移出，低位补0；当左移移出的数据位正数为1负数为0时（符号位与被移出的位不同），发生溢出。一次。为保证不发生溢出，移位数据的最高有效位必须与符号位相同","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":16,"id":"a6a5a3c9-12b6-4468-8c89-a7e24c1a0089","page_size":[595,841],"block_position":"16-9"},{"bbox":[86,352,498,380],"type":"text","angle":0,"index":11,"text":"因此，在硬件补码实现算数左移时，直接将数据的最高有效位移入符号位，当不发生溢出时，不会改变机器数的符号","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":16,"id":"9ed3b95e-b316-4c3a-872d-a3e7957fe28e","page_size":[595,841],"block_position":"16-10"},{"bbox":[87,419,119,435],"type":"title","angle":0,"index":12,"text":"# 右移","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":16,"id":"9109470a-5763-46fb-9fe1-ca10b5b078fe","page_size":[595,841],"block_position":"16-11"},{"bbox":[86,470,235,481],"type":"text","angle":0,"index":13,"text":"逻辑右移，低位移出，高位补0","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":16,"id":"22f6fb57-7de7-4f9f-b221-9c15e4ef3b1b","page_size":[595,841],"block_position":"16-12"},{"bbox":[86,486,349,497],"type":"text","angle":0,"index":14,"text":"对于原码的算数右移，符号位不变，低位移出，高位补0","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":16,"id":"af4fa793-c07d-4b73-b138-9f7ab7484af4","page_size":[595,841],"block_position":"16-13"},{"bbox":[87,501,132,513],"type":"text","angle":0,"index":15,"text":"算数右移","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":16,"id":"50c04229-968c-45c5-ac66-126c0d5990eb","page_size":[595,841],"block_position":"16-14"},{"bbox":[86,517,320,528],"type":"text","angle":0,"index":16,"text":"对于补码，符号位不变，低位移出，高位补符号位","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":16,"id":"02aabac2-ab30-4a0d-b322-1a476b1e52f9","page_size":[595,841],"block_position":"16-15"},{"bbox":[86,533,297,544],"type":"text","angle":0,"index":17,"text":"对于原码，符号位不变，低位移出，高位补0","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":16,"id":"4dae426a-a7cd-4f4c-8467-ac572a967548","page_size":[595,841],"block_position":"16-16"},{"bbox":[86,579,343,591],"type":"text","angle":0,"index":18,"text":"C语言中一个特性就是支持按位进行布尔运算（位运算）","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":16,"id":"dd831dc7-cbe8-411c-89d5-f05fb408090d","page_size":[595,841],"block_position":"16-17"},{"bbox":[87,595,236,607],"type":"text","angle":0,"index":19,"text":"位运算的用法就是实现掩码运算","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":16,"id":"127d3263-29ad-498e-ab9e-a20f5bd4514d","page_size":[595,841],"block_position":"16-18"},{"bbox":[87,610,152,622],"type":"text","angle":0,"index":20,"text":"特定的位序列","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":16,"id":"64169c34-da4d-4de3-aa9d-dee9ea3dd57f","page_size":[595,841],"block_position":"16-19"},{"bbox":[87,626,281,638],"type":"text","angle":0,"index":21,"text":"比如说和0xFF，进行与运算，就是其本身","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":16,"id":"bf05f0c7-08dd-4332-b974-b2347e2f99f9","page_size":[595,841],"block_position":"16-20"},{"bbox":[86,676,243,693],"type":"title","angle":0,"index":22,"text":"# 5、机器数编码与真值","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":16,"id":"a26dc9ec-877d-4e10-a16e-9a1371e580fe","page_size":[595,841],"block_position":"16-21"},{"bbox":[86,731,412,743],"type":"text","angle":0,"index":23,"text":"为什么原码、补码、反码、移码 作为机器数的时候，符号位算作 $2 \\land \\mathsf { n ? }$","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":16,"id":"de5325aa-c42c-4b91-9cdd-fe764fa5e86c","page_size":[595,841],"block_position":"16-22"},{"bbox":[87,746,132,759],"type":"text","angle":0,"index":24,"text":"关于移码","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":16,"id":"79c35b89-20fa-4f71-918b-e3d7c642f216","page_size":[595,841],"block_position":"16-23"}],[{"bbox":[86,79,504,107],"type":"text","angle":0,"index":0,"text":"以 8 位数为例，总共能表示 256 个数，把这些数加上一个固定的值，从而形成新的码值（还是 8 位），这就是移码的定义。例如，可以把有符号数映射到 0 - 255 的段上。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":17,"id":"21857443-5f35-464e-8009-39eee01a1b4f","page_size":[595,841],"block_position":"17-0"},{"bbox":[86,110,504,139],"type":"text","angle":0,"index":1,"text":"移码的优势：原来的大小关系不变，且一一对应（没有两种表示的 0），很容易判断大小（如判断是最小值或者最大值）","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":17,"id":"8a6aa0ef-d08a-4e2f-89c7-1b8e75563d4f","page_size":[595,841],"block_position":"17-1"},{"bbox":[86,141,418,154],"type":"text","angle":0,"index":2,"text":"64 为机器上，不同的数据类型，所占的字节数不同，数值范围取值不同","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":17,"id":"46666c09-a4cb-46e4-8a90-5a4d3a04bc36","page_size":[595,841],"block_position":"17-2"},{"bbox":[86,157,383,170],"type":"text","angle":0,"index":3,"text":"Long 在 64 位机器上占 8 个字节 32 位机器上，long 占 4 个字节","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":17,"id":"702b5596-2a22-433d-8486-5fb123e42b46","page_size":[595,841],"block_position":"17-3"},{"bbox":[86,172,311,185],"type":"text","angle":0,"index":4,"text":"Unsigned关键字 数字只能为非负数，无符号数","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":17,"id":"4fb72390-a053-4215-b863-60d67beceff0","page_size":[595,841],"block_position":"17-4"},{"bbox":[83,186,595,491],"index":5,"angle":0,"type":"table_body","img_path":"/","id":"09dac327-ae41-4774-9eda-aa1355d078d7","color":{"line":"rgba(103, 194, 63, 1)","fill":"rgba(103, 194, 63, 1)"},"table_body":"
C data typeMinHexadecimalMaxHexadecimalBytes
[signed] char-2^70x802^7-10x7F1
Unsigned char02^8-10xFF1
Short-2^150x80002^15-10x7FFF2
Unsigned short02^16-10xFFFFFF2
Int-2^310x8(7个0)2^31-10x7(7个F)4
Unsigned int02^32-10x(8个F)4
Long-2^630x8(15个0)2^63-10x7(15个F)8
Unsigned long02^64-10x(16个F)8
Long long
Int32_t
Uint 32_t
Int 64_t
Uint64_t
Float
Double
Long double
","page_idx":17,"page_size":[595,841],"block_position":"17-5"},{"bbox":[88,506,462,696],"index":6,"angle":0,"type":"image","img_path":"/1a41381584803073f6746fb38769bedaa0499f690915a2f9652a86f1e498a1d5.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.6285714285714286,"page_idx":17,"id":"79bceb50-a19d-483c-a4cb-3c7e5f7f71c8","page_size":[595,841],"block_position":"17-6"},{"bbox":[86,711,312,724],"type":"text","angle":0,"index":7,"text":"假设一个整数的数据类型有w位，用向量x表示","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":17,"id":"12060da4-f4e1-4f2b-9121-41394034f2ab","page_size":[595,841],"block_position":"17-7"},{"bbox":[87,732,244,749],"type":"text","angle":0,"index":8,"text":"For vector $\\vec { x } = [ x _ { w - 1 } , x _ { w - 2 } , \\cdots , x _ { 0 } ]$","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":17,"id":"fc6abc11-aa62-4f3a-bd9e-2f887e183c02","page_size":[595,841],"block_position":"17-8"}],[{"bbox":[88,77,267,91],"type":"interline_equation","angle":0,"index":0,"text":"$$\nB 2 U _ {w} (\\vec {x}) \\doteq x _ {w - 1} \\cdot 2 ^ {w - 1} + x _ {w - 2} \\cdot 2 ^ {w - 2} \\dots\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":18,"id":"0b751e0e-4b88-421b-9322-b34a75627c10","page_size":[595,841],"block_position":"18-0"},{"bbox":[86,110,250,123],"type":"text","angle":0,"index":1,"text":"B2U 的意思是 binary to unsigned","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":18,"id":"7d4dc482-3211-409c-b6d7-14e2c2f8cd8a","page_size":[595,841],"block_position":"18-1"},{"bbox":[87,126,258,138],"type":"text","angle":0,"index":2,"text":"对于有符号数的编码采取补码的方式","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":18,"id":"340c4c53-0bfd-4374-804d-5795b9301702","page_size":[595,841],"block_position":"18-2"},{"bbox":[88,140,277,153],"type":"interline_equation","angle":0,"index":3,"text":"$$\nB 2 T _ {w} (\\vec {x}) \\dot {=} x _ {w - 1} \\cdot - 2 ^ {w - 1} + x _ {w - 2} \\cdot 2 ^ {w - 2} \\dots\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":18,"id":"e02fb4e1-2b7a-44c2-80c6-d88d16b3995e","page_size":[595,841],"block_position":"18-3"},{"bbox":[86,172,342,185],"type":"text","angle":0,"index":4,"text":"这里最高位为1时表示负数，最高位为0时表示非负数","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":18,"id":"d8d4008a-fa1b-4d96-93fe-ce43487d6ab3","page_size":[595,841],"block_position":"18-4"},{"bbox":[87,188,185,200],"type":"text","angle":0,"index":5,"text":"最高位也叫做符号位","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":18,"id":"5e1ca648-26be-4902-9c73-4102e1f107ad","page_size":[595,841],"block_position":"18-5"},{"bbox":[86,203,394,216],"type":"text","angle":0,"index":6,"text":"关于符号位，需要理解负权重的概念，而不能简单的当成一个负号","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":18,"id":"61ef61c0-04b4-44bd-8a2c-91d37f71be67","page_size":[595,841],"block_position":"18-6"},{"bbox":[87,219,310,232],"type":"text","angle":0,"index":7,"text":"记住对于无符号数，最高位的1表示的不是权重","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":18,"id":"79221144-9232-4752-b4fd-105f2580be88","page_size":[595,841],"block_position":"18-7"},{"bbox":[87,235,182,248],"type":"text","angle":0,"index":8,"text":"也就是说， $- 2 \\land 3 = - 8$","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":18,"id":"40d00b17-e026-4397-b310-a755ebad3c97","page_size":[595,841],"block_position":"18-8"},{"bbox":[87,250,299,263],"type":"text","angle":0,"index":9,"text":"-1在有符号数全为1，但在无符号数为最大值","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":18,"id":"c192cfe3-cc34-4c1c-9dfd-d39d665ab782","page_size":[595,841],"block_position":"18-9"},{"bbox":[86,266,335,280],"type":"text","angle":0,"index":10,"text":"如果在计算的时候一个是有符号数，一个是无符号数，","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":18,"id":"1f52824d-7b55-4b93-8c5d-b0c5634db230","page_size":[595,841],"block_position":"18-10"},{"bbox":[86,281,287,294],"type":"text","angle":0,"index":11,"text":"C语言会隐式地将有符号数转换为无符号数","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":18,"id":"4b195ac0-cd10-4051-b43e-cc519cbd7c54","page_size":[595,841],"block_position":"18-11"},{"bbox":[86,346,307,365],"type":"title","angle":0,"index":12,"text":"# 6、溢出与取模运算的数学关系","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":18,"id":"27edf8b0-b912-4efc-9783-4532b390c9b6","page_size":[595,841],"block_position":"18-12"},{"bbox":[86,401,331,415],"type":"text","angle":0,"index":13,"text":"设我们有两个 w 位无符号整数 a 和 b，其和为 S，即","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":18,"id":"2f1819af-ba7b-4963-8744-bc8c2c08e35a","page_size":[595,841],"block_position":"18-13"},{"bbox":[87,418,132,429],"type":"interline_equation","angle":0,"index":14,"text":"$$\nS = a + b\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":18,"id":"dc41792d-f381-47a6-a609-8896b21795f3","page_size":[595,841],"block_position":"18-14"},{"bbox":[86,433,504,461],"type":"text","angle":0,"index":15,"text":"由于二进制表示限定为 w 位，系统只能表示 0 到 2w−1 内的数。因此，任何 S 超出这一范围的部分都会被丢弃。用数学语言描述就是：实际存储的结果 R 为","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":18,"id":"99630ce3-5a95-4ee5-b561-314a5ed9fab8","page_size":[595,841],"block_position":"18-15"},{"bbox":[87,465,158,476],"type":"interline_equation","angle":0,"index":16,"text":"$$\nR = S \\bmod 2 ^ {\\wedge} w\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":18,"id":"b0a074bc-8f69-4277-8886-e20811afe942","page_size":[595,841],"block_position":"18-16"},{"bbox":[86,480,504,507],"type":"text","angle":0,"index":17,"text":"也就是说，在加法运算中，丢弃溢出位的操作等同于计算 S 对 $_ { 2 } \\wedge _ { \\mathsf { W } }$ 取模。这正是计算机硬件中处理无符号整数溢出的方式","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":18,"id":"6c7a362b-aca2-4595-97ab-0981e7dd1e10","page_size":[595,841],"block_position":"18-17"},{"bbox":[86,511,504,539],"type":"text","angle":0,"index":18,"text":"很多人可能会疑惑，既然阶码字段有 8 位，那么为什么不选择 $2 ^ { \\wedge } 7 = 1 2 8$ 作为偏移量？原因在于：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":18,"id":"5b6e54c0-4f1e-46eb-82a7-bbf5cae4a934","page_size":[595,841],"block_position":"18-18"},{"bbox":[104,542,503,585],"type":"text","angle":0,"index":19,"text":"对称分布的需求：以 127 为偏移量，可以使得存储阶码为 127 时实际指数为 0。这种设计使得正指数和负指数在规格化数中分布较为对称，便于硬件实现和算法设计。","id":"3d74eee5-a558-45b9-8373-8e1be2672904","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":18,"page_size":[595,841],"block_position":"18-19"},{"bbox":[104,589,504,631],"type":"text","angle":0,"index":20,"text":"历史约定与标准化：IEEE754 标准规定的偏移量就是 127，它的选择经过广泛验证并且与现有的硬件架构和软件设计高度契合。采用 127 而非 128 使得编码与译码的过程更加简便，同时避免了 0 不对称的问题。","id":"926b08cc-230a-4e1d-adc0-c914248ee45c","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":18,"page_size":[595,841],"block_position":"18-20"},{"bbox":[104,636,504,693],"type":"text","angle":0,"index":21,"text":"具体来说，设若采用 128 作为偏移量，则当存储阶码 E 为 128 时，实际指数为0；但这会使得整个指数范围整体右移，从而使得可表示的最小负指数与最大正指数的数量不均衡，不符合 IEEE754 对于规格化数的要求。选择 127 则能使得 0 成为一个中心值，既便于表达接近1 的数值，又能合理覆盖较大范围的指数。","id":"d4413f69-9f78-4714-92f3-c03bebee832c","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":18,"page_size":[595,841],"block_position":"18-21"},{"bbox":[86,698,242,710],"type":"title","angle":0,"index":23,"text":"# 5.3. 关于阶码真值为 -127 和 128","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":18,"id":"dbb9824b-0287-4e0e-8c1d-4ee5728fb657","page_size":[595,841],"block_position":"18-22"},{"bbox":[86,714,498,742],"type":"text","angle":0,"index":24,"text":"一般我们正常探讨的阶码区间是 $- 1 2 6 \\mathsf { D } \\sim 1 2 7 \\mathsf { D }$ ，而真值 -127D 的阶码为 0000 0000B，真值 128D 的阶码为 1111 1111B。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":18,"id":"3e62b43b-45c9-489c-bebe-818297e75645","page_size":[595,841],"block_position":"18-23"}],[{"bbox":[86,79,196,91],"type":"title","angle":0,"index":0,"text":"# 5.3.1. 阶码真值为 -127","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":19,"id":"3dc83d81-8db1-4355-ae87-e259c3bcd8ed","page_size":[595,841],"block_position":"19-0"},{"bbox":[86,95,498,121],"type":"text","angle":0,"index":1,"text":"当阶码全为 0 ，尾数不全为 0，表示 非规格化小数 ，用来表示比最小绝对值还要小的数，即","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":19,"id":"2ec96be0-dc2f-461e-9f81-ee320fa22ba6","page_size":[595,841],"block_position":"19-1"},{"bbox":[86,125,260,138],"type":"text","angle":0,"index":2,"text":"尾数码 隐含的最高位不是 1，而是 0；","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":19,"id":"7f0b254c-2852-48ed-be33-1a89686cc7a6","page_size":[595,841],"block_position":"19-2"},{"bbox":[86,142,250,154],"type":"text","angle":0,"index":3,"text":"阶码真值 固定为 -126，而非 -127；","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":19,"id":"540b98c4-894a-4418-8f98-b138bc0230b8","page_size":[595,841],"block_position":"19-3"},{"bbox":[86,157,301,169],"type":"text","angle":0,"index":4,"text":"当阶码全为 0 ，尾数全为 0，表示 真值 $+ / - 0$","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":19,"id":"1ed93c99-8155-4d7b-952e-e5b4df26ed01","page_size":[595,841],"block_position":"19-4"},{"bbox":[86,172,193,185],"type":"title","angle":0,"index":5,"text":"# 5.3.2. 阶码真值为 128","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":19,"id":"797262d5-82a0-408c-be0a-10fd42d5a6b1","page_size":[595,841],"block_position":"19-5"},{"bbox":[105,188,364,200],"type":"text","angle":0,"index":6,"text":"1. 当阶码全为 1 ，尾数全为 0，表示 正负无穷大 +/- ∞","id":"bd358104-0360-48d9-acf1-0a684ca0673e","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":19,"page_size":[595,841],"block_position":"19-6"},{"bbox":[104,203,433,216],"type":"text","angle":0,"index":7,"text":"2. 当阶码全为 1 ，尾数不全为 0，表示非数值 NaN（Not a Number）","id":"a05eadd7-3523-49a1-a898-7c3bbeb003b5","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":19,"page_size":[595,841],"block_position":"19-7"},{"bbox":[86,219,285,232],"type":"text","angle":0,"index":9,"text":"如 0/0， $\\infty - \\infty$ 等非法运算的结果即为 NaN","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":19,"id":"1e41eae9-9547-47c7-b04b-f5f61c045577","page_size":[595,841],"block_position":"19-8"},{"bbox":[86,234,332,248],"type":"text","angle":0,"index":10,"text":"汉字输入法程序：将汉字输入计算机转换成汉字内码","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":19,"id":"b948bd10-07b9-4758-8d56-76d8f47aa279","page_size":[595,841],"block_position":"19-9"},{"bbox":[87,250,481,263],"type":"text","angle":0,"index":11,"text":"1、输入—汉字输入码，也称作外码， 由西文字符编码而成（拼音编码、字形编码等）","id":"ca9eb417-4e5b-4943-878c-563f7dd2847d","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":19,"page_size":[595,841],"block_position":"19-10"},{"bbox":[86,265,508,294],"type":"text","angle":0,"index":12,"text":"2、存储、交换和检索—内码 ，两个字节表示。汉字内码在计算机中是唯一的。（区位码、国标码、汉字内码2个字节最高位均为“1”）","id":"660c1915-377b-43ce-827d-8024ec0fdd61","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":19,"page_size":[595,841],"block_position":"19-11"},{"bbox":[86,296,502,325],"type":"text","angle":0,"index":13,"text":"3、交换—交换码，是指不同的具有汉字处理功能的计算机系统之间在交换汉字信息所用的代码标准。","id":"44de7722-535d-4795-850c-47823ba1beed","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":19,"page_size":[595,841],"block_position":"19-12"},{"bbox":[86,328,386,341],"type":"text","angle":0,"index":14,"text":"4、输出——字形码 点阵表示法 字模码：用于汉字的显示和打印","id":"eddca3ab-ab56-4c85-981b-ab9ea6d00a37","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":19,"page_size":[595,841],"block_position":"19-13"},{"bbox":[104,343,433,356],"type":"text","angle":0,"index":16,"text":"汉字字库——— 所有汉字的字模点阵代码按顺序集中存放根据内码查表","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":19,"id":"deefb166-0931-4736-9983-5ba77de5901d","page_size":[595,841],"block_position":"19-14"},{"bbox":[104,359,359,372],"type":"text","angle":0,"index":17,"text":"字形检索程序：将汉字的机内代码转化为汉字的字形码","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":19,"id":"a98008c2-1649-484c-af5a-c7ede1df5443","page_size":[595,841],"block_position":"19-15"},{"bbox":[87,390,142,402],"type":"title","angle":0,"index":18,"text":"# 整数的运算","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":19,"id":"3e6ce85e-a652-486e-8a55-c9e19fd10a35","page_size":[595,841],"block_position":"19-16"},{"bbox":[87,406,149,419],"type":"text","angle":0,"index":19,"text":"计算值： $x { + } y$","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":19,"id":"2f161afc-ed4a-41f3-9675-d2710c8a709a","page_size":[595,841],"block_position":"19-17"},{"bbox":[86,422,258,434],"type":"text","angle":0,"index":20,"text":"实际值：计算机中实际上保存的结果","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":19,"id":"17fafaf5-221e-475b-ad97-88c75c08d468","page_size":[595,841],"block_position":"19-18"},{"bbox":[86,453,487,486],"type":"text","angle":0,"index":21,"text":"${ } _ { w y } ^ { w }$ $w$","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":19,"id":"590f247d-0a86-434f-aeed-7b5954b9c979","page_size":[595,841],"block_position":"19-19"},{"bbox":[86,499,336,513],"type":"text","angle":0,"index":22,"text":"溢出时，计算值 $\\mathop { }$ 实际值 $\\pm 2 \\land \\_$ （这里相当于是原码！）","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":19,"id":"1c18dacb-0a02-42aa-a5e6-f36bac5da790","page_size":[595,841],"block_position":"19-20"},{"bbox":[87,515,247,528],"type":"text","angle":0,"index":23,"text":"如何判定运算结果是否发生了溢出","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":19,"id":"a95ebe9b-3f53-4d18-ad51-c0535b632fb8","page_size":[595,841],"block_position":"19-21"},{"bbox":[86,533,263,655],"index":24,"angle":0,"type":"algorithm","text":"Int uadd.ok(unsigned x,unsigned y) \n{ unsigned sum $\\equiv$ x+y; If (sum $\\rightharpoondown$ x) \nReturn 1; else return 0; \n}","id":"6a65322b-3206-4293-9eba-2ecae163b10c","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":19,"page_size":[595,841],"block_position":"19-22"},{"bbox":[87,661,142,673],"type":"title","angle":0,"index":25,"text":"# 有符号整数","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":19,"id":"d1aca1bb-b0a0-4a9d-b18f-6c753cd2768e","page_size":[595,841],"block_position":"19-23"},{"bbox":[86,677,449,705],"type":"text","angle":0,"index":26,"text":"为了避免数据大小的扩张，最终结果将截断为w位；即实际上数字只占w-1位两个异号的数字肯定不会溢出","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":19,"id":"7ca6294a-940c-4055-83f5-9e73e36b71ba","page_size":[595,841],"block_position":"19-24"},{"bbox":[87,708,205,720],"type":"text","angle":0,"index":27,"text":"两个同号的才有可能溢出","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":19,"id":"1aa08c43-18fc-4ecd-9c0e-58f287f4233e","page_size":[595,841],"block_position":"19-25"}],[{"bbox":[88,75,406,263],"index":0,"angle":0,"type":"image","img_path":"/3390337029ead83d93ec3a52189a1c769867939c392af0161ac824c78e907384.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.534453781512605,"page_idx":20,"id":"581a2b04-fea0-4841-af79-ef73a17074d8","page_size":[595,841],"block_position":"20-0"},{"bbox":[88,265,148,279],"type":"text","angle":0,"index":1,"text":"正溢出/上溢","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":20,"id":"b1d87059-31ba-4b20-b0f2-6b2a2e3482f2","page_size":[595,841],"block_position":"20-1"},{"bbox":[88,280,147,294],"type":"text","angle":0,"index":2,"text":"负溢出/下溢","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":20,"id":"d6b84f5e-8aed-424e-8b4d-8089efe64f91","page_size":[595,841],"block_position":"20-2"},{"bbox":[88,296,185,310],"type":"text","angle":0,"index":3,"text":"减法转换成加法来做","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":20,"id":"11f23155-9e45-4896-8644-faca266a546e","page_size":[595,841],"block_position":"20-3"},{"bbox":[88,327,199,342],"index":4,"angle":0,"type":"algorithm","text":"$x - y = x + (-y) = x + (-y + 1)$","id":"346e178b-67a3-422a-b9a7-a3e63d73945f","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":20,"page_size":[595,841],"block_position":"20-4"},{"bbox":[88,342,403,507],"index":5,"angle":0,"type":"image","img_path":"/28aaa54c06c24037d9b1537962c7c3302913f8ecd66b2e073b85e38b433cb4c3.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.5294117647058824,"page_idx":20,"id":"57e83ebd-d570-4c7b-b729-991c98c4df44","page_size":[595,841],"block_position":"20-5"},{"bbox":[88,577,455,626],"type":"interline_equation","angle":0,"index":6,"text":"$$\nF o r x a n d y, x + \\mathbf {\\Lambda} _ {w} ^ {t} y = \\left\\{ \\begin{array}{l l} x + y - 2 ^ {w - 1} - 2 ^ {w - 1} = x + y - 2 ^ {w}, 2 ^ {w - 1} \\leq x + y, \\text {正 溢 出} \\\\ x + y, - 2 ^ {w - 1} \\leq x + y < 2 ^ {w - 1} \\\\ x + y + 2 ^ {w}, x + y < - 2 ^ {w - 1}, \\text {负 溢 出} \\end{array} \\right.\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":20,"id":"0d9aea1e-c66f-4e81-ae2f-304974508df6","page_size":[595,841],"block_position":"20-6"},{"bbox":[86,640,505,684],"type":"text","angle":0,"index":7,"text":"对于正溢出，正溢出实际上是让符号位从 1变成0，计算值 $\\equiv$ 实际值 $+ 2 \\land _ { \\mathsf { W } , }$ ,它没被截断，最高位由0变成了1，这两个数本来就没有- $\\mathbf { \\mathcal { Z } ^ { \\wedge } }$ （w-1)的权重结果有了，那么实际值就要加上2^（w-1），又因为补码的定义，又得减去 $2 \\setminus ( \\mathsf { w } - 1 )$ ","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":20,"id":"4f650390-2fb5-4bdc-851e-691ce8bc858c","page_size":[595,841],"block_position":"20-7"},{"bbox":[86,687,505,715],"type":"text","angle":0,"index":8,"text":"对于负溢出，计算值 $=$ 实际值- ${ \\mathcal { 2 } } ^ { \\wedge } \\mathsf { w }$ ，这里因为原来两个最高位符号位从 1变成0，两个数本来有- ${ \\mathcal { 2 } } ^ { \\wedge } \\mathsf { w }$ 的权重结果没了。那么实际值就要减去个- $. 2 \\land _ { \\mathsf { W } }$ ","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":20,"id":"fcbaa8ad-28da-4336-8d3a-8d91be510fd3","page_size":[595,841],"block_position":"20-8"},{"bbox":[87,717,158,730],"type":"text","angle":0,"index":9,"text":"如何判断溢出？","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":20,"id":"eea47d05-f517-4818-905f-0123dc177abd","page_size":[595,841],"block_position":"20-9"},{"bbox":[86,733,268,746],"type":"text","angle":0,"index":10,"text":"两个正数相加，得到结果为负，正溢出","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":20,"id":"03312a55-791c-4ae0-8145-9b5c2e36a1e8","page_size":[595,841],"block_position":"20-10"},{"bbox":[87,749,264,761],"type":"text","angle":0,"index":11,"text":"两个负数相加，得到结果 $\\geqslant 0$ ，负溢出","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":20,"id":"be12bc84-1002-40db-b082-162f4615665b","page_size":[595,841],"block_position":"20-11"}],[{"bbox":[86,79,132,91],"type":"text","angle":0,"index":0,"text":"加法逆元","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":21,"id":"57e4cc71-025a-412b-8150-0145bf3ebf49","page_size":[595,841],"block_position":"21-0"},{"bbox":[88,93,260,106],"type":"interline_equation","angle":0,"index":1,"text":"$$\nF o r x, 0 \\leq x < 2 ^ {w}, x + x ^ {\\prime} = x ^ {\\prime} + x = 0\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":21,"id":"89736407-94a6-49db-9768-6a2af9a9c75c","page_size":[595,841],"block_position":"21-1"},{"bbox":[86,126,135,139],"type":"interline_equation","angle":0,"index":2,"text":"$$\ny - x - > y + x ^ {\\prime}.\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":21,"id":"568c3d05-fee3-436e-ba51-9a84dd594072","page_size":[595,841],"block_position":"21-2"},{"bbox":[86,141,252,154],"type":"text","angle":0,"index":3,"text":"对于无符号整型来说， $\\mathsf { x } + \\mathsf { x } ^ { \\prime } { = } 2 \\mathsf { \\Lambda } \\mathsf { w } { = } 0$","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":21,"id":"7934346f-3a28-4b18-bf3e-bf24fef67390","page_size":[595,841],"block_position":"21-3"},{"bbox":[88,157,182,190],"type":"interline_equation","angle":0,"index":4,"text":"$$\nx ^ {\\prime} = \\left\\{ \\begin{array}{l} x, x = 0 \\\\ 2 ^ {w} - x, x > 0 \\end{array} \\right.\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":21,"id":"12c847aa-eba4-4171-9b75-885c4c43f100","page_size":[595,841],"block_position":"21-4"},{"bbox":[86,203,279,216],"type":"text","angle":0,"index":5,"text":"对于补码表示的有符号数的逆元比较简单","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":21,"id":"42c8d96d-4765-4012-b69f-51250a00658f","page_size":[595,841],"block_position":"21-5"},{"bbox":[88,219,208,253],"type":"interline_equation","angle":0,"index":6,"text":"$$\nx ^ {\\prime} = \\left\\{ \\begin{array}{l} - x, x > T M i n _ {w} \\\\ T M i n _ {w}, x = T M i n _ {w} \\end{array} \\right.\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":21,"id":"01f86ba1-3252-49d0-ae84-4de163607c76","page_size":[595,841],"block_position":"21-6"},{"bbox":[86,265,269,279],"type":"text","angle":0,"index":7,"text":"由于补码最大值比最小值的绝对值要小","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":21,"id":"9dfc395b-5eba-48c0-b5db-2200b728b5ca","page_size":[595,841],"block_position":"21-7"},{"bbox":[87,281,157,293],"type":"text","angle":0,"index":8,"text":"即 $0 1 1 1 < 1 0 0 0$","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":21,"id":"e9de86d9-6b90-46b9-895a-8069bcb3e35e","page_size":[595,841],"block_position":"21-8"},{"bbox":[86,296,307,310],"type":"text","angle":0,"index":9,"text":"关于 最小值的逆元要通过负溢出 的方法来实现","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":21,"id":"44b9e3d6-fde2-4fd2-9c5a-a1e78c74b5d2","page_size":[595,841],"block_position":"21-9"},{"bbox":[88,312,101,324],"type":"text","angle":0,"index":10,"text":"即","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":21,"id":"e2103857-007b-4799-b76c-32707364f90b","page_size":[595,841],"block_position":"21-10"},{"bbox":[88,327,221,340],"type":"interline_equation","angle":0,"index":11,"text":"$$\nT \\min _ {w} + T \\min _ {w} = - 2 ^ {w} = 0\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":21,"id":"31ee60f9-15ef-451f-8b13-caad2565e94d","page_size":[595,841],"block_position":"21-11"},{"bbox":[86,359,490,388],"type":"text","angle":0,"index":12,"text":"X、y 都为 w 位，乘积结果可能为 2w 位，c 语言定义无符号数乘法所产生的结果是 w 位因此，z=xy mod $_ { 2 } \\wedge _ { \\mathsf { W } }$","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":21,"id":"db5a5da4-244e-49a7-8b72-b50e9a97ff09","page_size":[595,841],"block_position":"21-12"},{"bbox":[87,391,288,404],"type":"text","angle":0,"index":13,"text":"对于有符号数，我们有 z=U2T(xymod2^w)","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":21,"id":"6aafdc8f-c035-4aad-9a90-8778132117a8","page_size":[595,841],"block_position":"21-13"},{"bbox":[86,406,501,434],"type":"text","angle":0,"index":14,"text":"X’y’ mod 2^w=(xy) mod ${ 2 } ^ { \\wedge } \\mathsf { w } .$ .即有符号整数和无符号整数高位截断后结果的位级表示相同整数的乘法往往利用移位运算（拆解成与多个 $2 ^ { \\land } \\mathsf { k }$ 相乘再相加减）","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":21,"id":"bddba71f-ae63-4c20-aa17-331e8bfbb3d4","page_size":[595,841],"block_position":"21-14"},{"bbox":[87,437,301,450],"type":"text","angle":0,"index":15,"text":"整数的除法遇到除不尽的情况，总是向0舍入","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":21,"id":"28053928-95a0-4a72-afa5-8c404a3b8706","page_size":[595,841],"block_position":"21-15"},{"bbox":[87,453,420,465],"type":"text","angle":0,"index":16,"text":"但是，移位的时候会导致向下舍入。为此，我们要在移位之前加入偏置。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":21,"id":"f1c97978-c7a1-4302-af83-4d4548f9cc7a","page_size":[595,841],"block_position":"21-16"},{"bbox":[86,468,464,481],"type":"text","angle":0,"index":17,"text":"即如果要右移 k 位，在低 k 位加上 $2 \\land k - 1$ , 向 $k { + 1 }$ 产生一个进位，实现了向 0 取整。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":21,"id":"4d4400ac-f47e-4957-9a7a-6ff438666984","page_size":[595,841],"block_position":"21-17"},{"bbox":[87,484,206,497],"type":"text","angle":0,"index":18,"text":"即用整除实现了向上取整","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":21,"id":"256f085f-7f4e-4a56-b2fa-e6920bb26cd0","page_size":[595,841],"block_position":"21-18"},{"bbox":[87,499,136,512],"type":"text","angle":0,"index":19,"text":"举个例子：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":21,"id":"04713107-eec1-4322-825f-22f41af0aef3","page_size":[595,841],"block_position":"21-19"},{"bbox":[88,515,109,527],"type":"interline_equation","angle":0,"index":20,"text":"$$\nK = 0\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":21,"id":"57c82174-688d-4807-8204-ba1fed9c9361","page_size":[595,841],"block_position":"21-20"},{"bbox":[88,530,223,542],"type":"interline_equation","angle":0,"index":21,"text":"$$\n1 1 0 0 1 1 1 1 1 1 0 0 1 1 0 0 - 1 2 3 4 0\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":21,"id":"ad62f10c-d3e3-4d9c-a6e0-b15e19c03a29","page_size":[595,841],"block_position":"21-21"},{"bbox":[87,546,343,560],"type":"interline_equation","angle":0,"index":22,"text":"$$\nK = 4 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 - 7 7 2 \\text {而} 1 2 3 4 0 / 2 ^ {\\wedge} k = - 7 7 1. 2 5;\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":21,"id":"adc06bd8-737e-47fb-adc9-3b285f032c27","page_size":[595,841],"block_position":"21-22"},{"bbox":[86,561,439,575],"type":"text","angle":0,"index":23,"text":"加上偏置，1100111111011011，右移四位有 1111110011111101,即-771。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":21,"id":"fcb2c5ca-f3ee-4625-b625-0abb141e2f83","page_size":[595,841],"block_position":"21-23"},{"bbox":[110,576,227,589],"type":"text","angle":0,"index":24,"text":"division by a power of 2","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":21,"id":"dd779831-9ba9-426c-afab-9756781774e3","page_size":[595,841],"block_position":"21-24"},{"bbox":[88,593,248,608],"type":"interline_equation","angle":0,"index":25,"text":"$$\n(x < 0? x + (1 < < k) - 1: x) > > K\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":21,"id":"e53e86e0-38b1-4078-8992-fa3f173e2e7f","page_size":[595,841],"block_position":"21-25"},{"bbox":[86,624,268,653],"type":"text","angle":0,"index":26,"text":"但是，除以2不能推广到除以任意整数浮点数","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":21,"id":"9bf39ba2-7392-46f3-add1-f35b138a6819","page_size":[595,841],"block_position":"21-26"}],[{"bbox":[82,130,511,257],"index":0,"angle":0,"type":"table_body","img_path":"/","id":"36a4c067-4648-4a35-b71a-171d050e80e2","color":{"line":"rgba(103, 194, 63, 1)","fill":"rgba(103, 194, 63, 1)"},"table_body":"
类型总 位 数尾数阶码真值计算
短 实 数32248\\( N = {\\left( -1\\right) }^{M} \\times \\left( {{1.5}{M}_{1}M{2\\ldots }{M}_{n}}\\right) \\times {2}^{E - {127}} \\)
长 实 数645311\\( N = {\\left( -1\\right) }^{M} \\times \\left( {{1.5}{M}_{1}M{2\\ldots }{M}_{n}}\\right) \\times {2}^{E - {1023}} \\)
临 时 实数806515
","page_idx":22,"page_size":[595,841],"block_position":"22-0"},{"bbox":[89,309,530,533],"index":1,"angle":0,"type":"image","img_path":"/3caf6d389607f56b60584b40fcc4fecb687f2270ed1d9b484c2da9a93b7e2872.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.7411764705882353,"page_idx":22,"id":"7fcab1f8-1677-4145-b596-38366d19a812","page_size":[595,841],"block_position":"22-1"},{"bbox":[88,546,169,560],"type":"text","angle":0,"index":2,"text":"符号位 阶码 尾数","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":22,"id":"b51277ff-80b1-40d1-948d-56da5cc4d704","page_size":[595,841],"block_position":"22-2"},{"bbox":[88,613,176,629],"type":"title","angle":0,"index":3,"text":"# 7、IEEE754","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":22,"id":"0e064bc5-5764-4feb-97c5-58d179075564","page_size":[595,841],"block_position":"22-3"},{"bbox":[88,666,141,679],"type":"text","angle":0,"index":4,"text":"Float32bit","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":22,"id":"bd433287-7405-47e8-8a30-f92da96422a4","page_size":[595,841],"block_position":"22-4"},{"bbox":[88,682,151,695],"type":"text","angle":0,"index":5,"text":"Double64bit","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":22,"id":"d0d381b8-4b6f-46df-9ea5-04f1fb793598","page_size":[595,841],"block_position":"22-5"}],[{"bbox":[105,177,332,195],"type":"text","angle":0,"index":1,"text":"我梦里的财富：+302657264526￥","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":23,"id":"24bed605-51f9-4bc8-800b-4698c3a94780","page_size":[595,841],"block_position":"23-0"},{"bbox":[522,153,548,168],"type":"text","angle":0,"index":3,"text":"阶码","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":23,"id":"a7f399a5-5942-4557-abe7-c47b1c329267","page_size":[595,841],"block_position":"23-1"},{"bbox":[351,200,381,218],"type":"text","angle":0,"index":4,"text":"y","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":23,"id":"25549c5e-c001-457a-936d-4cfcd8d8bb11","page_size":[595,841],"block_position":"23-2"},{"bbox":[394,200,419,215],"type":"text","angle":0,"index":5,"text":"符号","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":23,"id":"1b5a6c10-c4a6-4d96-a9c6-1fe0575c7a4b","page_size":[595,841],"block_position":"23-3"},{"bbox":[452,200,478,214],"type":"text","angle":0,"index":6,"text":"尾数","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":23,"id":"1e294c89-cdc2-4737-bc63-c2572c2295c5","page_size":[595,841],"block_position":"23-4"},{"bbox":[100,248,233,262],"type":"text","angle":0,"index":8,"text":"符号：决定数值的正负性","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":23,"id":"37c38dd0-3df1-47cc-a4b5-019471df5f94","page_size":[595,841],"block_position":"23-5"},{"bbox":[101,263,373,276],"type":"text","angle":0,"index":9,"text":"尾数：影响数值的精度。尾数的位数越多，精度越高","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":23,"id":"00bbb036-fb7d-481b-935f-cb76cee1601a","page_size":[595,841],"block_position":"23-6"},{"bbox":[101,277,255,290],"type":"text","angle":0,"index":10,"text":"阶码：反映小数点的实际位置","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":23,"id":"0d97c694-848b-4355-acee-a9175a24e576","page_size":[595,841],"block_position":"23-7"},{"bbox":[101,291,258,305],"type":"text","angle":0,"index":11,"text":"基数：K进制通常默认基数为K","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":23,"id":"beb5f436-e07b-4fb4-99a2-7c42c9411a5b","page_size":[595,841],"block_position":"23-8"},{"bbox":[101,306,379,319],"type":"text","angle":0,"index":12,"text":"规格化：确保尾数的最高位非0数位刚好在小数点之前","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":23,"id":"c6a0b179-3de3-43dc-ba19-68de8dee0c9d","page_size":[595,841],"block_position":"23-9"},{"bbox":[88,327,153,341],"type":"text","angle":0,"index":13,"text":"阶码确定范围","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":23,"id":"6e36678a-cdf0-4874-a086-357b1831f452","page_size":[595,841],"block_position":"23-10"},{"bbox":[88,343,153,356],"type":"text","angle":0,"index":14,"text":"尾数影响精度","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":23,"id":"2fcfc5eb-e628-4f2f-99a2-8127a05efbb9","page_size":[595,841],"block_position":"23-11"},{"bbox":[88,370,419,457],"index":15,"angle":0,"type":"image","img_path":"/79f181b47490d71aa33641df7b5c4485f39a62657deff27543ee4ad27dd2b53e.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.5563025210084034,"page_idx":23,"id":"656e3696-b5d6-4c9b-9d2d-0944d4324a79","page_size":[595,841],"block_position":"23-12"},{"bbox":[88,513,183,528],"type":"interline_equation","angle":0,"index":16,"text":"$$\nV = (- 1) ^ {S} \\times M \\times 2 ^ {E}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":23,"id":"4a32a3f6-fb22-4749-93e0-4cefc1c248ec","page_size":[595,841],"block_position":"23-13"},{"bbox":[86,546,207,560],"type":"text","angle":0,"index":17,"text":"尾数用原码定点小数表示","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":23,"id":"7df4b3a3-96fe-4c64-a661-4cbd4fac4db8","page_size":[595,841],"block_position":"23-14"},{"bbox":[86,561,236,575],"type":"text","angle":0,"index":18,"text":"阶码用移码，规定偏置值为127","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":23,"id":"62193979-4d70-4580-8922-7611bddc517b","page_size":[595,841],"block_position":"23-15"},{"bbox":[86,577,473,591],"type":"text","angle":0,"index":19,"text":"$\\mathsf { S } { = } 0 _ { - }$ ,正数； $s { = } 1$ 负数；M 为小数部分，尾数部分，frac。E 为指数部分，阶码，exp。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":23,"id":"0a48c08d-43af-4cf9-ad86-2181da586d29","page_size":[595,841],"block_position":"23-16"},{"bbox":[87,593,345,606],"type":"text","angle":0,"index":20,"text":"Emin=1.emax $= 2 5 4$ ，对半分，所以要减去 $2 5 4 / 2 { = } 1 2 7$ ；","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":23,"id":"d99fcfae-0eaa-4641-975c-3e4ba07e4aa9","page_size":[595,841],"block_position":"23-17"},{"bbox":[88,608,357,621],"type":"text","angle":0,"index":21,"text":"第一位总是1，因此没必要显示出来，所以尾数部分要加1","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":23,"id":"9baada0e-04ad-4ed8-946d-9f590bbf58cc","page_size":[595,841],"block_position":"23-18"},{"bbox":[89,623,291,721],"index":22,"angle":0,"type":"image","img_path":"/e50dc1d79cdffb23905de3ed3b7c0658a8254a152177a16d4d0e0392f652513b.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.33949579831932775,"page_idx":23,"id":"29e177b1-d553-4811-840f-5d7f779197aa","page_size":[595,841],"block_position":"23-19"}],[{"bbox":[88,79,214,91],"type":"header","angle":0,"index":-99999,"text":"单精度记得减去 127e-bias","color":{"line":"rgba(164, 164, 164, 1)","fill":"rgba(164, 164, 164, 1)"},"page_idx":24,"is_discarded":true,"id":"c0a92cd8-4796-4f0e-94ab-f37be372abf1","page_size":[595,841],"block_position":"24-0"},{"bbox":[88,121,405,280],"index":1,"angle":0,"type":"image","img_path":"/bd23b66fa0ae5d5aa0cccc7dda113d13d37aca406c550155e1c82dd36201b0e2.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.5327731092436975,"page_idx":24,"id":"ca9906f1-c92a-4eff-bc19-1e5bec171260","page_size":[595,841],"block_position":"24-1"},{"bbox":[110,285,340,300],"type":"text","angle":0,"index":2,"text":"如何将十进制真值转换为偏置值为M的移码？","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":24,"id":"d91a8166-6699-4f3c-b7b3-24e0af07bfc8","page_size":[595,841],"block_position":"24-2"},{"bbox":[111,313,244,327],"type":"text","angle":0,"index":3,"text":"","id":"187a40f3-cf78-4b83-8441-be94a93b597b","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":24,"page_size":[595,841],"block_position":"24-3"},{"bbox":[111,327,325,341],"type":"text","angle":0,"index":4,"text":"②按“无符号整数”规则转换为指定位数","id":"5b365da3-d707-4491-a418-414597f03634","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":24,"page_size":[595,841],"block_position":"24-4"},{"bbox":[87,375,238,387],"type":"title","angle":0,"index":6,"text":"# 小数点前的 1 省略了（隐藏了 1）","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":24,"id":"1eac9c27-a35d-430b-8f7a-a98412df4bfc","page_size":[595,841],"block_position":"24-5"},{"bbox":[88,388,511,593],"index":7,"angle":0,"type":"image","img_path":"/d598243f6708b4a1a023068860747b875a9ef2e74e3149a5cb201ad75a8e9e35.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.7109243697478992,"page_idx":24,"id":"e4fc7169-a331-448b-b656-0fe1cfee5a84","page_size":[595,841],"block_position":"24-6"},{"bbox":[86,624,428,637],"type":"text","angle":0,"index":8,"text":"1、当阶码字段二进制位不全为 0，也不全为 1 时，（0 和 255），规格化","id":"eecaee48-4a59-4bbf-9f4c-bae23e48ddc9","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":24,"page_size":[595,841],"block_position":"24-7"},{"bbox":[86,640,503,668],"type":"text","angle":0,"index":9,"text":"2、当阶码字段全为 0，非规格化.1、尾数部分也全为 0，则当 $\\mathsf { S } { = } 0$ ，表示正 0， $s { = } 1$ ，负0；","id":"41ddef57-0c08-468f-b06b-4e17b4aa39d9","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":24,"page_size":[595,841],"block_position":"24-8"},{"bbox":[87,671,390,684],"type":"text","angle":0,"index":11,"text":"表示非常接近 0 的数；如果尾数不为 0，则 $\\mathsf { E } { = } \\mathsf { 1 }$ -bias， $\\mathsf { M } = \\mathsf { f }$ 不加 1","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":24,"id":"6fb8886b-1dc1-4932-9a9f-6fdeda5d017d","page_size":[595,841],"block_position":"24-9"}],[{"bbox":[88,75,465,257],"index":0,"angle":0,"type":"image","img_path":"/650d5305479445f75aede3bdffbb25a65884bf601e7cfc1f140fcc4261742161.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.6336134453781512,"page_idx":25,"id":"0ef06b7f-7028-49ba-9b94-66ec5e03b1f5","page_size":[595,841],"block_position":"25-0"},{"bbox":[87,265,505,293],"type":"text","angle":0,"index":1,"text":"3、当阶码字段全为 1，特殊值；当尾数为 0 时， $\\mathsf { S } { = } 0$ ，正无穷； $s { = } 1$ ，负无穷；当尾数不为0时，表示NaN表示不是一个数","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":25,"id":"38b64552-a769-47cb-b63e-be9d501f8685","page_size":[595,841],"block_position":"25-1"},{"bbox":[88,294,462,462],"index":2,"angle":0,"type":"image","img_path":"/c7544ae05a23243dd7e02061d4e04648f67639f1185b2a400c3cdfb32356d57d.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.6285714285714286,"page_idx":25,"id":"bc4bc743-b4c8-43df-a593-a0e2e94829b5","page_size":[595,841],"block_position":"25-2"},{"bbox":[105,472,152,483],"index":3,"angle":0,"type":"table_caption","text":"单精度为例","id":"179748c3-7758-437d-9ab5-64d9f9e96f3d","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":25,"page_size":[595,841],"block_position":"25-3"},{"bbox":[101,484,284,599],"index":4,"angle":0,"type":"table_body","img_path":"/","id":"2998a11b-cbd5-4b05-b224-e81c103b9b3e","color":{"line":"rgba(103, 194, 63, 1)","fill":"rgba(103, 194, 63, 1)"},"table_body":"
MsEM意义
0/100±0
0/10非0非规格化数
0/11~254任意规格化数
0/12550±无穷大
0/1255非0NaN
","page_idx":25,"page_size":[595,841],"block_position":"25-4"},{"bbox":[293,583,404,594],"index":5,"angle":0,"type":"table_footnote","text":"NaN:非数 (not a number)","id":"b4c1fda6-f472-4183-b25f-3186b817145e","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":25,"page_size":[595,841],"block_position":"25-5"},{"bbox":[99,626,247,751],"index":6,"angle":0,"type":"table_body","img_path":"/","id":"24265f56-3e98-4567-9e5e-01530e2e333c","color":{"line":"rgba(103, 194, 63, 1)","fill":"rgba(103, 194, 63, 1)"},"table_body":"
0J J J J J JJ J………J JH9N
0J J J J J J……H9N
0J J J J J J00………0JH9N
0J J J J J J00………00+∞
0J J J J J JJ J………J J粤羊锁怀正貌
0…………锁怀正貌
00000000J00………00粤羊锁怀正貌
000000000J J………J J粤羊非锁怀正貌
0…………非锁怀正貌
00000000000………0J粤羊非锁怀正貌
00000000000………00+0
W2EW解锁
","page_idx":25,"page_size":[595,841],"block_position":"25-6"},{"bbox":[257,624,404,751],"index":7,"angle":0,"type":"table_body","img_path":"/","id":"602f1a4a-8d95-4554-a2ef-1cb8e7ff705f","color":{"line":"rgba(103, 194, 63, 1)","fill":"rgba(103, 194, 63, 1)"},"table_body":"
JJ J J J J J JJ J………J JU9U
JJ J J J J J J……U9U
JJ J J J J J J00………0JU9U
JJ J J J J J J00………00--∞
JJ J J J J J JJ J………J J晋1非顿报快改新
J………………顿报快改新
J0000000J00………00晋1非顿报快改新
J00000000J J………J J晋1非顿报快改新
J………………非顿报快改新
J0000000000………0J晋1非顿报快改新
J0000000000………00-0
W2EW熟瑶
","page_idx":25,"page_size":[595,841],"block_position":"25-7"}],[{"bbox":[89,77,268,89],"type":"text","angle":0,"index":0,"text":"·阶码：是2n-1的移码， $\\mathtt { E } =$ [E']移=2n-1+E'","id":"690594b3-e2e8-4fbf-8873-b4a6ef81b1ad","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"page_size":[595,841],"block_position":"26-0"},{"bbox":[89,91,390,116],"type":"text","angle":0,"index":1,"text":"·隐藏位：单、双精度浮点数，尾数规格化的“1”，放置于整数位，并将其隐藏；临时实数无隐藏位","id":"8f3af00e-f7d5-4959-869d-480b5454b6b3","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"page_size":[595,841],"block_position":"26-1"},{"bbox":[89,119,238,131],"type":"text","angle":0,"index":2,"text":"■符号位：尾数的符号位Ms在最高位","id":"bac20471-1c8e-4e0a-b138-9d7dbbb16b95","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"page_size":[595,841],"block_position":"26-2"},{"bbox":[121,138,364,214],"index":4,"angle":0,"type":"table_body","img_path":"/","id":"6307c99c-a53a-4d1d-b92d-2bacaf421176","color":{"line":"rgba(103, 194, 63, 1)","fill":"rgba(103, 194, 63, 1)"},"table_body":"
类型真值计算
单精度规格化: \\( \\mathrm{N} = \\left( {-1}\\right) {}^{\\mathrm{{Ms}} \\times }\\left( {{1.}{\\mathrm{M}}_{1}{\\mathrm{M}}_{2}\\cdots {\\mathrm{M}}_{\\mathrm{n}}}\\right) \\times {2}^{\\mathrm{E} - {127}} \\) 非规格化: \\( \\mathrm{N} = \\left( {-1}\\right) {}^{\\mathrm{{Ms}} \\times }\\left( {{0.}{\\mathrm{M}}_{1}{\\mathrm{M}}_{2}\\cdots {\\mathrm{M}}_{\\mathrm{n}}}\\right) \\times {2}^{-{126}} \\)
双精度规格化: \\( \\mathrm{N} = \\left( {-1}\\right) {}^{\\mathrm{{Ms}} \\times }\\left( {{1.}{\\mathrm{M}}_{1}{\\mathrm{M}}_{2}\\cdots {\\mathrm{M}}_{\\mathrm{n}}}\\right) \\times {2}^{\\mathrm{E} - {1023}} \\) 非规格化: \\( \\mathrm{N} = \\left( {-1}\\right) {}^{\\mathrm{{Ms}} \\times }\\left( {{0.}{\\mathrm{M}}_{1}{\\mathrm{M}}_{2}\\cdots {\\mathrm{M}}_{\\mathrm{n}}}\\right) \\times {2}^{-{1022}} \\)
","page_idx":26,"page_size":[595,841],"block_position":"26-3"},{"bbox":[98,236,327,248],"type":"text","angle":0,"index":5,"text":"例3.10若X和Y均是IEEE754标准的单精度浮点数。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"id":"ddb659b1-8cf9-443d-a7de-446351e03054","page_size":[595,841],"block_position":"26-4"},{"bbox":[110,251,327,263],"type":"text","angle":0,"index":6,"text":"（1）若× $=$ -135.625，求X的规格化浮点数表示。","id":"6ae91818-d51e-4865-9bb9-e18296c2ef6a","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"page_size":[595,841],"block_position":"26-5"},{"bbox":[110,265,359,278],"type":"text","angle":0,"index":7,"text":"(2）若浮点数Y的存储形式为41360000H，求Y的真值。","id":"6dc15e0d-4574-4af9-9c99-2071a3ba28f9","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"page_size":[595,841],"block_position":"26-6"},{"bbox":[94,282,281,295],"type":"text","angle":0,"index":9,"text":"（1）真值→IEEE754规格化单精度浮点数","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"id":"2b14da8c-f107-41c6-beb5-884a1532a078","page_size":[595,841],"block_position":"26-7"},{"bbox":[94,296,340,310],"type":"text","angle":0,"index":10,"text":"$\\textcircled{1}$ 写出数据的二进制真值 $\\mathbf { x } =$ (-10000111.101） 2","id":"bad29e5e-7731-46cf-b8ed-8f763f01a34a","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"page_size":[595,841],"block_position":"26-8"},{"bbox":[94,311,332,323],"type":"text","angle":0,"index":11,"text":"$\\textcircled{2}$ 转换为M $\\times 2 ^ { E }$ 的形式：M' ${ \\bf \\delta } = \\pm 1 . \\times { \\bf x } \\ldots \\times$ ，E'为整数","id":"039967a4-14bf-4cd4-845d-1b08c22a2eb7","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"page_size":[595,841],"block_position":"26-9"},{"bbox":[105,325,401,337],"type":"text","angle":0,"index":13,"text":"X=-1.0000111101×27 M'=-1.0000111101 E'=+7","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"id":"de0fd640-14f5-4e45-bf84-33ddd5660660","page_size":[595,841],"block_position":"26-10"},{"bbox":[94,339,351,353],"type":"text","angle":0,"index":14,"text":"： $\\textcircled{3}$ 写出尾数M'的原码，尾数数值隐藏（舍去）整数位的“1\"","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"id":"d91cd4c4-737b-479f-96dd-4ae553521fec","page_size":[595,841],"block_position":"26-11"},{"bbox":[105,354,377,366],"type":"text","angle":0,"index":15,"text":"$\\boldsymbol { \\ M } _ { S } = 1$ 尾数数值M $\\mathtt { \\mathtt { = 0 0 0 } }$ 0111 1010 0000 0000 0000","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"id":"9dc69eb2-5bfe-40da-bc57-43eb37a166b5","page_size":[595,841],"block_position":"26-12"},{"bbox":[94,368,398,381],"type":"text","angle":0,"index":16,"text":"： $\\textcircled{4}$ 写出阶码E'的移码E： $\\mathsf { E } = [ \\mathsf { E } ^ { \\prime } ] _ { \\scriptscriptstyle 1 \\mathscr { B } } = 1 2 7 + \\mathsf { E } ^ { \\prime } = 1 2 7 + 7 = 1 3 4 = 1 0 0 ($ 00110B","id":"10824b18-877e-4724-8e06-157dcc15d08f","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"page_size":[595,841],"block_position":"26-13"},{"bbox":[94,383,254,395],"type":"text","angle":0,"index":17,"text":"： $\\textcircled{5}$ 按照格式排列E和M：即MsEM","id":"a294f49a-79c7-4975-87ca-aceb5046d059","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"page_size":[595,841],"block_position":"26-14"},{"bbox":[105,396,371,407],"type":"text","angle":0,"index":19,"text":"$[ \\mathsf { X } ] _ { \\overrightarrow { \\jmath } } = \\uparrow$ 10000110 000 0111 1010 0000 0000 0000B=C307A000H","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"id":"d047e650-a488-41cb-bbc5-2b90031e24a9","page_size":[595,841],"block_position":"26-15"},{"bbox":[100,446,241,460],"type":"title","angle":0,"index":20,"text":"# 例3.10（2）浮点数 真值","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":26,"id":"bbc9d01a-df0e-4013-8bef-ff769adb16b8","page_size":[595,841],"block_position":"26-16"},{"bbox":[257,437,314,460],"type":"title","angle":0,"index":21,"text":"# 阶码8位，2n-1的移码","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":26,"id":"76ac8e3e-b394-4934-b811-7e4ef5b5b70c","page_size":[595,841],"block_position":"26-17"},{"bbox":[113,463,409,476],"type":"text","angle":0,"index":22,"text":"$\\textcircled{1}$ 浮点数的二进制编码：按照格式分，写出M、阶码E和尾数数值M","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"id":"985f975f-3b40-40cb-885a-ce83cdab15aa","page_size":[595,841],"block_position":"26-18"},{"bbox":[127,479,434,507],"type":"interline_equation","angle":0,"index":23,"text":"$$\n\\begin{array}{l} \\cdot [ \\mathrm {Y} ] _ {\\text {浮}} = 4 1 3 6 0 0 0 0 \\mathrm {H} = 0 1 0 0 / 0 0 0 1 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 B \\\\ \\cdot \\mathrm {M} _ {\\mathrm {s}} = 0 \\quad \\mathrm {E} = 1 0 0 0 0 0 1 0 \\mathrm {B} = 1 3 0 \\quad \\mathrm {M} = 0 1 1 0 1 1 0 0 0 0 0 0 0 \\\\ \\end{array}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":26,"id":"20ef7b9f-9549-478a-9dc9-cd5ad3cf3647","page_size":[595,841],"block_position":"26-19"},{"bbox":[88,510,362,522],"type":"text","angle":0,"index":24,"text":"添加隐 ·阶码编码E不是全0也不是全1，可判定Y是规格化浮点数","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"id":"acf0d88e-2e77-47fe-86a8-28e654169196","page_size":[595,841],"block_position":"26-20"},{"bbox":[88,524,373,538],"type":"text","angle":0,"index":25,"text":"藏位1写出尾数的真值M’： $\\pmb { M } _ { S } \\mathbf { = } 0$ ，表明是正数添加隐藏位1","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"id":"52d7e218-0d66-4785-b8a4-19e7d4f016db","page_size":[595,841],"block_position":"26-21"},{"bbox":[94,548,324,559],"type":"text","angle":0,"index":26,"text":"数符+","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"id":"e7975f14-7709-439f-95a3-7d42427ed055","page_size":[595,841],"block_position":"26-22"},{"bbox":[125,556,402,568],"type":"text","angle":0,"index":27,"text":"求出阶码的真值E'：Y是单精度浮点数，故E'=E-127=130-127=3","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"id":"96b96596-3d84-405f-9872-1a1d37d7401e","page_size":[595,841],"block_position":"26-23"},{"bbox":[113,571,355,613],"type":"interline_equation","angle":0,"index":29,"text":"$$\n\\begin{array}{l} Y = M ^ {\\prime} \\times 2 ^ {E ^ {\\prime}} = + 1. 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 \\times 2 ^ {3} \\\\ = + 1 0 1 1. 0 1 1 B = + 1 1. 3 7 5 \\\\ \\end{array}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":26,"id":"23c60bfd-c7f1-4247-82c5-78c9255a5d05","page_size":[595,841],"block_position":"26-24"},{"bbox":[87,624,258,637],"type":"text","angle":0,"index":30,"text":"但是，浮点数只能近似表示实数运算","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"id":"2d132bfe-a270-4282-9b6a-7b8a8703fcba","page_size":[595,841],"block_position":"26-25"},{"bbox":[88,640,150,652],"type":"text","angle":0,"index":31,"text":"1、向上舍入","id":"b25769fe-ee81-4ba6-8323-8e0497081585","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"page_size":[595,841],"block_position":"26-26"},{"bbox":[88,655,150,667],"type":"text","angle":0,"index":32,"text":"2、向下舍入","id":"ef2c0714-3296-4c71-8aa7-55361cf5a3cd","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"page_size":[595,841],"block_position":"26-27"},{"bbox":[88,671,150,683],"type":"text","angle":0,"index":33,"text":"3、向零舍入","id":"b99361b8-1892-4847-9cdb-43a10ebb4eef","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"page_size":[595,841],"block_position":"26-28"},{"bbox":[87,687,182,699],"type":"text","angle":0,"index":35,"text":"4、四舍六入五取偶","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"id":"987bbc1e-6420-43c8-9907-163c8c244f3d","page_size":[595,841],"block_position":"26-29"},{"bbox":[87,702,324,714],"type":"text","angle":0,"index":36,"text":"Int ->float 同样 32 位不会发生溢出但是会失去精度","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"id":"09142f47-bb24-4e33-86ad-2a9ec47c09b9","page_size":[595,841],"block_position":"26-30"},{"bbox":[87,718,303,730],"type":"text","angle":0,"index":37,"text":"Int/float->double 不发生溢出，可以保留精度","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"id":"422f16b8-1807-4cab-bce5-1d6bd9099fbd","page_size":[595,841],"block_position":"26-31"},{"bbox":[87,734,366,746],"type":"text","angle":0,"index":38,"text":"Double->float float 数值更小会溢出；float 精度更小会舍入","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"id":"a1ced649-48f3-4752-af26-5070654a7b9d","page_size":[595,841],"block_position":"26-32"},{"bbox":[87,749,306,761],"type":"text","angle":0,"index":39,"text":"Float 、double->int 1、向 0 舍入 2、发生溢出","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":26,"id":"d5e25cdc-8732-4102-b022-16930b40a81e","page_size":[595,841],"block_position":"26-33"},{"bbox":[422,605,441,623],"index":40,"angle":0,"type":"image","img_path":"/bfa78e06b0d3913c28c391fec9983e9560c657cdba21f6186a404da3be4f5b19.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.2,"page_idx":26,"id":"0f9cdcba-a13c-46f6-9143-49a80fba0021","page_size":[595,841],"block_position":"26-34"}],[{"bbox":[88,79,164,91],"index":0,"angle":0,"type":"image_caption","text":"大端法与小端法","id":"ea8071a4-1412-443a-986b-55c590c98821","color":{"line":"rgba(13, 83, 222 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":27,"page_size":[595,841],"block_position":"27-0"},{"bbox":[88,91,555,332],"index":1,"angle":0,"type":"image","img_path":"/c18707fdc6690cbbeb12755c25664031e3864720f676bdd884409cae44b965d7.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.7848739495798319,"page_idx":27,"id":"c17a8da5-520b-4072-a6de-ff6db800b4ca","page_size":[595,841],"block_position":"27-1"},{"bbox":[88,343,121,356],"index":2,"angle":0,"type":"image_caption","text":"全加器","id":"f68e7bcb-275f-440f-b671-924416c6859d","color":{"line":"rgba(13, 83, 222 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":27,"page_size":[595,841],"block_position":"27-2"},{"bbox":[88,356,556,623],"index":3,"angle":0,"type":"image","img_path":"/fc5f82e5e9be2a5c3b02fbe81cb70ad9ef2ad7623210873829e13a3b41d79e02.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.7865546218487395,"page_idx":27,"id":"2e848fc0-912f-4943-8980-7ae3f9324dab","page_size":[595,841],"block_position":"27-3"},{"bbox":[88,655,252,669],"type":"text","angle":0,"index":4,"text":"串行进位加法器（行波进位加法器）","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":27,"id":"b8b5fb5e-6fbb-4a86-a28c-f166304d3887","page_size":[595,841],"block_position":"27-4"}],[{"bbox":[99,95,423,190],"index":0,"angle":0,"type":"image","img_path":"/97427437348e9fdabf7e1f1dd98d4ee87c5cacd20c88a229ec6fe0060a545d10.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.5445378151260504,"page_idx":28,"id":"9d0dc43c-c7cf-4498-92b5-f7f3287e81e6","page_size":[595,841],"block_position":"28-0"},{"bbox":[87,218,164,232],"type":"text","angle":0,"index":1,"text":"先行进位加法器","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":28,"id":"423ff0c7-a243-4a6c-b0fd-8b1225280e84","page_size":[595,841],"block_position":"28-1"},{"bbox":[88,234,132,248],"type":"text","angle":0,"index":2,"text":"乘法运算","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":28,"id":"98588e54-d717-4328-be22-b412ed592b8b","page_size":[595,841],"block_position":"28-2"},{"bbox":[88,249,132,264],"type":"text","angle":0,"index":3,"text":"除法运算","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":28,"id":"41a7d321-b763-41de-92b5-99868b217200","page_size":[595,841],"block_position":"28-3"},{"bbox":[93,279,515,466],"index":4,"angle":0,"type":"image","img_path":"/20dbaf06f5585bbdff9ba7e4458ceb025cb910d7536b1db144cebd7cca1b0b28.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.7092436974789916,"page_idx":28,"id":"d9eafa5f-a430-47fb-9bec-152b6dbd92b4","page_size":[595,841],"block_position":"28-4"},{"bbox":[87,499,398,528],"type":"text","angle":0,"index":5,"text":" 汉字输入：在西文标准键盘上，通过不同的字符组合，将汉字输入计算机，转换为汉字内码的过程","id":"0595d8b0-a408-4803-b11e-d3823473b8ce","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":28,"page_size":[595,841],"block_position":"28-5"},{"bbox":[88,530,365,544],"type":"text","angle":0,"index":6,"text":" 汉字输入码：也称外码，由不同的西文字符组合成的编码","id":"4bf2284f-6857-4ec8-896e-673390f7dfde","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":28,"page_size":[595,841],"block_position":"28-6"},{"bbox":[88,546,180,560],"type":"text","angle":0,"index":7,"text":" 汉字输入码种类：","id":"fd0c8ab0-7cdf-4930-b267-3f6f5746787c","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":28,"page_size":[595,841],"block_position":"28-7"},{"bbox":[87,576,270,591],"type":"text","angle":0,"index":9,"text":"数字编码：区位码、国标码、电报码等","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":28,"id":"c1531f3b-ff4f-4fe9-a542-3f19757cc569","page_size":[595,841],"block_position":"28-8"},{"bbox":[87,608,248,622],"type":"text","angle":0,"index":10,"text":"拼音编码：搜狗拼音、微软拼音等","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":28,"id":"97fedaed-cfbd-47d8-832c-ff0b4052c3ce","page_size":[595,841],"block_position":"28-9"},{"bbox":[87,640,248,653],"type":"text","angle":0,"index":11,"text":"字形编码：五笔字型输入法、郑码","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":28,"id":"d1c7474d-21b3-4f48-bbd4-2d34e7d008e7","page_size":[595,841],"block_position":"28-10"},{"bbox":[87,670,207,684],"type":"text","angle":0,"index":12,"text":"音形编码：自然码、钱码","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":28,"id":"5f795090-c269-4b5f-967a-6843403b71e6","page_size":[595,841],"block_position":"28-11"},{"bbox":[86,686,384,700],"type":"text","angle":0,"index":13,"text":"汉字内码：用于汉字信息的存储、交换、检索等操作的机内代码","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":28,"id":"1482a380-1ea6-47cd-afc9-ecd49a3eab2d","page_size":[595,841],"block_position":"28-12"},{"bbox":[87,702,351,715],"type":"text","angle":0,"index":14,"text":" 一般采用两个字节表示，汉字内码在计算机中是唯一的","id":"02d87d12-d61a-4cea-9504-b62af739e02a","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":28,"page_size":[595,841],"block_position":"28-13"},{"bbox":[88,717,233,730],"type":"text","angle":0,"index":15,"text":" 汉字内码涉及以下几种编码：","id":"f6a185e9-de2f-4f08-9ec3-30fab5dbb9e2","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":28,"page_size":[595,841],"block_position":"28-14"},{"bbox":[87,733,162,746],"type":"text","angle":0,"index":16,"text":" （1）区位码","id":"ad47c163-df3e-4c07-a099-ac63f554442c","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":28,"page_size":[595,841],"block_position":"28-15"},{"bbox":[87,748,445,762],"type":"text","angle":0,"index":17,"text":" 汉字编码的国家标准：GB2312-1980《信息交换用汉字编码字符集·基本集》","id":"cdddc5ed-4b2c-4f6c-a510-d31a124c1128","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":28,"page_size":[595,841],"block_position":"28-16"}],[{"bbox":[87,79,282,91],"type":"text","angle":0,"index":0,"text":" 共收录了 6763 个汉字、682 个图形符号","id":"13c9a078-d1e4-436f-b507-d0e09d6b26f9","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-0"},{"bbox":[87,95,312,107],"type":"text","angle":0,"index":1,"text":"• 一级常用汉字：3755 个，按拼音字母顺序排列","id":"8c024eb0-02a5-4c1d-bd5a-37093b4a2a3c","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-1"},{"bbox":[87,110,302,122],"type":"text","angle":0,"index":2,"text":"• 二级次常用汉字：3008 个，按偏旁部首排列","id":"88678628-1b0d-4af6-bd87-3a76bed8fa5f","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-2"},{"bbox":[87,125,436,138],"type":"text","angle":0,"index":3,"text":" 两个字节编码汉字，每个字节各取 7 位，可编码 $1 2 8 \\times 1 2 8 = 1 6 3 8 4$ 个字符","id":"2853b596-e530-4fc3-b7c7-202e16e35d15","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-3"},{"bbox":[87,141,420,154],"type":"text","angle":0,"index":4,"text":" 将所有的汉字及符号组成一个 $9 4 \\times 9 4$ 的方阵，行 “区”，列 “位”","id":"6554dc46-c82e-41de-95f7-c7295bcf999c","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-4"},{"bbox":[87,157,406,169],"type":"text","angle":0,"index":5,"text":" 每个汉字与符号都位于某个区的某个位上，区号和位号 “区位码”","id":"a5a5d2cf-7f70-476b-af3a-6955b05d8ac9","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-5"},{"bbox":[87,172,473,185],"type":"text","angle":0,"index":6,"text":" 例如：“中”字位于 54 区 48 位 “中”字的区位码即为“5448  （2）国标码","id":"823a985a-1fde-42d3-a8de-5aa123757518","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-6"},{"bbox":[87,188,278,200],"type":"text","angle":0,"index":7,"text":" 国标码 $\\mid =$ 区位码 $+ 2 0 2 0 \\mathsf { H }$ ，占用两个字节","id":"49f25985-c6bd-415d-bb5c-a7f060596689","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-7"},{"bbox":[87,203,233,216],"type":"text","angle":0,"index":8,"text":" 例如“中”字：区位码 $\\mathbf { = } 5 4 4 8$","id":"f754bee5-9222-4bf8-b2b1-8dac5242beb9","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-8"},{"bbox":[87,219,266,232],"type":"text","angle":0,"index":9,"text":"• 区码和位码转化为 16 进制， ${ \\bf = 3 6 3 0 H }$","id":"72fe91f5-f1a4-4df0-aa34-4ece7d460d4e","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-9"},{"bbox":[87,235,242,247],"type":"text","angle":0,"index":10,"text":"• 国标码 $\\lvert = 3 6 3 0 \\rvert + 2 0 2 0 \\ H = 5 6 5 0 \\ H$","id":"2860890b-4b58-4524-9542-c429a8ab36cc","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-10"},{"bbox":[87,250,172,263],"type":"text","angle":0,"index":11,"text":" （3）汉字内码","id":"f3ee5c88-2f0b-4049-b317-886043b70302","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-11"},{"bbox":[87,265,403,279],"type":"text","angle":0,"index":12,"text":" 西文字符：七位的 ASCII 码，当用一个字节表示时，最高位为“0”","id":"9b7d1044-39ab-41da-a43b-a6bda5a93af4","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-12"},{"bbox":[87,281,433,294],"type":"text","angle":0,"index":13,"text":" 汉字内码：汉字内码 $=$ 汉字国标码 $\\pm 8 0 8 0 \\mathsf { H }$ ，2 个字节的最高位均为“1”","id":"2d96b74a-6ee7-4df9-8ef1-e90af0289aff","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-13"},{"bbox":[87,297,320,310],"type":"text","angle":0,"index":14,"text":"• 例如“中”字的机内码 $\\lvert = 5 6 5 0 \\rvert + 8 0 8 0 \\ H = \\mathrm { D } 6 \\mathrm { D } 0 \\mathsf { H }$","id":"2f5cebe2-e3da-4d17-819a-0811bb5f5dce","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-14"},{"bbox":[87,312,234,325],"type":"text","angle":0,"index":15,"text":" 文本文件中储存的是汉字内码","id":"390f5ff2-a375-4b97-b10b-e0ba4f8276e5","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-15"},{"bbox":[87,328,450,341],"type":"text","angle":0,"index":16,"text":"汉字处理系统中字形信息： $\\textcircled{1}$ 用活字或文字版的母体字形形式； $\\textcircled{2}$ 点阵表示法、","id":"32886713-3b94-4c12-931f-79f4cbfb1f91","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-16"},{"bbox":[87,343,352,356],"type":"text","angle":0,"index":17,"text":"矢量表示法等形式，最基本的，应用也最广泛的是字模码","id":"3bfa45ed-c9f8-4f1d-92b6-77403dffc5d1","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-17"},{"bbox":[87,359,433,387],"type":"text","angle":0,"index":18,"text":" 字模码：用点阵形式表示与存储汉字字形代码，它是汉字的输出形式，用于汉字的显示和打印","id":"ac7e392a-b292-4065-9ecd-d9aa6cd1d7db","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-18"},{"bbox":[87,391,312,403],"type":"text","angle":0,"index":19,"text":" 根据汉字输出的要求不同，点阵的规模也不同：","id":"c9cd205e-4c31-4b74-8a80-2bfa464e7c4c","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-19"},{"bbox":[87,407,263,418],"type":"text","angle":0,"index":20,"text":"• 简易型汉字： $1 6 \\times 1 6$ ， 32 字节/汉字","id":"fa292e43-c185-4938-9610-bb6b06cda96d","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-20"},{"bbox":[87,422,263,434],"type":"text","angle":0,"index":21,"text":"• 普及型汉字： $2 4 \\times 2 4$ ， 72 字节/汉字","id":"e1ab30b7-c011-4f4a-adf6-9c734f211520","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-21"},{"bbox":[87,438,266,449],"type":"text","angle":0,"index":22,"text":"• 提高型汉字： $3 2 \\times 3 2$ ，128 字节/汉字","id":"454c8bbf-3f84-49f1-b424-96e96af638c4","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-22"},{"bbox":[87,453,266,465],"type":"text","angle":0,"index":23,"text":"• 精密型汉字： $4 8 \\times 4 8$ ，288 字节/汉字","id":"c9ebbffa-7d7e-4f5a-82b3-031bd4fbd9ba","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-23"},{"bbox":[87,468,423,481],"type":"text","angle":0,"index":24,"text":" 汉字字库：将所有汉字的字模点阵代码按顺序集中存放，构成了汉字库","id":"03ed5ae7-cd2b-4907-a7c2-e2e4fd9df57d","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-24"},{"bbox":[87,484,308,497],"type":"text","angle":0,"index":25,"text":" 字形检索程序：将汉字的机内代码转化为汉字","id":"c2492f88-62fa-48a7-99e9-34e07c3534f9","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-25"},{"bbox":[87,515,132,528],"type":"title","angle":0,"index":27,"text":"# 补码加减","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":29,"id":"48834d91-a3f3-4ed6-8830-fc7cf1d4c234","page_size":[595,841],"block_position":"29-26"},{"bbox":[105,534,214,547],"type":"text","angle":0,"index":28,"text":"补码的加法运算公式：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"id":"ba464391-3fd3-48e8-8c1d-6dafee5d416d","page_size":[595,841],"block_position":"29-27"},{"bbox":[117,550,214,564],"type":"interline_equation","angle":0,"index":29,"text":"$$\n= [ X + Y ] _ {\\text {补}} = [ X ] _ {\\text {补}} + [ Y ] _ {\\text {补}}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":29,"id":"643c6afc-052e-4642-83c5-23f81ff282f0","page_size":[595,841],"block_position":"29-28"},{"bbox":[260,533,368,545],"type":"text","angle":0,"index":30,"text":"补码的减法运算公式：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"id":"66942a8f-221a-4fd6-87c2-f0dc27310787","page_size":[595,841],"block_position":"29-29"},{"bbox":[272,549,378,576],"type":"interline_equation","angle":0,"index":31,"text":"$$\n\\begin{array}{l} - [ X - Y ] _ {\\text {补}} = [ X + (- Y) ] _ {\\text {补}} \\\\ = [ \\mathrm {X} ] _ {\\text {补}} + [ - \\mathrm {Y} ] _ {\\text {补}} \\\\ \\end{array}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":29,"id":"1a3ee014-63f2-403f-84f8-3db304aea236","page_size":[595,841],"block_position":"29-30"},{"bbox":[112,569,136,580],"type":"text","angle":0,"index":32,"text":"证明：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"id":"7197b2d1-cc16-4b3f-b149-3abcce4fe7e2","page_size":[595,841],"block_position":"29-31"},{"bbox":[116,581,251,594],"type":"interline_equation","angle":0,"index":33,"text":"$$\n[ X ] _ {\\text {补}} = 2 ^ {n + 1} + X \\quad (\\mathrm {m o d} 2 ^ {n + 1})\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":29,"id":"4f8270b5-1529-47d2-bf73-7bca35acb621","page_size":[595,841],"block_position":"29-32"},{"bbox":[116,598,251,611],"type":"interline_equation","angle":0,"index":34,"text":"$$\n[ Y ] _ {\\text {补}} = 2 ^ {n + 1} + Y \\quad (\\mathrm {m o d} 2 ^ {n + 1})\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":29,"id":"d8018866-e290-4597-b85a-b858a39e7456","page_size":[595,841],"block_position":"29-33"},{"bbox":[116,614,336,662],"type":"interline_equation","angle":0,"index":35,"text":"$$\n\\begin{array}{l} [ X ] _ {\\text {补}} + [ Y ] _ {\\text {补}} = 2 ^ {n + 1} + X + 2 ^ {n + 1} + Y \\quad (\\mathrm {m o d} 2 ^ {n + 1}) \\\\ = 2 ^ {n + 1} + (X + Y) \\quad (\\text {m o d} 2 ^ {n + 1}) \\\\ = [ X + Y ] _ {\\text {补}} \\quad (\\mathrm {m o d} 2 ^ {n + 1}) \\\\ \\end{array}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":29,"id":"57dfe660-d807-4e6c-91b5-375830c97dad","page_size":[595,841],"block_position":"29-34"},{"bbox":[99,672,271,684],"type":"text","angle":0,"index":36,"text":"任意两数之和的补码 $=$ 两数的补码之和","id":"7602772b-8221-44dc-8b89-cf6d05638677","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-35"},{"bbox":[99,687,362,698],"type":"text","angle":0,"index":37,"text":"任意两数之差的补码 $=$ 被减数的补码与减数相反数的补码之和","id":"69a48a98-5c60-43df-a642-66f27f982ddc","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":29,"page_size":[595,841],"block_position":"29-36"}],[{"bbox":[123,96,270,116],"type":"title","angle":0,"index":0,"text":"# 求补运算：[Y]补→[-Y]补","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":30,"id":"7fd1ccd5-d05d-40c0-a7cf-194ac4d279aa","page_size":[595,841],"block_position":"30-0"},{"bbox":[94,125,396,141],"type":"text","angle":0,"index":1,"text":"求补规则：将 $[ Y ] _ { \\ast \\mathrm { h } }$ 包括符号位在内每一位取反，末位加1。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":30,"id":"8b9c7114-7955-4577-8bf5-ddeb5a1c86e6","page_size":[595,841],"block_position":"30-1"},{"bbox":[94,145,261,161],"type":"text","angle":0,"index":2,"text":"若 $[ \\boldsymbol { \\Upsilon } _ { \\sharp \\flat } = \\boldsymbol { \\Upsilon } _ { \\mathsf { s } }$ $\\mathsf { Y } _ { 1 } . . . . . \\mathsf { Y } _ { \\mathsf { n } }$ ，则：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":30,"id":"b88af523-6181-4038-9162-3cc3ce9bb6e8","page_size":[595,841],"block_position":"30-2"},{"bbox":[108,165,255,182],"type":"interline_equation","angle":0,"index":3,"text":"$$\n- [ - Y ] _ {\\text {补}} = \\overline {{Y _ {S}}} \\overline {{Y _ {1}}} \\dots \\dots \\overline {{Y _ {n}}} + 1\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":30,"id":"5ea6a647-3c58-439a-ba83-e0b4c61e330b","page_size":[595,841],"block_position":"30-3"},{"bbox":[94,186,256,201],"type":"text","angle":0,"index":4,"text":"若[Y]补 $\\mathbf { \\Psi } = \\mathsf { Y } _ { \\mathsf { S } } . \\mathsf { Y } _ { 1 } . . . . . \\mathsf { Y } _ { \\mathsf { n } }$ ，则：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":30,"id":"795c1d27-1a09-4acf-a0c6-5da635829fe2","page_size":[595,841],"block_position":"30-4"},{"bbox":[108,206,302,223],"type":"interline_equation","angle":0,"index":5,"text":"$$\n- [ - Y ] _ {\\text {补}} = \\overline {{Y _ {S}}} \\overline {{Y _ {1}}} \\dots \\dots \\overline {{Y _ {n}}} + 0. 0 \\dots \\dots 0 1\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":30,"id":"6424b2b9-3540-4c7e-bd3f-0d5dbbb84bf6","page_size":[595,841],"block_position":"30-5"},{"bbox":[86,231,258,243],"type":"text","angle":0,"index":6,"text":"：溢出：运算结果超出机器数的表示范围","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":30,"id":"ac8ed20b-9e58-4f8b-93cc-5cecf0098e94","page_size":[595,841],"block_position":"30-6"},{"bbox":[87,248,186,259],"type":"text","angle":0,"index":7,"text":"计算机硬件必须具备：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":30,"id":"c1dfec5c-cac7-4227-ba80-9e999a18a776","page_size":[595,841],"block_position":"30-7"},{"bbox":[98,263,245,275],"type":"text","angle":0,"index":8,"text":"·能够检测运算结果是否发生溢出；","id":"15374a18-920e-4c6d-8246-f91b2d9aa2b9","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":30,"page_size":[595,841],"block_position":"30-8"},{"bbox":[98,279,245,290],"type":"text","angle":0,"index":9,"text":"·能够指示运算结果是否发生溢出；","id":"77b0dd50-ed3c-4bec-a185-abf590892ef9","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":30,"page_size":[595,841],"block_position":"30-9"},{"bbox":[309,234,420,246],"type":"text","angle":0,"index":11,"text":"补码加减运算判溢方法：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":30,"id":"bd2a14b5-1b0b-4829-ab14-3d1412d526a1","page_size":[595,841],"block_position":"30-10"},{"bbox":[324,250,391,262],"type":"text","angle":0,"index":12,"text":"·单符号位判溢","id":"59e32fdc-1602-4f38-8be3-afeaf1809aff","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":30,"page_size":[595,841],"block_position":"30-11"},{"bbox":[324,266,372,278],"type":"text","angle":0,"index":13,"text":"·进位判溢","id":"c2fa6a4c-437c-49b8-b32c-52a08a4d0c35","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":30,"page_size":[595,841],"block_position":"30-12"},{"bbox":[324,282,391,294],"type":"text","angle":0,"index":14,"text":"■双符号位判溢","id":"c4249346-3be2-4e76-8b94-54deffacd9fd","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":30,"page_size":[595,841],"block_position":"30-13"},{"bbox":[86,295,251,307],"type":"text","angle":0,"index":16,"text":"对于加减运算，可能发生溢出的情况：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":30,"id":"410eba60-d3f4-46e1-815e-ce5b80b16d81","page_size":[595,841],"block_position":"30-14"},{"bbox":[98,311,185,323],"type":"text","angle":0,"index":17,"text":"■同号（两数）相加","id":"3d2937ee-aec5-4672-affd-5ce2a4e1a351","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":30,"page_size":[595,841],"block_position":"30-15"},{"bbox":[98,326,185,338],"type":"text","angle":0,"index":18,"text":"·异号（两数）相减","id":"be13c7da-042b-4f6e-a2d2-a906aa8fb463","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":30,"page_size":[595,841],"block_position":"30-16"},{"bbox":[109,350,138,362],"type":"text","angle":0,"index":20,"text":"Why?","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":30,"id":"1c469c40-5280-46b1-89f1-f9a136482000","page_size":[595,841],"block_position":"30-17"},{"bbox":[201,322,310,334],"type":"text","angle":0,"index":21,"text":"一定会发生溢出的情况：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":30,"id":"dc521032-cf88-4b08-9850-e8ec96ef9a93","page_size":[595,841],"block_position":"30-18"},{"bbox":[214,338,361,350],"type":"text","angle":0,"index":22,"text":"正数相加，且运算结果符号位为1","id":"19f07fff-d1de-4b2b-b384-d253fd37a5c5","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":30,"page_size":[595,841],"block_position":"30-19"},{"bbox":[214,354,362,366],"type":"text","angle":0,"index":23,"text":"·负数相加，且运算结果符号位为0","id":"8f396100-19a6-4faf-b0c2-f1b00a072fc2","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":30,"page_size":[595,841],"block_position":"30-20"},{"bbox":[214,370,371,382],"type":"text","angle":0,"index":24,"text":"·正数－负数，且运算结果符号位为1","id":"55c245c6-e115-43d0-a9c3-495dcf2f59ed","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":30,"page_size":[595,841],"block_position":"30-21"},{"bbox":[214,386,372,397],"type":"text","angle":0,"index":25,"text":"■负数－正数，且运算结果符号位为0","id":"81da1aa3-3181-4ee4-b712-85b5ee2b8d5b","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":30,"page_size":[595,841],"block_position":"30-22"},{"bbox":[413,397,426,412],"type":"title","angle":0,"index":27,"text":"# 18","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":30,"id":"3eea55c5-6736-460d-a632-509cce182ae4","page_size":[595,841],"block_position":"30-23"},{"bbox":[126,425,238,439],"type":"title","angle":0,"index":28,"text":"# （1）单符号位判溢方法","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":30,"id":"60498487-0e28-4b53-b941-13b417b42f73","page_size":[595,841],"block_position":"30-24"},{"bbox":[133,445,249,460],"type":"text","angle":0,"index":29,"text":"$\\overline { { A D D } } / S U B = 0$ ：做加法","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":30,"id":"a46c161b-aaa7-46ee-b85d-312ab5c3adb4","page_size":[595,841],"block_position":"30-25"},{"bbox":[134,465,249,478],"type":"text","angle":0,"index":30,"text":"$\\overline { { A D D } } / S U B = 1$ ：做减法","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":30,"id":"cb0e967f-2eb1-44c5-847c-ecf5c9959ab6","page_size":[595,841],"block_position":"30-26"},{"bbox":[292,425,410,439],"type":"text","angle":0,"index":31,"text":"【例4.3】的4种情况：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":30,"id":"fd86c9ab-d785-4487-b2fd-c1037fe95e6e","page_size":[595,841],"block_position":"30-27"},{"bbox":[279,443,397,484],"type":"interline_equation","angle":0,"index":32,"text":"$$\n\\begin{array}{l} [ \\mathrm {X} ] _ {\\text {补}} = \\mathrm {X} _ {S} \\mathrm {X} _ {1} \\dots \\dots \\mathrm {X} _ {n} \\\\ [ \\mathrm {Y} ] _ {\\text {补}} = \\mathrm {Y} _ {S} \\mathrm {Y} _ {1} \\dots \\dots \\mathrm {Y} _ {n} \\\\ [ X \\pm Y ] _ {\\text {补}} = F _ {s} F _ {1} \\dots \\dots F _ {n} \\\\ \\end{array}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":30,"id":"ea541fca-d7d0-4d5c-97ed-72e0d78adf12","page_size":[595,841],"block_position":"30-28"},{"bbox":[107,491,519,614],"index":33,"angle":0,"type":"table_body","img_path":"/","id":"74ca5268-a0ae-408f-a294-b1c0b5730636","color":{"line":"rgba(103, 194, 63, 1)","fill":"rgba(103, 194, 63, 1)"},"table_body":"
运算操作数XXS操作数YYS运算结果FFS溢出情况
X+Y正数0正数0负数1正溢出
X+Y负数1负数1正数0负溢出
X-Y正数0负数1负数1正溢出
X-Y负数1正数0正数0负溢出
","page_idx":30,"page_size":[595,841],"block_position":"30-29"},{"bbox":[107,623,165,637],"type":"text","angle":0,"index":34,"text":"$\\boldsymbol { \\mathsf { V } } = \\boldsymbol { \\mathsf { 1 } }$ ：溢出","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":30,"id":"43fa7ee6-0c47-4c35-a7b8-282a9c58bc34","page_size":[595,841],"block_position":"30-30"}],[{"bbox":[99,76,210,91],"type":"title","angle":0,"index":0,"text":"# （3）双符号位判溢方法","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":31,"id":"006e6569-2d12-4810-be48-46531209ce1c","page_size":[595,841],"block_position":"31-0"},{"bbox":[108,95,468,125],"type":"text","angle":0,"index":1,"text":"·X和Y采用双符号位补码参加运算，正数的双符号位为00，负数的双符号位为11；当运算结果的两位符号Fs1 $\\bar { \\mathsf { F } } _ { 5 2 }$ 不同时（01或10），发生溢出。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":31,"id":"66dc388a-3cd7-492c-b178-a320257febcb","page_size":[595,841],"block_position":"31-1"},{"bbox":[138,133,247,179],"type":"interline_equation","angle":0,"index":2,"text":"$$\n\\frac {\\mathrm {X} _ {\\mathrm {S}} \\mathrm {X} _ {\\mathrm {S}} \\mathrm {X} _ {1} \\mathrm {X} _ {2} \\dots \\dots \\mathrm {X} _ {\\mathrm {n}}}{\\mathrm {Y} _ {\\mathrm {S}} \\mathrm {Y} _ {\\mathrm {S}} \\mathrm {Y} _ {1} \\mathrm {Y} _ {2} \\dots \\dots \\mathrm {Y} _ {\\mathrm {n}}}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":31,"id":"2ed4d094-5c22-4a40-8a03-9a61494964e4","page_size":[595,841],"block_position":"31-2"},{"bbox":[278,134,478,179],"type":"interline_equation","angle":0,"index":3,"text":"$$\n\\begin{array}{r l} & \\mathrm {X} _ {\\mathrm {S}} \\mathrm {X} _ {1} \\mathrm {X} _ {2} \\dots \\dots \\mathrm {X} _ {\\mathrm {n}} \\\\ + & \\mathrm {Y} _ {\\mathrm {S}} \\mathrm {Y} _ {1} \\mathrm {Y} _ {2} \\dots \\dots \\mathrm {Y} _ {\\mathrm {n}} \\\\ \\hline & \\mathrm {F} _ {\\mathrm {S}} \\mathrm {F} _ {1} \\mathrm {F} _ {2} \\dots \\dots \\mathrm {F} _ {\\mathrm {n}} \\end{array} \\quad \\begin{array}{r l} & \\mathrm {F} _ {\\mathrm {S} 1} = \\mathrm {X} _ {\\mathrm {S}} \\oplus \\mathrm {Y} _ {\\mathrm {S}} \\oplus \\mathrm {C} _ {\\mathrm {S}} \\\\ & \\mathrm {F} _ {\\mathrm {S} 2} = \\mathrm {F} _ {\\mathrm {S}} \\end{array}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":31,"id":"8fd5fa21-af2c-4677-9b25-6df18e5eb2f0","page_size":[595,841],"block_position":"31-3"},{"bbox":[151,195,422,211],"type":"interline_equation","angle":0,"index":4,"text":"$$\n\\begin{array}{l} \\mathbf {V} = \\mathbf {F} _ {\\mathbf {S} 1} \\oplus \\mathbf {F} _ {\\mathbf {S} 2} \\\\ \\cdot \\mathbf {V} = \\mathbf {F} _ {\\mathbf {S} 1} \\oplus \\mathbf {F} _ {\\mathbf {S} 2} = \\mathbf {X} _ {\\mathbf {S}} \\oplus \\mathbf {Y} _ {\\mathbf {S}} \\oplus \\mathbf {C} _ {\\mathbf {S}} \\oplus \\mathbf {F} _ {\\mathbf {S}} \\\\ \\end{array}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":31,"id":"b5b2ea00-748a-4357-ade4-3fc1c8e95a37","page_size":[595,841],"block_position":"31-4"},{"bbox":[152,216,387,232],"type":"text","angle":0,"index":5,"text":"=Fs1 $\\bar { \\mathsf { F } } _ { S 2 } = 0 1$ ，则正溢出； $\\bar { \\mathsf { F } } _ { 5 1 } \\mathsf { F } _ { 5 2 } = 1 0$ ，则负溢出。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":31,"id":"f0191495-2fe2-4807-8339-0e60284c2f49","page_size":[595,841],"block_position":"31-5"},{"bbox":[86,277,232,288],"type":"text","angle":0,"index":6,"text":"核心部件：一个普通的二进制并行加法器。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":31,"id":"76e18074-5fbd-41c6-8d53-2758280d2ead","page_size":[595,841],"block_position":"31-6"},{"bbox":[87,290,167,301],"type":"text","angle":0,"index":7,"text":"A:累加器，存放[X]补","id":"2c2ee6e3-86b2-457e-80a3-33af8ab42432","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":31,"page_size":[595,841],"block_position":"31-7"},{"bbox":[88,303,166,314],"type":"text","angle":0,"index":8,"text":"B:寄存器，存放 $[ \\boldsymbol { \\mathsf { Y } } ] _ { \\sharp \\flat }$","id":"98087c12-f0eb-4e01-a09d-2385043d79f6","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":31,"page_size":[595,841],"block_position":"31-8"},{"bbox":[88,317,124,327],"type":"text","angle":0,"index":10,"text":"取反电路：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":31,"id":"2cf619aa-b850-43d7-8e64-8dcd9f6f7512","page_size":[595,841],"block_position":"31-9"},{"bbox":[89,329,210,353],"type":"text","angle":0,"index":11,"text":"·控制信号P $\\cdot = 1$ ，取反电路工作；$\\mathsf { P } \\mathsf { = } \\mathsf { 0 }$ ：不工作 (不取反)","id":"2bc592e4-dcb2-4290-828a-dbed8a1dbcb4","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":31,"page_size":[595,841],"block_position":"31-10"},{"bbox":[90,355,148,365],"type":"text","angle":0,"index":12,"text":"· P= ADD/SUB","id":"67014c06-8daf-47e5-affa-1e09a5fc131e","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":31,"page_size":[595,841],"block_position":"31-11"},{"bbox":[213,294,388,384],"index":14,"angle":0,"type":"image","img_path":"/ae54ce06282a8e6bd6869a6dae889b392853294a3eb61a65b62d54b612cdaac3.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.29411764705882354,"page_idx":31,"id":"77ade641-2992-425e-b7b8-c72e3ba369a7","page_size":[595,841],"block_position":"31-12"},{"bbox":[87,381,123,391],"type":"title","angle":0,"index":15,"text":"# 工作原理：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":31,"id":"1c8b2dbf-9317-41c8-9b06-0b626a4e137d","page_size":[595,841],"block_position":"31-13"},{"bbox":[89,394,315,405],"type":"text","angle":0,"index":16,"text":"- ADD/SUB ${ \\tt = } 0$ ：补码加法器，B寄存器→并行加法器 $[ \\mathsf { P } \\mathsf { \\tau } ] = \\mathsf { 0 } ]$","id":"711af817-b5f5-4094-b025-ce5125800684","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":31,"page_size":[595,841],"block_position":"31-14"},{"bbox":[89,407,359,417],"type":"text","angle":0,"index":17,"text":"·ADD/SUB=1:补码减法器，B取反→并行加法器（ $\\scriptstyle \\mathbf { P } = 1$ ），且并行加法器","id":"13cefb36-60da-4efc-96e9-c782f609d2ce","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":31,"page_size":[595,841],"block_position":"31-15"},{"bbox":[98,419,338,426],"type":"text","angle":0,"index":19,"text":"的最低位的进位-1 即R取反加1：相当干rY1..加r-V1.. →减法运算","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":31,"id":"39b32a48-f2e2-48c7-9de6-3cc706eabee5","page_size":[595,841],"block_position":"31-16"},{"bbox":[351,416,381,427],"index":20,"angle":0,"type":"image","img_path":"/d9d5837f8365fb673cb70ee9ba3a74bd16f123df640119ed41a51adfb2ae366a.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.2,"page_idx":31,"id":"d900ae9a-9471-4d74-9c29-9f425c6ab9c5","page_size":[595,841],"block_position":"31-17"},{"bbox":[88,437,132,449],"type":"title","angle":0,"index":21,"text":"# 乘法实现","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":31,"id":"a8a9ee9b-0b66-45ea-ba8f-81987c2344fb","page_size":[595,841],"block_position":"31-18"},{"bbox":[120,469,383,646],"index":22,"angle":0,"type":"image","img_path":"/4e246a115c30e7de0c4f12d19cb99bf90bc9cd7e8afda36ca1d83dca0bfc5c41.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.44201680672268906,"page_idx":31,"id":"df3f0be4-a67a-47c8-85ec-ed6fb3ae7842","page_size":[595,841],"block_position":"31-19"}],[{"bbox":[92,75,136,83],"type":"title","angle":0,"index":0,"text":"# 昇法少骤","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":32,"id":"73a4117f-435e-48eb-8519-79672cf0a5b4","page_size":[595,841],"block_position":"32-0"},{"bbox":[92,88,212,101],"type":"text","angle":0,"index":1,"text":"X [X]原=Xs X, Xx....Xn","id":"c3ef1ea0-7abb-4324-bb15-b40da37529b9","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":32,"page_size":[595,841],"block_position":"32-1"},{"bbox":[92,105,210,117],"type":"text","angle":0,"index":2,"text":"[Y]原=Ys Y, Y....Yn","id":"d8bd1996-030a-4d3c-9b02-424b6048b547","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":32,"page_size":[595,841],"block_position":"32-2"},{"bbox":[92,121,211,133],"type":"text","angle":0,"index":3,"text":"： $\\mathbf { P } { = } \\mathbf { X } { \\cdot } \\mathbf { Y }$ ，Ps是积的符号","id":"31796b90-86af-4290-b5bb-c907ee2f00bf","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":32,"page_size":[595,841],"block_position":"32-3"},{"bbox":[92,137,239,149],"type":"text","angle":0,"index":5,"text":"$\\textcircled{1}$ 符号位单独处理 Ps=Xs Ys","id":"9849ed51-1cee-4786-bc52-84c7a0f18189","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":32,"page_size":[595,841],"block_position":"32-4"},{"bbox":[92,153,249,167],"type":"text","angle":0,"index":6,"text":"$\\textcircled{2}$ 绝对值进行数值运算|P|=|X|*|Y|","id":"b4b033ac-da40-4119-a154-ed43b83e787c","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":32,"page_size":[595,841],"block_position":"32-5"},{"bbox":[92,169,440,197],"type":"text","angle":0,"index":7,"text":"$\\textcircled{3}$ 初始部分积为0，从乘数最低位开始累加、右移： $\\yen 123$ ，部分积加|X|， $\\scriptstyle \\pmb { \\ Y } _ { \\mathbf { l } = \\mathbf { 0 } }$部分积加0，累加结果右移一位，得新部分积。","id":"4eab991f-c9c8-4798-94ee-eac599bdde12","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":32,"page_size":[595,841],"block_position":"32-6"},{"bbox":[92,201,276,213],"type":"text","angle":0,"index":8,"text":"$\\textcircled{4}$ 累加右移n次，即 $\\mathbf { \\beta } = \\mathbf { n }$","id":"4c38a9ba-4b40-443e-a516-cf1a77dd6776","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":32,"page_size":[595,841],"block_position":"32-7"},{"bbox":[89,245,108,255],"index":10,"angle":0,"type":"image","img_path":"/cae87f09a7a831e5a8b40bbdeee629097938a3a1a74a22e443e586a8ee6afeb5.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.2,"page_idx":32,"id":"7e4f66d4-0ff9-4a0e-a950-d5fa6fcd5653","page_size":[595,841],"block_position":"32-8"},{"bbox":[104,255,318,422],"index":11,"angle":0,"type":"image","img_path":"/e9f01da7655ec11fc4a057bacb897b4b59ba6b38198840dcaf3782c713afc75c.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.3596638655462185,"page_idx":32,"id":"f527fbdd-80d3-49ff-ba69-c5568f44ebcc","page_size":[595,841],"block_position":"32-9"},{"bbox":[324,301,464,361],"index":12,"angle":0,"type":"image","img_path":"/c9d69a7ab9cac99299f1038b5f374410d4c9dd5a62edfb63afd19f1e01341604.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.23529411764705882,"page_idx":32,"id":"4da5e776-efa9-45be-a2a7-c54dfc16d67a","page_size":[595,841],"block_position":"32-10"},{"bbox":[337,374,407,386],"type":"title","angle":0,"index":13,"text":"# 控制逻辑电路","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":32,"id":"62dd813f-c194-4dfd-b334-8625158be822","page_size":[595,841],"block_position":"32-11"},{"bbox":[348,391,450,401],"type":"text","angle":0,"index":14,"text":"$\\scriptstyle \\mathbf { Q } _ { n } = \\mathbf { 0 }$ : +0 (0...0&B)","id":"112ae518-c18a-4d81-9cd7-70574f331a70","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":32,"page_size":[595,841],"block_position":"32-12"},{"bbox":[348,405,451,416],"type":"text","angle":0,"index":15,"text":"$\\scriptstyle \\mathbf { Q } _ { n } = 1$ : +|X| (11...1&B)","id":"79d644e4-328c-42e1-b418-dcacaf8ccfd5","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":32,"page_size":[595,841],"block_position":"32-13"},{"bbox":[446,423,464,439],"index":17,"angle":0,"type":"image","img_path":"/55167d2f731515103cb555f2a8a983360cf03536b770a98fecac758e276be506.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.2,"page_idx":32,"id":"10b975ab-1ab7-490c-8009-64123b3a2db2","page_size":[595,841],"block_position":"32-14"},{"bbox":[122,470,270,487],"type":"title","angle":0,"index":18,"text":"# 3、原码乘法的硬件实现","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":32,"id":"baa0a70b-49f6-4963-9524-fb4d5c22a74f","page_size":[595,841],"block_position":"32-15"},{"bbox":[95,499,189,513],"type":"text","angle":0,"index":19,"text":"A:累加寄存器","id":"2dffb7e1-e712-4e26-90b9-8c6c35581fbf","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":32,"page_size":[595,841],"block_position":"32-16"},{"bbox":[95,519,199,533],"type":"text","angle":0,"index":20,"text":"B:被乘数寄存器","id":"779d0365-252c-489e-b915-2a1a359f74bc","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":32,"page_size":[595,841],"block_position":"32-17"},{"bbox":[95,539,189,553],"type":"text","angle":0,"index":21,"text":"Q:乘数寄存器","id":"acff6050-935f-4ee3-bc93-36e4f914d0a7","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":32,"page_size":[595,841],"block_position":"32-18"},{"bbox":[95,560,279,575],"type":"text","angle":0,"index":22,"text":"桶形移位器：F、Q联合逻辑右移","id":"8b123c74-8d9d-4538-ad9f-e4ad827e83c7","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":32,"page_size":[595,841],"block_position":"32-19"},{"bbox":[110,578,292,592],"type":"text","angle":0,"index":24,"text":"A-{C，F.F1)Q-{Fn1)","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":32,"id":"5b63b644-9baf-4f18-a35b-2bf7242f10a9","page_size":[595,841],"block_position":"32-20"},{"bbox":[307,470,476,600],"index":25,"angle":0,"type":"image","img_path":"/50c123f3e8175837087fdfcd305333c9c9036c5008f2054a02668e8566c45fd6.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.28403361344537814,"page_idx":32,"id":"426bac4a-c8bf-4427-9a31-bffa6d728c38","page_size":[595,841],"block_position":"32-21"},{"bbox":[120,606,150,620],"type":"title","angle":0,"index":26,"text":"# 初始：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":32,"id":"b8edca27-20b7-4106-bd0e-ee808ea57e3c","page_size":[595,841],"block_position":"32-22"},{"bbox":[105,624,142,636],"type":"text","angle":0,"index":27,"text":"A=0","id":"63ef5ff0-1c81-477d-9688-0ca814212d8d","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":32,"page_size":[595,841],"block_position":"32-23"},{"bbox":[105,641,150,655],"type":"text","angle":0,"index":28,"text":"B=|X|","id":"ff9ae9d3-3695-4759-8513-2869d2ee98de","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":32,"page_size":[595,841],"block_position":"32-24"},{"bbox":[105,659,151,672],"type":"text","angle":0,"index":29,"text":"Q=IYI","id":"0d7d4426-0694-4999-bb9e-ea768fa1e362","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":32,"page_size":[595,841],"block_position":"32-25"},{"bbox":[105,677,169,688],"type":"text","angle":0,"index":30,"text":"计数器=n","id":"6bf1bc3e-f9d0-4f21-8b33-dbc657b804a7","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":32,"page_size":[595,841],"block_position":"32-26"},{"bbox":[186,629,269,645],"type":"title","angle":0,"index":32,"text":"# 累加、右移n次","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":32,"id":"611e98fd-ba36-4efc-a240-43233883270c","page_size":[595,841],"block_position":"32-27"},{"bbox":[185,646,270,670],"index":33,"angle":0,"type":"image","img_path":"/cee718a471c69c493caac3a6ae32770ed50a1dfbd57d645b620c0ef6a559157a.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.2,"page_idx":32,"id":"250b1a19-1570-4818-b74b-5cc0943ecc12","page_size":[595,841],"block_position":"32-28"},{"bbox":[321,606,351,620],"type":"title","angle":0,"index":34,"text":"# 结果：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":32,"id":"319a0bd7-9eaa-4fed-90e3-a80cf6fe37eb","page_size":[595,841],"block_position":"32-29"},{"bbox":[282,624,395,638],"type":"text","angle":0,"index":35,"text":"A=乘积绝对值高位","id":"c3c4b613-f114-43c5-914b-b0663c83981f","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":32,"page_size":[595,841],"block_position":"32-30"},{"bbox":[282,640,330,655],"type":"text","angle":0,"index":36,"text":"B =｜X)","id":"5ffc73cd-592b-42ac-bf55-9ac9a9b6f171","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":32,"page_size":[595,841],"block_position":"32-31"},{"bbox":[282,659,395,671],"type":"text","angle":0,"index":37,"text":"$\\pmb { \\mathrm { Q } } =$ 乘积绝对值低位","id":"74dbdae7-cbc8-4d06-a4a1-9ac50153b96b","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":32,"page_size":[595,841],"block_position":"32-32"},{"bbox":[282,676,345,688],"type":"text","angle":0,"index":38,"text":"计数器 $\\mathtt { \\mathtt { = 0 } }$","id":"4348d888-98d9-47c4-a811-7343240f3dd5","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":32,"page_size":[595,841],"block_position":"32-33"},{"bbox":[448,677,467,696],"index":40,"angle":0,"type":"image","img_path":"/35618de2ffe45452a153e0af96cb4963364157976dd9ea747ea1ac8ccbe444b9.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.2,"page_idx":32,"id":"d2cc634a-ec01-4932-9f73-b2d37f182142","page_size":[595,841],"block_position":"32-34"}],[{"bbox":[101,78,229,95],"type":"title","angle":0,"index":0,"text":"# 原码一位乘法流程：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":33,"id":"532ba6c1-542f-4cbd-b540-e7ddc2d30925","page_size":[595,841],"block_position":"33-0"},{"bbox":[91,108,348,310],"index":1,"angle":0,"type":"image","img_path":"/0c453e8e70a0be8534b121ac4c245278583c49001e1d8fb673fd9262cba1b395.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.4319327731092437,"page_idx":33,"id":"6128816e-7fa4-432d-8526-24f51f9e30c9","page_size":[595,841],"block_position":"33-1"},{"bbox":[384,74,464,319],"index":2,"angle":0,"type":"image","img_path":"/a36d031b37fdd38c2990cb53473d9ab5f781d7bc3d220d4963c8e5341bc4d63e.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.2,"page_idx":33,"id":"d4840523-0473-4fc9-bddf-e566980252fb","page_size":[595,841],"block_position":"33-2"},{"bbox":[88,343,111,356],"type":"title","angle":0,"index":3,"text":"# 除法","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":33,"id":"325b3f7f-5bc3-42d6-aee2-04cb2fd54a62","page_size":[595,841],"block_position":"33-3"},{"bbox":[95,365,262,378],"type":"text","angle":0,"index":4,"text":"X=+0.1011，Y=-0.1101，求X÷Y","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":33,"id":"dcf6c189-cd57-42ce-bd44-326aadc54b84","page_size":[595,841],"block_position":"33-4"},{"bbox":[95,382,150,394],"type":"title","angle":0,"index":5,"text":"# 手工除法：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":33,"id":"047674e9-e216-44c3-a7c7-fb334f74294b","page_size":[595,841],"block_position":"33-5"},{"bbox":[109,396,258,409],"type":"text","angle":0,"index":6,"text":"·判断被除数是否大于除数，决定商0/1。","id":"4bcbf3b1-fa64-4341-934e-389cdb341166","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":33,"page_size":[595,841],"block_position":"33-6"},{"bbox":[109,411,332,423],"type":"text","angle":0,"index":7,"text":"■若商1，则减除数（得部分余数），再添加一位数或者添加0","id":"e93a2766-43f9-4b92-b05e-6d7d5f9ef498","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":33,"page_size":[595,841],"block_position":"33-7"},{"bbox":[109,425,252,436],"type":"text","angle":0,"index":8,"text":"·若商0，则直接添加一位数或者添加0","id":"a2f01046-9eaa-4d0a-8311-961b05eecb9c","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":33,"page_size":[595,841],"block_position":"33-8"},{"bbox":[95,446,238,458],"type":"title","angle":0,"index":10,"text":"# 改进手工算法 适合机器运算：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":33,"id":"92598adc-aa82-4e5d-9e3e-5649a2152d77","page_size":[595,841],"block_position":"33-9"},{"bbox":[108,461,347,484],"type":"text","angle":0,"index":11,"text":"·计算机通过做减法测试来实现判断：结果大于等于0，表明够商1；结果小于0，表明不够减，商0。","id":"60a8ecb7-4ad5-4c83-9e1e-1e7babf791c5","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":33,"page_size":[595,841],"block_position":"33-10"},{"bbox":[108,486,325,498],"type":"text","angle":0,"index":12,"text":"■计算机将部分余数左移一位，再直接与不右移的除数相减。","id":"9b041d02-cf96-4f16-bc59-b02394f74533","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":33,"page_size":[595,841],"block_position":"33-11"},{"bbox":[95,502,235,513],"type":"title","angle":0,"index":14,"text":"# 即：减（+除数相反数的补码）","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":33,"id":"c42770a6-fb32-4559-984d-3192f7b40c6b","page_size":[595,841],"block_position":"33-12"},{"bbox":[123,518,193,530],"type":"text","angle":0,"index":15,"text":"左移，构成循环","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":33,"id":"7c11290f-424e-49e3-aada-e619323a9822","page_size":[595,841],"block_position":"33-13"},{"bbox":[265,534,282,544],"index":16,"angle":0,"type":"image","img_path":"/080881940dddf1c0a012c30525b5c825fe4016a68c3cf727c989870893f7a3b6.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.2,"page_idx":33,"id":"a8b0dae6-52b7-416d-8246-40a0824ee908","page_size":[595,841],"block_position":"33-14"},{"bbox":[333,359,455,485],"index":17,"angle":0,"type":"image","img_path":"/bc67a26ef8c12a855344bd8b9a0214ec1762b77d8e934cbed0ba98eaad5f8e08.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.20504201680672268,"page_idx":33,"id":"2d98c0f4-26fe-4a0a-8830-144a33f8ecd2","page_size":[595,841],"block_position":"33-15"}],[{"bbox":[86,75,473,301],"index":0,"angle":0,"type":"image","img_path":"/f60008b096af71284ca25b36cf55312ff0d5181018ae1d26bb5b13719529cfef.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.6504201680672269,"page_idx":34,"id":"5e653356-3046-4f85-ae52-7f72ce42e385","page_size":[595,841],"block_position":"34-0"},{"bbox":[132,353,428,472],"index":1,"angle":0,"type":"image","img_path":"/913d33a05eded314c13c28fbf1daa186986245ed66e8eb12b6d67956866f8a7e.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.49747899159663866,"page_idx":34,"id":"63be185e-0637-4267-ad51-31a0f9a62013","page_size":[595,841],"block_position":"34-1"},{"bbox":[88,530,164,543],"type":"title","angle":0,"index":2,"text":"# 不恢复余数算法","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":34,"id":"d8389834-481b-487d-8467-9f233d15ea03","page_size":[595,841],"block_position":"34-2"},{"bbox":[102,555,549,589],"type":"text","angle":0,"index":3,"text":"又称为加减交替法：当不够减时，不恢复余数，用加上除数（+IYI）的办法来继续求下一位商，其他操作不变。","id":"9308e321-fac2-45b6-aaa1-955fb91e0204","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":34,"page_size":[595,841],"block_position":"34-3"},{"bbox":[102,593,247,609],"type":"text","angle":0,"index":4,"text":"加减交替法的规则如下：","id":"0c1c4abe-0d1e-4322-acf0-4d0b293caa48","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":34,"page_size":[595,841],"block_position":"34-4"},{"bbox":[119,613,524,631],"type":"text","angle":0,"index":6,"text":"余数为正：商上1，求下一位商的办法，是余数左移一位，再减去除数；","id":"2ff6dfc4-dcbb-4822-b449-3726101b9efb","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":34,"page_size":[595,841],"block_position":"34-5"},{"bbox":[119,635,523,651],"type":"text","angle":0,"index":7,"text":"余数为负：商上0，求下一位商的办法，是余数左移一位，再加上除数。","id":"709d9f94-744a-4738-a4d7-ab7c2a1e3ed3","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":34,"page_size":[595,841],"block_position":"34-6"},{"bbox":[119,657,522,673],"type":"text","angle":0,"index":8,"text":"若最后一次上商为0，而又需得到正确余数，则最后一次仍需恢复余数。","id":"753e6821-561c-41b1-8882-7786ecd3f02c","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":34,"page_size":[595,841],"block_position":"34-7"},{"bbox":[105,680,161,698],"type":"text","angle":0,"index":10,"text":"\"Why?","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":34,"id":"05633b19-b1ed-428a-a458-4a4febad18f0","page_size":[595,841],"block_position":"34-8"}],[{"bbox":[114,79,402,256],"index":0,"angle":0,"type":"image","img_path":"/52d547c67d42a9203c76f16d5b457286133f23e717cfb269e410a277f0f94a48.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.48403361344537815,"page_idx":35,"id":"cea06f98-3d68-4070-a8c7-51629882d5f1","page_size":[595,841],"block_position":"35-0"},{"bbox":[89,303,320,502],"index":1,"angle":0,"type":"image","img_path":"/1635b02d62a20c8866fd2f847b7be51a7eb63e2baf3207aed8f554ea8f18d46a.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.38823529411764707,"page_idx":35,"id":"52049f4a-e93e-4d11-99a5-badf9a23c7ef","page_size":[595,841],"block_position":"35-1"},{"bbox":[338,296,460,310],"type":"text","angle":0,"index":2,"text":"： $\\textcircled{1}$ 如何控制加减交替？","id":"d7051a7b-271c-4c72-a71c-939e78ffdeb5","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":35,"page_size":[595,841],"block_position":"35-2"},{"bbox":[339,313,415,327],"type":"text","angle":0,"index":3,"text":"： $\\textcircled{2}$ 如何上商？","id":"1d52eaf9-c254-49ec-afe9-d3efc7b9cb16","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":35,"page_size":[595,841],"block_position":"35-3"},{"bbox":[339,331,511,362],"type":"text","angle":0,"index":4,"text":"$\\textcircled{3}$ 加减与移位次数如何控制，结果在哪里？","id":"0e2ba0db-f98e-4d83-9fbc-f63661ec4ef8","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":35,"page_size":[595,841],"block_position":"35-4"},{"bbox":[339,370,467,384],"type":"text","angle":0,"index":5,"text":"$\\textcircled{1}$ 加减交替：控制逻辑","id":"5c9c8a2b-37e5-4365-a302-68f0e3d9b22c","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":35,"page_size":[595,841],"block_position":"35-5"},{"bbox":[351,388,507,415],"type":"text","angle":0,"index":7,"text":"$\\scriptstyle \\mathbf { Q } _ { \\mathrm { n } } = 1$ 表明够减一下一次做减法→B中的|Y|取反（11...11B)","id":"f16d28ab-8500-42f7-adb8-99f33f0ea214","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":35,"page_size":[595,841],"block_position":"35-6"},{"bbox":[351,418,502,445],"type":"text","angle":0,"index":8,"text":"$\\scriptstyle \\mathbf { Q } _ { \\mathrm { n } } = \\mathbf { 0 }$ 表明不够减一下一次做加法→B中的|Y|不取反 (0...00B)","id":"ed5288fa-8934-4b7b-ac62-2d8080acd0a2","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":35,"page_size":[595,841],"block_position":"35-7"},{"bbox":[327,450,420,464],"type":"title","angle":0,"index":10,"text":"# $\\textcircled{2}$ 上商：Fs取反","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":35,"id":"6db6a075-fe45-485e-a79b-04c5c5234823","page_size":[595,841],"block_position":"35-8"},{"bbox":[339,467,443,481],"type":"text","angle":0,"index":11,"text":"·Fs=0表明够减 $\\scriptstyle \\mathbf { Q } _ { \\mathsf { n } } =$","id":"efdcbe7f-d8c7-4580-9e70-91e5ae20990d","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":35,"page_size":[595,841],"block_position":"35-9"},{"bbox":[339,484,420,511],"type":"text","angle":0,"index":12,"text":"$\\bar { \\mathsf { F } } _ { \\mathsf { S } } \\mathsf { = }$ 1表明不够减→Qn=0","id":"0c027faf-900b-4625-88df-c82dc5a8489a","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":35,"page_size":[595,841],"block_position":"35-10"},{"bbox":[440,457,520,518],"index":14,"angle":0,"type":"image","img_path":"/3f2316993b77cc87c3b76fb52c1b9a866d3d27a79298726c073a1420897aecdd.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.2,"page_idx":35,"id":"65b0306b-f2f2-4d0f-881b-9c6be4d5e1bf","page_size":[595,841],"block_position":"35-11"},{"bbox":[88,561,143,575],"type":"footer","angle":0,"index":1000014,"text":"定点运算器","color":{"line":"rgba(164, 164, 164, 1)","fill":"rgba(164, 164, 164, 1)"},"page_idx":35,"is_discarded":true,"id":"6b78796f-6785-45cb-a0f1-f2183296ac21","page_size":[595,841],"block_position":"35-12"}],[{"bbox":[102,84,140,99],"type":"title","angle":0,"index":0,"text":"# 构成：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":36,"id":"40423fbf-02f7-49ed-8568-4f2ef6d86dd1","page_size":[595,841],"block_position":"36-0"},{"bbox":[108,104,176,117],"type":"text","angle":0,"index":1,"text":"内部总线IB","id":"7645cd60-53e1-4940-877e-b25ef4514968","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":36,"page_size":[595,841],"block_position":"36-1"},{"bbox":[108,123,141,135],"type":"text","angle":0,"index":2,"text":"· ALU","id":"1609efb5-36c6-4360-b494-b59ecfe4f45e","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":36,"page_size":[595,841],"block_position":"36-2"},{"bbox":[108,142,221,154],"type":"text","angle":0,"index":3,"text":"·2个暂存器：LA和LB","id":"6b97f8e2-cdac-4d31-8a52-552a2f6b698d","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":36,"page_size":[595,841],"block_position":"36-3"},{"bbox":[108,160,254,174],"type":"text","angle":0,"index":4,"text":"·通用寄存器堆GPR：n+1个","id":"86d4fcec-eaea-4997-9993-097c66ae8fdc","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":36,"page_size":[595,841],"block_position":"36-4"},{"bbox":[248,86,521,191],"index":6,"angle":0,"type":"image","img_path":"/e985aecc3e9eb9e76340b5366b6fa387f7ab170ac283a9cc5778b77f921838fd.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.4588235294117647,"page_idx":36,"id":"b2095fdd-3691-49eb-969d-ebacc27813b0","page_size":[595,841],"block_position":"36-5"},{"bbox":[100,193,247,209],"type":"text","angle":0,"index":7,"text":"· $\\mathrm { L A } _ { \\mathrm { i n } } = 1$ ：IB上数据写入LA","id":"fa83595e-06be-4f61-bf99-ae9ea5bbe2d2","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":36,"page_size":[595,841],"block_position":"36-6"},{"bbox":[101,213,248,227],"type":"text","angle":0,"index":8,"text":"： $\\mathsf { L B } _ { \\mathrm { i n } } = 1$ :IB上数据写入LB","id":"07c63871-35c0-49e5-ac85-7872c5843d12","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":36,"page_size":[595,841],"block_position":"36-7"},{"bbox":[101,232,266,262],"type":"text","angle":0,"index":9,"text":"ALUOP：功能码/运算码，选择ALU执行的运算","id":"14b2a64e-c8fe-4df7-b084-c1fea8aad53a","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":36,"page_size":[595,841],"block_position":"36-8"},{"bbox":[101,267,257,297],"type":"text","angle":0,"index":10,"text":"$\\mathtt { A L U } _ { \\mathrm { o u t } } = \\mathbb { 1 }$ ：ALU的运算结果（即输出端F）→IB","id":"05f80c2f-e298-41a9-910b-2996ca6f7c0f","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":36,"page_size":[595,841],"block_position":"36-9"},{"bbox":[279,194,446,208],"type":"text","angle":0,"index":12,"text":"RA：执行读操作的寄存器地址","id":"c7f49245-8e61-48e9-8de3-ac27d80bb691","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":36,"page_size":[595,841],"block_position":"36-10"},{"bbox":[280,213,451,227],"type":"text","angle":0,"index":13,"text":"WA：执行写操作的寄存器地址","id":"8a41713f-9847-429e-ab07-a7abcffeb1b4","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":36,"page_size":[595,841],"block_position":"36-11"},{"bbox":[280,232,512,263],"type":"text","angle":0,"index":14,"text":"$\\mathtt { G R } _ { \\mathtt { o u t } } = 1$ ：读出RA指定的寄存器数据送到IB上(Reg[RA]→IB)","id":"7d1ff337-a524-41ed-a2b0-3f3e8c0470de","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":36,"page_size":[595,841],"block_position":"36-12"},{"bbox":[280,266,512,299],"type":"text","angle":0,"index":15,"text":"$\\mathsf { G R } _ { \\mathrm { i n } } = 1$ ：将IB上的数据写入由写地址WA选中的寄存器 (IB→Reg[WA])","id":"e6360b9c-2a22-4323-b4da-995e13ddc084","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":36,"page_size":[595,841],"block_position":"36-13"},{"bbox":[87,354,250,382],"type":"text","angle":0,"index":17,"text":"$\\gtrdot$ 数据通路：指数据在硬件系上流动的过程与控制步骤","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":36,"id":"2198c9b0-7ecc-4ff9-bf5d-ecd15b731ca8","page_size":[595,841],"block_position":"36-14"},{"bbox":[216,356,464,451],"index":18,"angle":0,"type":"image","img_path":"/125f1f976a45bde61707512608d443be1397a84c51bebbeef84d0565bd4ae8b7.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.41680672268907565,"page_idx":36,"id":"c4c2a7be-2cec-45f9-8555-809f17d1eaf5","page_size":[595,841],"block_position":"36-15"},{"bbox":[86,458,323,470],"type":"text","angle":0,"index":19,"text":"在总线上传送数据的数据通路：需要一个CPU周期","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":36,"id":"02b8eb87-81e0-43ca-b5f5-485e5fd27aab","page_size":[595,841],"block_position":"36-16"},{"bbox":[96,474,307,486],"type":"text","angle":0,"index":20,"text":"源部件将数据送上总线；目的部件从总线上接收数据","id":"4c27fe3a-a3db-4860-b979-309cdb8fce31","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":36,"page_size":[595,841],"block_position":"36-17"},{"bbox":[96,488,434,512],"type":"text","angle":0,"index":21,"text":"任何要把数据送上总线的源部件，其数据输出端必须以三态输出的形式与总线连接，并由使能信号控制","id":"ccf11f89-d28f-4ae0-bb8b-f3943d776373","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":36,"page_size":[595,841],"block_position":"36-18"},{"bbox":[96,514,434,535],"type":"text","angle":0,"index":22,"text":"·对于某个总线系统来说，各个总线源部件的数据输出使能信号不能同时有效：任何时刻只能允许一个部件将数据送上总线以保证分时高用总线","id":"9ddd97ed-6d23-4655-9902-d87b5b9e2798","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":36,"page_size":[595,841],"block_position":"36-19"}],[{"bbox":[167,77,329,92],"type":"header","angle":0,"index":-99999,"text":"（）车芯线给构","color":{"line":"rgba(164, 164, 164, 1)","fill":"rgba(164, 164, 164, 1)"},"page_idx":37,"is_discarded":true,"id":"aedbfc41-b376-44f8-94a7-49de8182e487","page_size":[595,841],"block_position":"37-0"},{"bbox":[106,109,118,127],"index":1,"angle":0,"type":"image","img_path":"/8c546a5f5a7aab5fcbb5bf8368f8ffbbd6e20baab9c2b514f1bcfa342a332678.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.2,"page_idx":37,"id":"8557340d-691f-46a7-8fb8-d798086984a5","page_size":[595,841],"block_position":"37-1"},{"bbox":[123,111,595,157],"type":"text","angle":0,"index":2,"text":"【例4.10】假设在单总线运算器中，完成一条指令ADDR，R作 $\\mathbb { R } _ { 2 } + \\mathbb { R } _ { 7 } \\mathbb { R } _ { 3 }$ ，则分析该操作的数据通路，需要几个CPU周期？","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":37,"id":"a98472de-e685-4dec-a887-e9d07fe753cb","page_size":[595,841],"block_position":"37-2"},{"bbox":[108,163,479,304],"index":3,"angle":0,"type":"image","img_path":"/8195232877e38e022ce58354bf3e0f8e7017782e37ce393611d5c1f08bbd1c6a.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.6235294117647059,"page_idx":37,"id":"be483a81-d04c-4b91-a0bb-b7e4787dcb33","page_size":[595,841],"block_position":"37-3"},{"bbox":[540,241,593,260],"type":"text","angle":0,"index":4,"text":"需要","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":37,"id":"5e9255b3-206b-4691-8049-1a86e9369835","page_size":[595,841],"block_position":"37-4"},{"bbox":[89,306,595,423],"index":5,"angle":0,"type":"table_body","img_path":"/","id":"8800b0ab-3606-44a3-a7f3-770246f5a120","color":{"line":"rgba(103, 194, 63, 1)","fill":"rgba(103, 194, 63, 1)"},"table_body":"
步骤操作发送的信号
1R2→LARA=2, GRout=1, LAin=1
2R7→LBRA=7, GRout=1, LBin=1
3ALU执行F=A+B运算，结果F→R3ALU_OP=加法功能码，ALU_out=1,
","page_idx":37,"page_size":[595,841],"block_position":"37-5"},{"bbox":[88,433,111,459],"index":6,"angle":0,"type":"image","img_path":"/d814906f52ca58133470d1ec963e40201e7792ebe345adbefb39a1651947d1be.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.2,"page_idx":37,"id":"c36a45b5-4d18-4cd0-92cf-be171463dc66","page_size":[595,841],"block_position":"37-6"},{"bbox":[101,456,524,490],"type":"text","angle":0,"index":7,"text":"X 【例4.10】假设在单总线运算器中，完成一条指令ADD $\\pmb { \\mathsf { R } } _ { 3 }$ ${ \\sf R } _ { 2 }$ ，R的运算操$\\mathsf { E R } _ { 2 } + \\mathsf { R } _ { 7 } \\to \\mathsf { R } _ { 3 }$ ，则分析该操作的数据通路，需要几个CPU周期？","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":37,"id":"6968759c-15bf-42ed-9251-70ce1b786470","page_size":[595,841],"block_position":"37-7"},{"bbox":[102,494,365,593],"index":8,"angle":0,"type":"image","img_path":"/a7fb5924317ec14cc0f9c5e3f8fb93545692880d72c48a901eeeba9aab0db9c9.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.44201680672268906,"page_idx":37,"id":"1adc469a-a6ab-4826-95c8-18fdb76d88a6","page_size":[595,841],"block_position":"37-8"},{"bbox":[89,595,537,679],"index":9,"angle":0,"type":"table_body","img_path":"/","id":"a8cdde1c-506a-437e-8aee-f901edc454f3","color":{"line":"rgba(103, 194, 63, 1)","fill":"rgba(103, 194, 63, 1)"},"table_body":"
步骤操作发送的信号
1R2→LARA=2, GRout=1, LAin=1
2R7→LBRA=7, GRout=1, LBin=1
3ALU执行F=A+B运算,结果F→R3ALU_OP=加法功能码, ALU_out=1, GRin=1, WA=3
","page_idx":37,"page_size":[595,841],"block_position":"37-9"},{"bbox":[408,548,517,564],"type":"text","angle":0,"index":10,"text":"需要3个CPU周期","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":37,"id":"2b4020d1-8ed6-49dc-88d2-288a35e32589","page_size":[595,841],"block_position":"37-10"},{"bbox":[277,674,295,686],"index":11,"angle":0,"type":"image","img_path":"/1ea251a75cc631e8da1edd057cec79441fb72193971d3eef097821a86412e2de.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.2,"page_idx":37,"id":"bf42cf91-4e42-43ae-bc12-3b0910474889","page_size":[595,841],"block_position":"37-11"}],[{"bbox":[100,84,135,97],"type":"title","angle":0,"index":0,"text":"# 构成：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":38,"id":"e2311225-e766-4097-b36d-64605392769d","page_size":[595,841],"block_position":"38-0"},{"bbox":[105,100,226,114],"type":"text","angle":0,"index":1,"text":"·2条内部总线：IB1、IB2","id":"fd5a7387-cdeb-4b46-acae-0c770a78e17e","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":38,"page_size":[595,841],"block_position":"38-1"},{"bbox":[105,119,135,129],"type":"text","angle":0,"index":2,"text":"· ALU","id":"306c11c2-a811-46ad-b969-05b26bafc516","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":38,"page_size":[595,841],"block_position":"38-2"},{"bbox":[106,136,168,148],"type":"text","angle":0,"index":3,"text":"·暂存器：LC","id":"63f24b14-6811-496e-afba-eebb7c8349db","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":38,"page_size":[595,841],"block_position":"38-3"},{"bbox":[106,153,238,165],"type":"text","angle":0,"index":4,"text":"·通用寄存器堆GPR：n+1个","id":"10fbe156-b905-4dc1-866a-72e5d001ec22","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":38,"page_size":[595,841],"block_position":"38-4"},{"bbox":[273,78,471,179],"index":6,"angle":0,"type":"image","img_path":"/a87051a1213d96b6ac50fd128c53e03bcfdec6caf2a3592e7cd20df2d14f35b1.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.33277310924369746,"page_idx":38,"id":"63d5516b-f872-4953-95c7-518e55b2df80","page_size":[595,841],"block_position":"38-5"},{"bbox":[95,186,267,198],"type":"text","angle":0,"index":7,"text":"： $\\iota C _ { \\mathrm { i n } } = 1$ ：ALU运算结果写入LC，即F→LC","id":"343c574c-e6a1-4367-9398-1de46287b568","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":38,"page_size":[595,841],"block_position":"38-6"},{"bbox":[95,200,284,212],"type":"text","angle":0,"index":8,"text":"$\\dot { } \\cdot \\mathsf { L C } _ { \\mathsf { o u t } } = 1$ ：LC中数据送上总线IB1，即LC→IB1","id":"eac9fa0b-9b73-46e0-923a-c9574bb398d6","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":38,"page_size":[595,841],"block_position":"38-7"},{"bbox":[95,215,224,226],"type":"text","angle":0,"index":9,"text":"$\\ast$ ALU_OP:ALU功能码/运算码","id":"0073cc77-968b-445e-b682-37042bbd8875","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":38,"page_size":[595,841],"block_position":"38-8"},{"bbox":[95,229,260,240],"type":"text","angle":0,"index":10,"text":"$\\ast$ RA1：执行读出数据到IB1的寄存器地址","id":"428c8d58-a348-4503-9c4d-2eb16026d5af","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":38,"page_size":[595,841],"block_position":"38-9"},{"bbox":[95,243,260,255],"type":"text","angle":0,"index":11,"text":"$\\ast$ RA2：执行读出数据到IB2的寄存器地址","id":"d2c05d68-55ff-4652-b506-d5136710c203","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":38,"page_size":[595,841],"block_position":"38-10"},{"bbox":[95,258,227,269],"type":"text","angle":0,"index":12,"text":"$^ \\ast$ WA：执行写操作的寄存器地址","id":"f8c85cff-319c-46b1-ae17-e427f5719a93","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":38,"page_size":[595,841],"block_position":"38-11"},{"bbox":[291,187,470,211],"type":"text","angle":0,"index":14,"text":"$\\mathsf { G R } _ { \\mathsf { o u t 1 } } = 1$ ：读出RA1指定的寄存器数据送到IB1上，即Reg[RA1]→IB1","id":"8c556bc2-de29-4938-a6c9-4c010ce73b6a","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":38,"page_size":[595,841],"block_position":"38-12"},{"bbox":[291,214,470,238],"type":"text","angle":0,"index":15,"text":"$\\mathsf { G R } _ { \\mathsf { o u t } 2 } = 1$ ：读出RA2指定的寄存器数据送到IB2上，即Reg[RA2]→IB2","id":"437b11ad-6c9c-47bc-847a-a23d78c7f8e9","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":38,"page_size":[595,841],"block_position":"38-13"},{"bbox":[291,240,470,264],"type":"text","angle":0,"index":16,"text":"$\\mathsf { G R } _ { \\mathrm { i n } } = 1$ ：将IB1上的数据写入由写地址WA中的寄存器，即IB1→Reg[WA]","id":"cc80a51e-2946-42a9-b5be-823d72009d0d","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":38,"page_size":[595,841],"block_position":"38-14"},{"bbox":[88,283,119,322],"index":18,"angle":0,"type":"image","img_path":"/75625929eabda9a925a66bd9baf77befd3d36f41294bd86703c1f96680c42d1e.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.2,"page_idx":38,"id":"b28d1ebd-e13d-42cd-897c-3c888f49958d","page_size":[595,841],"block_position":"38-15"},{"bbox":[152,285,271,306],"type":"title","angle":0,"index":19,"text":"# （2）双总线结构","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":38,"id":"343c0fa3-6996-4774-9e53-e8a74a28cacb","page_size":[595,841],"block_position":"38-16"},{"bbox":[107,319,309,388],"type":"text","angle":0,"index":20,"text":"【例4.11】假设在双总线运算器中，同样完成指令ADD ${ \\sf R } _ { 3 }$ $\\mathsf { R } _ { 2 }$ $\\mathsf { R } _ { 7 }$的运算操作 $R _ { 2 } + R _ { 7 } R _ { 3 }$ ，分析数据通路，需要几个CPU周期？","id":"1ee6887c-a140-4996-bf6c-6f72ce851478","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":38,"page_size":[595,841],"block_position":"38-17"},{"bbox":[110,410,220,425],"type":"text","angle":0,"index":21,"text":"需要2个CPU周期","id":"894d3e15-c2af-4048-be91-32d03cc3a0c5","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":38,"page_size":[595,841],"block_position":"38-18"},{"bbox":[316,312,568,433],"index":23,"angle":0,"type":"image","img_path":"/2f5b4666b8610e3c937ac6d9db58dffad8bf5997aa2c849c2a86b02e3a84305b.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.4235294117647059,"page_idx":38,"id":"aae8addf-f26a-4cbe-9315-c18554202e78","page_size":[595,841],"block_position":"38-19"},{"bbox":[99,437,559,512],"index":24,"angle":0,"type":"table_body","img_path":"/","id":"58acc4e8-7fcb-4ad9-b531-6aed3f28502c","color":{"line":"rgba(103, 194, 63, 1)","fill":"rgba(103, 194, 63, 1)"},"table_body":"
步骤操作发送的信号
1R2→IB1, R7→IB2, F=A+B, F→LCRA1=2, RA2=7, ALU_OP=加法功能码,GRout1=1, GRout2=1, LCin=1
2LC→R3LCout=1, GRin=1, WA=3
","page_idx":38,"page_size":[595,841],"block_position":"38-20"},{"bbox":[103,513,401,525],"type":"text","angle":0,"index":25,"text":"思考：如果LC暂存器输出端连接到IB2上，能否完成上述操作？","id":"d10c1adc-3a12-4838-8c13-36fc4f70bcc9","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":38,"page_size":[595,841],"block_position":"38-21"},{"bbox":[103,529,542,558],"type":"text","angle":0,"index":26,"text":"总结：在分析总线结构的运算器数据通路时，基本的原则：在一个CPU周期内，某条总线上的数据必须是唯一的，且不能保留至下一个CPU周期。","id":"e658613d-2b3c-4e20-94d4-cd167b3f1dc2","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":38,"page_size":[595,841],"block_position":"38-22"}],[{"bbox":[96,84,567,102],"type":"text","angle":0,"index":0,"text":"特征：按照运算操作的过程与控制需求，部件之间由专用的独立线路进行连接","id":"d2fec72d-0c55-4c3c-a2b3-218bbf056343","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":39,"page_size":[595,841],"block_position":"39-0"},{"bbox":[96,107,462,124],"type":"text","angle":0,"index":1,"text":"特点：线路比较复杂，但是传输效率高，适用于流水线CPU","id":"be94cb2f-4ada-4d7e-8f25-8a8e59cebf89","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":39,"page_size":[595,841],"block_position":"39-1"},{"bbox":[119,142,258,158],"index":3,"angle":0,"type":"image_caption","text":"单周期CPU的运算器","id":"5fbd56e6-0af8-444b-a238-908b691cfed1","color":{"line":"rgba(13, 83, 222 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":39,"page_size":[595,841],"block_position":"39-2"},{"bbox":[101,163,276,290],"index":4,"angle":0,"type":"image","img_path":"/a7e3272769accbdabd6a76fd92b15f114f238570452f7eb9ae49f9f25ff03f10.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.29411764705882354,"page_idx":39,"id":"74055e56-50ae-49d2-8437-9cd18c3366d7","page_size":[595,841],"block_position":"39-3"},{"bbox":[98,296,302,312],"index":5,"angle":0,"type":"image_caption","text":"每条指令只需一个CPU周期完成","id":"110e08b2-cc95-466b-860b-36602bb46c12","color":{"line":"rgba(13, 83, 222 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":39,"page_size":[595,841],"block_position":"39-4"},{"bbox":[381,143,520,160],"index":6,"angle":0,"type":"image_caption","text":"多周期CPU的运算器","id":"008b4dbc-e0ef-4b82-9783-ca499b097189","color":{"line":"rgba(13, 83, 222 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":39,"page_size":[595,841],"block_position":"39-5"},{"bbox":[337,166,577,292],"index":7,"angle":0,"type":"image","img_path":"/dd24d6faebf55dcbf9ad5485c350bf3bc364b5b8f7b499d47a4200f6e1f95dd1.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.40336134453781514,"page_idx":39,"id":"539cf106-db7e-476c-a800-52f5e6134bd1","page_size":[595,841],"block_position":"39-6"},{"bbox":[352,296,558,312],"index":8,"angle":0,"type":"image_caption","text":"每条指令需要多个CPU周期完成","id":"efe8fe25-2b14-41ad-b2a7-eed5e51ec8bc","color":{"line":"rgba(13, 83, 222 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":39,"page_size":[595,841],"block_position":"39-7"},{"bbox":[92,344,195,357],"index":9,"angle":0,"type":"image_caption","text":"单周期CPU的运算器","id":"4746d800-9431-49fa-9041-44aaf958f943","color":{"line":"rgba(13, 83, 222 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":39,"page_size":[595,841],"block_position":"39-8"},{"bbox":[89,358,218,451],"index":10,"angle":0,"type":"image","img_path":"/314d6cadb0bfe6466e978c155fecfc534eaf9f467fd04c79c80fc0bce91e1af4.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.21680672268907564,"page_idx":39,"id":"b17e5263-407b-4930-ba86-d86d37b79348","page_size":[595,841],"block_position":"39-9"},{"bbox":[88,460,169,473],"type":"text","angle":0,"index":11,"text":"·只需1个clk周期：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":39,"id":"f9e6e2e0-548d-4df7-8545-dd5863446bc1","page_size":[595,841],"block_position":"39-10"},{"bbox":[91,476,214,487],"type":"text","angle":0,"index":12,"text":"RAA=2,RBA=7,WA=3","id":"2885f801-8781-4341-b388-e8ea1c95bf3a","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":39,"page_size":[595,841],"block_position":"39-11"},{"bbox":[91,490,182,500],"type":"text","angle":0,"index":13,"text":"·ALU_OP=加法功能码","id":"76a170cc-3221-4c22-9026-36e14e7ed5ed","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":39,"page_size":[595,841],"block_position":"39-12"},{"bbox":[91,504,211,527],"type":"text","angle":0,"index":14,"text":"·Reg_W=1，在clk的边沿完成R2+R→R3操作","id":"cfe304f4-c726-4af7-bcd0-747c3f7b3043","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":39,"page_size":[595,841],"block_position":"39-13"},{"bbox":[229,344,302,358],"index":16,"angle":0,"type":"image_caption","text":"执行ADD R3,","id":"d4c22f3d-bedc-4525-9073-7e90c1255843","color":{"line":"rgba(13, 83, 222 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":39,"page_size":[595,841],"block_position":"39-14"},{"bbox":[240,359,455,452],"index":17,"angle":0,"type":"image","img_path":"/2a77f41d31aa31d653f723077162ad45fbdb4b02309f3ee781bfbda011629076.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.36134453781512604,"page_idx":39,"id":"1fdb00ea-13f8-4850-aa50-8bc96690275a","page_size":[595,841],"block_position":"39-15"},{"bbox":[243,454,358,467],"type":"text","angle":0,"index":18,"text":"需3个节拍（clk周期）：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":39,"id":"550d2da9-606b-4111-a6be-86be76ffaa83","page_size":[595,841],"block_position":"39-16"},{"bbox":[251,470,451,491],"type":"text","angle":0,"index":19,"text":"·第1个clk（读寄存器）： $\\mathsf { R } _ { 2 } { \\longrightarrow } \\mathsf { A }$ $\\scriptstyle \\mathsf { R } _ { 7 } \\to \\mathsf { B }$ :RAA $^ { 1 = 2 }$RB A=7","id":"5bb76a6c-853b-4966-b32e-1afe7d2b11b2","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":39,"page_size":[595,841],"block_position":"39-17"},{"bbox":[251,495,457,507],"type":"text","angle":0,"index":20,"text":"·第2个clk（执行）：A+B→F:ALU_OP=加法功能码","id":"6480545c-a9cf-41c6-b352-7598e8d70398","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":39,"page_size":[595,841],"block_position":"39-18"},{"bbox":[251,509,445,521],"type":"text","angle":0,"index":21,"text":"·第3个clk（写回）： $\\mathsf { F } { } \\mathsf { R } _ { 3 }$ :WA $^ { = 3 }$ ，Reg_W=1","id":"c868351b-9a21-4151-ad1f-94aa8422b5b5","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":39,"page_size":[595,841],"block_position":"39-19"},{"bbox":[433,522,451,533],"index":23,"angle":0,"type":"image","img_path":"/59c466468b213ccd281befcd1eebfaec5971995dd519d811b30d31d64f190ad7.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.2,"page_idx":39,"id":"7b83ee65-88ab-4ce7-97af-7299b1e6a3e2","page_size":[595,841],"block_position":"39-20"}],[{"bbox":[99,84,452,103],"type":"title","angle":0,"index":0,"text":"# 特征：能够对一组寄存器同时读出或者写入多个数据","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":40,"id":"35c5b4cf-2942-4cff-acdf-0b9ef0d79529","page_size":[595,841],"block_position":"40-0"},{"bbox":[100,113,206,148],"type":"title","angle":0,"index":1,"text":"# 三端口寄存器堆可以同时进行","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":40,"id":"fed69c86-18ea-4791-bf2d-b6e4b97faf1c","page_size":[595,841],"block_position":"40-1"},{"bbox":[119,153,181,168],"type":"text","angle":0,"index":2,"text":"·读A端口","id":"50428790-33cc-475f-a035-95762f3c6ef4","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":40,"page_size":[595,841],"block_position":"40-2"},{"bbox":[119,174,180,189],"type":"text","angle":0,"index":3,"text":"读B端口","id":"f5e428bd-67b4-44ba-a62d-349c47d654d3","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":40,"page_size":[595,841],"block_position":"40-3"},{"bbox":[119,195,184,210],"type":"text","angle":0,"index":4,"text":"·写入数据","id":"d383e9a2-5592-49f2-b808-a4935d2a42a7","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":40,"page_size":[595,841],"block_position":"40-4"},{"bbox":[87,218,204,234],"type":"title","angle":0,"index":6,"text":"# 寄存器堆：4×8位","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":40,"id":"fc514498-1171-4e89-a1de-04fc24e193eb","page_size":[595,841],"block_position":"40-5"},{"bbox":[105,238,199,253],"type":"text","angle":0,"index":7,"text":"$\\mathbb { R } _ { 0 } \\sim \\mathbb { R } _ { 3 } ,$ ，地址2位","id":"d0964443-ae6b-4317-af92-0242de495104","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":40,"page_size":[595,841],"block_position":"40-6"},{"bbox":[105,256,198,269],"type":"text","angle":0,"index":8,"text":"·RA_A:A口地址","id":"8e5136c8-4d46-4459-8d55-a22b56ffc267","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":40,"page_size":[595,841],"block_position":"40-7"},{"bbox":[105,274,218,287],"type":"text","angle":0,"index":9,"text":"·RA_D:A口读出数据","id":"2a070def-486a-4d63-a4ac-0af5257dbf06","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":40,"page_size":[595,841],"block_position":"40-8"},{"bbox":[105,290,196,305],"type":"text","angle":0,"index":10,"text":"RB_A:B口地址","id":"efc76f3c-ad16-45b8-b839-a423a7094548","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":40,"page_size":[595,841],"block_position":"40-9"},{"bbox":[105,308,217,322],"type":"text","angle":0,"index":11,"text":"RB_D:B口读出数据","id":"96244bc0-bb03-43bb-bd06-be42fb4874f5","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":40,"page_size":[595,841],"block_position":"40-10"},{"bbox":[228,105,570,327],"index":13,"angle":0,"type":"image","img_path":"/7f04dad3f2cd8523941ddb3b2e5073b147d88189f7b4c6de8b40c926dd617f13.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.5747899159663865,"page_idx":40,"id":"be85ec28-e378-4215-9b7c-81deaf86e1f5","page_size":[595,841],"block_position":"40-11"},{"bbox":[90,415,289,430],"type":"title","angle":0,"index":14,"text":"# 标志寄存器FR：又称为状态寄存器","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":40,"id":"20e0aabd-d663-4f22-9ded-2aaf743584f8","page_size":[595,841],"block_position":"40-12"},{"bbox":[349,414,452,429],"type":"title","angle":0,"index":15,"text":"# PSW:程序状态字","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":40,"id":"fc606f56-bade-4671-b52b-836677e838b6","page_size":[595,841],"block_position":"40-13"},{"bbox":[107,433,504,465],"type":"text","angle":0,"index":16,"text":"■用来保存ALU操作结果的某些状态，可作为外界对运算结果进行分析的依据，也可以用于判断程序是否要转移的条件","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":40,"id":"16ff2e29-103e-4ae7-95a5-706bce1846cc","page_size":[595,841],"block_position":"40-14"},{"bbox":[90,469,249,483],"type":"title","angle":0,"index":17,"text":"# 最基本的5种运算结果标志：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":40,"id":"dbb3c3d6-5b78-4d63-adb5-7f765086c303","page_size":[595,841],"block_position":"40-15"},{"bbox":[107,486,221,502],"type":"text","angle":0,"index":18,"text":"$\\textcircled{1}$ ZF：结果为零标志","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":40,"id":"581ad9e4-0ef2-4404-9e9f-ca857b2588d2","page_size":[595,841],"block_position":"40-16"},{"bbox":[125,506,261,521],"type":"text","angle":0,"index":19,"text":"·运算结果为全0，ZF置1","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":40,"id":"e2e64bee-ce80-4c22-a8f3-98719fde14d0","page_size":[595,841],"block_position":"40-17"},{"bbox":[299,504,469,523],"type":"interline_equation","angle":0,"index":20,"text":"$$\nZ F = \\overline {{F _ {n} + F _ {n - 1} + . . . . . . + F _ {0}}}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":40,"id":"7eda140a-9ad5-4bf9-b9e9-ebde65b460fb","page_size":[595,841],"block_position":"40-18"},{"bbox":[125,524,277,539],"type":"text","angle":0,"index":21,"text":"·运算结果不全为0，ZF置0","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":40,"id":"571a7886-22c6-4f51-acdb-e3d085d02c50","page_size":[595,841],"block_position":"40-19"},{"bbox":[107,543,420,557],"type":"text","angle":0,"index":22,"text":"$\\textcircled{2}$ CF：进位/借位标志位，CF标志只对无符号数运算有意义","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":40,"id":"b3d33a56-50d8-45fb-8776-9ccef53175e8","page_size":[595,841],"block_position":"40-20"},{"bbox":[125,561,418,576],"type":"text","angle":0,"index":23,"text":"·加法运算时：C=1则CF置1（表示有进位），否则置0","id":"d2a362d5-8356-4749-93f9-4a5a65a7ed35","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":40,"page_size":[595,841],"block_position":"40-21"},{"bbox":[125,580,465,595],"type":"text","angle":0,"index":24,"text":"·减法运算时： $\\subset = \\pmb { 0 }$ 则CF置1（表示不够减，有借位），否则置0","id":"a43d284b-6256-4371-844e-a7c626e822a5","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":40,"page_size":[595,841],"block_position":"40-22"},{"bbox":[143,602,176,626],"type":"text","angle":0,"index":26,"text":"最高位的进位","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":40,"id":"7f592b79-1252-498e-bc09-8cd259dd82ff","page_size":[595,841],"block_position":"40-23"},{"bbox":[240,603,470,628],"type":"interline_equation","angle":0,"index":27,"text":"$$\nC F = \\overline {{\\overline {{A D D}} / S U B}} \\cdot C + \\overline {{A D D}} / S U B \\cdot \\overline {{C}}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":40,"id":"9830cd40-1b53-4c3c-a5ea-34d1751db92b","page_size":[595,841],"block_position":"40-24"},{"bbox":[505,626,528,639],"index":28,"angle":0,"type":"image","img_path":"/131355cd6254e9395745464151013638000f1f37cc5df5cc5192d7004b5949af.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.2,"page_idx":40,"id":"4cfe26ee-0489-4d3f-bb5f-186c140cbeab","page_size":[595,841],"block_position":"40-25"}],[{"bbox":[127,74,537,88],"type":"text","angle":0,"index":0,"text":"③UF：溢出标志，反映有符亏数加减运算所得结果是否溢出；UF标志只对带","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":41,"id":"51c29d86-4815-420d-89b4-31019234d63f","page_size":[595,841],"block_position":"41-0"},{"bbox":[139,89,244,104],"type":"text","angle":0,"index":1,"text":"符号数运算有意义。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":41,"id":"caf102b7-594b-4742-8a6e-5bc45a34b475","page_size":[595,841],"block_position":"41-1"},{"bbox":[146,107,252,121],"type":"text","angle":0,"index":2,"text":"·运算溢出：OF=1","id":"d4946358-2a30-4f59-8960-3bae7b812a23","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":41,"page_size":[595,841],"block_position":"41-2"},{"bbox":[146,126,276,140],"type":"text","angle":0,"index":3,"text":"·运算没有溢出：OF $\\mathtt { \\mathtt { \\mathtt { = 0 } } }$","id":"a620f95d-5017-4cc3-bb31-33c10dcc10cd","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":41,"page_size":[595,841],"block_position":"41-3"},{"bbox":[314,95,525,158],"type":"interline_equation","angle":0,"index":5,"text":"$$\n\\begin{array}{c c} O F = \\overline {{A D D / S U B}} \\left(\\overline {{X _ {S}}} \\overline {{Y _ {S}}} F _ {S} + X _ {S} Y _ {S} \\overline {{F _ {S}}}\\right) \\\\ + \\overline {{A D D}} / S U B \\left(\\overline {{X _ {S}}} Y _ {S} F _ {S} + X _ {S} \\overline {{Y _ {S}}} \\overline {{F _ {S}}}\\right) \\\\ \\hline O F = C _ {1} \\oplus C _ {S} & O F = F _ {S 1} \\oplus F _ {S 2} \\end{array}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":41,"id":"e74249a2-2bf4-4e6f-ae8e-013acb12ed9c","page_size":[595,841],"block_position":"41-4"},{"bbox":[127,165,343,181],"type":"text","angle":0,"index":6,"text":"$\\textcircled{4}$ SF：符号标志，记录运算结果的符号。","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":41,"id":"7af98185-d0ab-4b2b-9ec8-e30501c4f0e8","page_size":[595,841],"block_position":"41-5"},{"bbox":[146,185,351,203],"type":"text","angle":0,"index":7,"text":"·为运算结果的最高位 SF =Fn","id":"c69a054f-813b-4fdb-a64a-97c5c9376c6f","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":41,"page_size":[595,841],"block_position":"41-6"},{"bbox":[146,206,512,222],"type":"text","angle":0,"index":8,"text":"·运算结果为正数时： $\\pmb { S F = 0 }$ ；为负数时： $s F { = } 1$ 。 (无溢出时才正确)","id":"b0980199-069e-4e0e-988c-1dc59f7cfe29","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":41,"page_size":[595,841],"block_position":"41-7"},{"bbox":[127,226,431,242],"type":"text","angle":0,"index":10,"text":"$\\textcircled{5}$ PF：奇偶标志，反映运算结果中“1”的个数的奇偶性","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":41,"id":"b3eae8cd-e675-4575-a480-e13c61fa762c","page_size":[595,841],"block_position":"41-8"},{"bbox":[146,245,340,260],"type":"text","angle":0,"index":11,"text":"·结果中“1”的个数为偶数：PF=1","id":"f44ffe5e-4ff1-4632-8925-df31289accc5","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":41,"page_size":[595,841],"block_position":"41-9"},{"bbox":[146,264,341,279],"type":"text","angle":0,"index":12,"text":"·结果中“1”的个数为奇数：PF=0","id":"b4bdab28-275d-4015-9e83-90de8f9687a3","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":41,"page_size":[595,841],"block_position":"41-10"},{"bbox":[353,250,549,275],"type":"interline_equation","angle":0,"index":14,"text":"$$\nP F = \\overline {{F _ {n} \\oplus F _ {n - 1} \\oplus \\dots . \\oplus F _ {0}}}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":41,"id":"08bb6916-23b5-442e-8718-0fc73efd7bed","page_size":[595,841],"block_position":"41-11"},{"bbox":[102,366,281,386],"type":"title","angle":0,"index":16,"text":"# 假设两个浮点数X和Y","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":41,"id":"212bc03a-3edb-46ba-a8a8-28da8be936c7","page_size":[595,841],"block_position":"41-12"},{"bbox":[224,399,350,426],"type":"interline_equation","angle":0,"index":17,"text":"$$\nX = M _ {X} \\times 2 ^ {E _ {X}}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":41,"id":"1926eade-4472-4a3a-9413-82cd2f2a9fb3","page_size":[595,841],"block_position":"41-13"},{"bbox":[414,398,537,426],"type":"interline_equation","angle":0,"index":18,"text":"$$\nY = M _ {Y} \\times 2 ^ {E _ {Y}}\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":41,"id":"05ef5253-9069-4bc6-ae4b-a7b4700c8481","page_size":[595,841],"block_position":"41-14"},{"bbox":[102,454,593,476],"type":"text","angle":0,"index":19,"text":"对齐小数点：使得阶码小的那个数变得与阶码大的那个数的阶码","id":"21ee312d-0463-432d-b785-0ab3aec1ea54","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":41,"page_size":[595,841],"block_position":"41-15"},{"bbox":[102,489,411,510],"type":"text","angle":0,"index":20,"text":"然后：对尾数（有效数位）做加减运算","id":"acd52312-50ca-4761-bc72-8f8a45d73f34","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":41,"page_size":[595,841],"block_position":"41-16"},{"bbox":[156,528,594,556],"type":"interline_equation","angle":0,"index":22,"text":"$$\nZ = X \\pm Y = \\left(M _ {X} \\cdot 2 ^ {\\left(E _ {X} - E _ {Y}\\right)} \\pm M _ {Y}\\right) \\times 2 ^ {E _ {Y}} \\quad E _ {X} \\leq\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":41,"id":"008aebcf-e0f0-4ac7-a815-085d02eb2ce6","page_size":[595,841],"block_position":"41-17"},{"bbox":[528,285,552,301],"type":"page_number","angle":0,"index":1000014,"text":"74","color":{"line":"rgba(164, 164, 164, 1)","fill":"rgba(164, 164, 164, 1)"},"page_idx":41,"is_discarded":true,"id":"5a891138-7291-4ed9-bcbd-31cd10ebab2d","page_size":[595,841],"block_position":"41-18"}],[{"bbox":[92,79,142,93],"type":"text","angle":0,"index":0,"text":"(2）对阶：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":42,"id":"a2020630-2612-4780-aba7-d58b52e8967a","page_size":[595,841],"block_position":"42-0"},{"bbox":[88,99,216,116],"type":"text","angle":0,"index":1,"text":"目标是：对齐小数点","id":"21fe47f0-06b8-4212-9dd7-08fd76462ee0","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":42,"page_size":[595,841],"block_position":"42-1"},{"bbox":[88,121,216,138],"type":"text","angle":0,"index":2,"text":"原则是：小阶对大阶","id":"4d56e093-1631-4348-b916-99a422d625bc","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":42,"page_size":[595,841],"block_position":"42-2"},{"bbox":[101,141,357,155],"type":"text","angle":0,"index":4,"text":"求阶差△E=Ex-Eγ，若△E≠0，即Ex≠E时需要对阶。","id":"5d5dda78-d7fb-4743-b462-57e3af2da2ed","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":42,"page_size":[595,841],"block_position":"42-3"},{"bbox":[101,158,389,172],"type":"text","angle":0,"index":5,"text":"若△E>0，则Ex>Eγ，M每右移一位， $\\mathbb { E } _ { \\mathsf { Y } ^ { + } }$ 1，直至 $\\mathsf { E } _ { \\mathsf { v } } = \\mathsf { E } _ { \\mathsf { X } }$","id":"2e9008f7-15bc-47b4-bb24-14bca5a51796","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":42,"page_size":[595,841],"block_position":"42-4"},{"bbox":[101,174,387,189],"type":"text","angle":0,"index":6,"text":"若△E<0，则 $\\mathsf { E } _ { \\mathsf { X } } { < } \\mathsf { E } _ { \\mathsf { Y } }$ $\\pmb { M } _ { \\mathbf { X } }$ 每右移一位， $\\mathtt { E _ { X } } + 1$ ，直至 $\\therefore x = E _ { y }$","id":"f6c0c6cc-0d53-43cc-b015-24ee0409f6ce","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":42,"page_size":[595,841],"block_position":"42-5"},{"bbox":[92,191,171,205],"type":"text","angle":0,"index":8,"text":"(3）尾数相加减","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":42,"id":"a4b68923-04d8-4512-b08d-5d8e03835b89","page_size":[595,841],"block_position":"42-6"},{"bbox":[101,208,398,222],"type":"text","angle":0,"index":9,"text":"·若做减法，先将操作数Y的尾数取相反数，再与Y的尾数相加","id":"f8c89e46-63db-440c-b639-9e5368ab51ed","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":42,"page_size":[595,841],"block_position":"42-7"},{"bbox":[101,225,464,253],"type":"text","angle":0,"index":10,"text":"■对阶时，右移多出的数位不丢弃（因为一般设置位数更宽的ALU进行计算，同时设置更宽的寄存器来存放中间运算结果)","id":"52cf21ff-9def-4da5-b4c8-0b36dd4b355f","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":42,"page_size":[595,841],"block_position":"42-8"},{"bbox":[461,255,481,267],"type":"text","angle":0,"index":12,"text":"82","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":42,"id":"12277ca0-d0c0-46c0-a67c-aabee3826c03","page_size":[595,841],"block_position":"42-9"},{"bbox":[117,292,265,308],"type":"title","angle":0,"index":13,"text":"# 浮点加减运算步骤","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":42,"id":"4ddf79b1-c5f0-4ec3-a907-66362cbdaaba","page_size":[595,841],"block_position":"42-10"},{"bbox":[86,322,460,338],"type":"text","angle":0,"index":14,"text":"【4）结果规格化：尾数运算的结果可能出现两种非规格化情况：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":42,"id":"19795ff4-27bb-49ba-b8a6-2affc1a8ef92","page_size":[595,841],"block_position":"42-11"},{"bbox":[96,343,449,360],"type":"text","angle":0,"index":15,"text":"·尾数溢出：需要右规（1次），即尾数右移1位，阶码+1","id":"a993b32b-ddd8-4c5d-9523-96ffab4aac8e","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":42,"page_size":[595,841],"block_position":"42-12"},{"bbox":[88,364,552,400],"type":"text","angle":0,"index":16,"text":"尾数| $< 2 ^ { - 1 }$ ：需要左规，即尾数左移1位，阶码-1，左规可能多次，直到尾数变为规格化形式。","id":"49c3789b-ad44-4df9-89f3-8b637ea93dd3","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":42,"page_size":[595,841],"block_position":"42-13"},{"bbox":[96,424,412,441],"type":"text","angle":0,"index":17,"text":"·先判断是否溢出，如果没有，再判断是否有前导零","id":"4bb86265-1950-4ffc-9fbd-b697604a8449","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":42,"page_size":[595,841],"block_position":"42-14"},{"bbox":[86,467,442,484],"type":"text","angle":0,"index":19,"text":"[5）舍入：将尾数多余的位数舍去，变成规定的浮点数格式","id":"746655a8-4eee-433e-8490-d9b2072d5515","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":42,"page_size":[595,841],"block_position":"42-15"},{"bbox":[96,488,417,505],"type":"text","angle":0,"index":20,"text":"舍入策略：舍去多余位数的方法，简单的舍入策略：","id":"63c0bcb2-91f9-426c-96e4-a0bae98a22bc","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":42,"page_size":[595,841],"block_position":"42-16"},{"bbox":[117,508,245,523],"type":"text","angle":0,"index":22,"text":"·截断法：多余的全舍去","id":"d3615f54-e660-479a-8dc4-99e8f5168130","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":42,"page_size":[595,841],"block_position":"42-17"},{"bbox":[117,526,496,540],"type":"text","angle":0,"index":23,"text":"·0舍1入法：多余位的最高位为1时，在尾数最低位上+1，否则舍去多余位","id":"d0e27b68-79cc-446a-9e19-355fd6381d18","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":42,"page_size":[595,841],"block_position":"42-18"},{"bbox":[118,544,336,557],"type":"text","angle":0,"index":24,"text":"·末位恒置1：始终在舍入结果的最末位置1","id":"0d5ad3a6-0882-4267-8123-c6f4e7539f4e","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":42,"page_size":[595,841],"block_position":"42-19"}],[{"bbox":[101,88,324,101],"type":"title","angle":0,"index":0,"text":"# IEEE754标准：规定了4种可选的舍入模式","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":43,"id":"5dec1272-c51c-4948-aa2b-4093f37d1b4d","page_size":[595,841],"block_position":"43-0"},{"bbox":[112,105,436,129],"type":"text","angle":0,"index":1,"text":"$\\textcircled{1}$ 向上舍入（总是朝+）：为正数时，只要多余位不全为0，就向最低有效位进1；为负数时，则采用简单的截断法","id":"0cbea41b-3d53-40c1-b189-7e7d045c0259","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":43,"page_size":[595,841],"block_position":"43-1"},{"bbox":[112,132,438,156],"type":"text","angle":0,"index":2,"text":"$\\textcircled{2}$ 向下舍入（总是朝－）：为正数时，只要多余位不全为0，就简单地截尾为负数时，则向最低有效位进1","id":"716d86d8-c5db-4d8c-a2ee-fc78a87bdd63","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":43,"page_size":[595,841],"block_position":"43-2"},{"bbox":[112,160,439,185],"type":"text","angle":0,"index":3,"text":"$\\textcircled{3}$ 向0舍入：即朝数轴的原点方向舍入，就是无论正数还是负数，都采用简单的截尾，从而使得绝对值总是变小。这种方法容易累积误差","id":"ff5e228f-a256-4bc3-8f08-573b824c5697","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":43,"page_size":[595,841],"block_position":"43-3"},{"bbox":[111,188,425,201],"type":"text","angle":0,"index":4,"text":"$\\textcircled{4}$ 就近舍入：即舍入到最接近的数，“四舍五入”。多余位=R,...Rn","id":"35d8f669-2653-4e74-9e81-d72e7ff5595c","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":43,"page_size":[595,841],"block_position":"43-4"},{"bbox":[127,203,231,213],"type":"text","angle":0,"index":6,"text":"·当R $\\scriptstyle 1 = 0$ ：截尾（即舍去）；","id":"93597609-ce14-4d15-82da-e29eb511c1bb","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":43,"page_size":[595,841],"block_position":"43-5"},{"bbox":[127,215,301,225],"type":"text","angle":0,"index":7,"text":"·当R $_ 1 = 1$ ,且R...R不全为0：向最低有效位进1；","id":"bcc1a7fc-dac4-470d-aa64-05da02f99e67","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":43,"page_size":[595,841],"block_position":"43-6"},{"bbox":[127,227,437,248],"type":"text","angle":0,"index":8,"text":"· $\\yen 123,456,7$ ：即等于一半（中点），则若最低有效位为0就截尾，若最低有效位为1就进1，以使得最低有效位总是为0","id":"f9e5f0be-9b51-40e7-ba09-417499c62914","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":43,"page_size":[595,841],"block_position":"43-7"},{"bbox":[102,251,405,264],"type":"text","angle":0,"index":10,"text":"中间结果设置了：保护位(guard)、舍入位(round)、粘滞位(sticky)","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":43,"id":"41d22f7f-e65f-4ba8-9405-5885b3183d4a","page_size":[595,841],"block_position":"43-8"},{"bbox":[103,304,385,505],"index":11,"angle":0,"type":"image","img_path":"/55a92cad7bcb03d99177cc82bcc618a4c22ad6fac867143503578508456fb4c6.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.47394957983193275,"page_idx":43,"id":"eb8269ea-61bd-4f92-bb68-7991438392ad","page_size":[595,841],"block_position":"43-9"},{"bbox":[417,486,437,503],"index":12,"angle":0,"type":"image","img_path":"/7749aefff1f44fe5f12bbb0be1645640461baee14490e7fc1b26359b4e945f52.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.2,"page_idx":43,"id":"3432ee4d-d27c-4f9c-818d-5fbc057b7c33","page_size":[595,841],"block_position":"43-10"}],[{"bbox":[88,75,114,106],"index":0,"angle":0,"type":"image","img_path":"/5f43ed1e5bce18a593cd23ba0865b39f93ba309eb7af27bdb85047d14e10b90e.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.2,"page_idx":44,"id":"ffbcb4d1-321e-41b7-b047-d0c82cc33a51","page_size":[595,841],"block_position":"44-0"},{"bbox":[136,74,264,90],"type":"title","angle":0,"index":1,"text":"# 浮点加减运算例题","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":44,"id":"998fbb5f-092a-4e15-b330-b01c4b41ce82","page_size":[595,841],"block_position":"44-1"},{"bbox":[117,101,207,118],"type":"title","angle":0,"index":2,"text":"# (2）尾数相加：","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":44,"id":"2836da28-824d-4b7f-ab96-b39073239aff","page_size":[595,841],"block_position":"44-2"},{"bbox":[145,123,296,140],"type":"interline_equation","angle":0,"index":3,"text":"$$\n\\left[ \\mathrm {M} _ {2} \\right] _ {\\text {补}} = 1. 1 0 0 0 0 0 1 (1 0 1)\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":44,"id":"dc963175-464c-4a1b-922a-9e98546ae317","page_size":[595,841],"block_position":"44-3"},{"bbox":[383,104,490,119],"type":"interline_equation","angle":0,"index":4,"text":"$$\n[ \\mathrm {M} _ {\\mathrm {X}} ] _ {\\text {补}} 1 1. 0 1 1 0 1 0 1\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":44,"id":"76db397c-f4bb-486a-80be-716a298d468d","page_size":[595,841],"block_position":"44-4"},{"bbox":[366,122,517,138],"type":"interline_equation","angle":0,"index":5,"text":"$$\n+ \\left[ \\mathbf {M} _ {\\mathbf {Y}} \\right] _ {\\text {补}} 0 0. 0 0 0 1 1 0 0 (1 0 1)\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":44,"id":"63ceff30-7a6a-4042-8a0f-1bfc17d841ce","page_size":[595,841],"block_position":"44-5"},{"bbox":[360,142,517,158],"type":"interline_equation","angle":0,"index":6,"text":"$$\n\\left[ \\mathbf {M} _ {\\mathrm {X}} + \\mathbf {M} _ {\\mathrm {Y}} \\right] _ {\\text {补}} 1 1. 1 0 0 0 0 0 1 (1 0 1)\n$$","color":{"line":"rgba(230, 122, 171, 1)","fill":"rgba(230, 122, 171, 1)"},"page_idx":44,"id":"f0e2b3f9-2e3c-4ba3-9339-07bbbcb0d588","page_size":[595,841],"block_position":"44-6"},{"bbox":[119,165,361,181],"type":"text","angle":0,"index":7,"text":"（3）结果规格化：首先判断：是否溢出？","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":44,"id":"eec131f4-37fe-4ee7-94d1-f31bd3585d1c","page_size":[595,841],"block_position":"44-7"},{"bbox":[251,182,393,195],"type":"text","angle":0,"index":8,"text":"因为双符号位为11，没有溢出","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":44,"id":"6a9172b1-ac3b-405e-a0c7-26cc0232d00a","page_size":[595,841],"block_position":"44-8"},{"bbox":[234,196,359,211],"type":"text","angle":0,"index":9,"text":"再检查：有无前导零？","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":44,"id":"177ff60b-4232-48a7-9d0d-1cf5bc49f68a","page_size":[595,841],"block_position":"44-9"},{"bbox":[251,212,444,239],"type":"text","angle":0,"index":10,"text":"因为 $\\boldsymbol { \\mathsf { M } } _ { \\mathrm { Z } } \\boldsymbol { \\mathrm { l } } _ { * \\mathrm { f } }$ 符号位和最高有效位相同 $= 1 . 1$故有一个前导零，须左规一位","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":44,"id":"023b8203-d517-4839-9a28-fa12be51779e","page_size":[595,841],"block_position":"44-10"},{"bbox":[234,241,418,255],"type":"text","angle":0,"index":11,"text":"左规一位：尾数左移1位，阶码-1","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":44,"id":"152356a9-5217-4cea-987c-1a9332259b95","page_size":[595,841],"block_position":"44-11"},{"bbox":[251,258,382,271],"type":"text","angle":0,"index":12,"text":"$[ \\mathbf { M } _ { 2 } ] _ { * \\mathrm { h } } = 1 . 0 0 0 0 0 1 1$ (01)","id":"23db2cc1-69f3-4142-ac47-afbe8e41113d","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":44,"page_size":[595,841],"block_position":"44-12"},{"bbox":[251,272,443,285],"type":"text","angle":0,"index":13,"text":"$[ \\ E _ { \\mathrm { Z } } ] _ { * \\mathrm { h } } = 0 0$ ，001 + 11, $1 1 1 = 0 0$ ，000","id":"ce4d396a-46f3-40dc-896b-d5d2197f455a","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":44,"page_size":[595,841],"block_position":"44-13"},{"bbox":[119,288,384,306],"type":"title","angle":0,"index":15,"text":"# (4）舍入：按照0舍1入法，尾数多余位舍去","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"level":1,"page_idx":44,"id":"c2732300-d0f0-4c44-8daf-096982c2215d","page_size":[595,841],"block_position":"44-14"},{"bbox":[131,309,348,323],"type":"text","angle":0,"index":16,"text":"结果为： $[ \\mathsf { X } + \\mathsf { Y } ] _ { \\dag \\Xi } = 0$ ，000 1.0000011","color":{"line":"rgba(13, 83, 222, 1)","fill":"rgba(13, 83, 222, 1)"},"page_idx":44,"id":"badce985-8b9c-4454-9a10-90d9f375aa23","page_size":[595,841],"block_position":"44-15"},{"bbox":[464,308,483,323],"index":17,"angle":0,"type":"image","img_path":"/cd1e8e31644d4311c85ff19418a4b8474f57ffd8021141b8b4cc57db704dfb8a.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.2,"page_idx":44,"id":"989ec1da-fde0-4375-914e-5bfd20a85be6","page_size":[595,841],"block_position":"44-16"},{"bbox":[507,308,518,323],"index":18,"angle":0,"type":"image","img_path":"/3696e23690406c549b23470efcee5693b5f60e0db09eef2133e90f7a62811e0a.jpg","color":{"line":"rgba(89, 92, 220, 1)","fill":"rgba(89, 92, 220, 1)"},"img_ratio":0.2,"page_idx":44,"id":"052b9f2b-987f-4dbf-8fb9-5ef8cda5a6a8","page_size":[595,841],"block_position":"44-17"}]],"mergeConnections":[]}