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\\boldsymbol { X } } _ { 1 } \\mathbf { \\boldsymbol { X } } _ { 2 } . . . . . . . \\mathbf { \\boldsymbol { X } _ { n } }", "score": 0.78 } ] } ] }, { "bbox": [ 158, 280, 316, 295 ], "type": "text", "angle": 0, "index": 16, "lines": [ { "bbox": [ 157, 276, 317, 294 ], "spans": [ { "bbox": [ 157, 276, 317, 294 ], "type": "text", "content": "若X=-0.Xx，则1.", "score": 0.627 }, { "bbox": [ 231, 280, 264, 290 ], "type": "inline_equation", "content": "\\boldsymbol { \\mathfrak { A } } \\boldsymbol { \\mathfrak { A } } [ \\mathbf { X } ] _ { E } = \\mathbf { 1 } .", "score": 0.71 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 86, 303, 233, 313 ], "type": "text", "angle": 0, "index": 18, "lines": [ { "bbox": [ 86, 303, 234, 314 ], "spans": [ { "bbox": [ 86, 303, 234, 314 ], "type": "text", "content": "（1）0的表示：0的反码表示有两种形式", "score": 0.996 } ] } ] }, { "bbox": [ 97, 317, 158, 326 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 97, 317, 158, 326 ], "spans": [ { "bbox": [ 97, 317, 158, 326 ], "type": "interline_equation", "content": "\\begin{array}{r l} {[ + 0 ] _ {\\text {反}} = 0 0 \\dots 0} \\end{array}", "image_path": "518fe401000087c650055a23fe44477c4c690ca58923fd0535f5cc1a5997d3c6.jpg" } ] } ], "index": 19 }, { "bbox": [ 201, 317, 252, 327 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 201, 317, 252, 327 ], "spans": [ { "bbox": [ 201, 317, 252, 327 ], "type": "interline_equation", "content": "[ - 0 ] _ {\\text {反}} = 1 1 \\dots 1", "image_path": "dc59cfd4c6d874afe3061e098bbeae13273490f13db6da829cbb951d46e61849.jpg" } ] } ], "index": 20 }, { "bbox": [ 86, 328, 329, 338 ], "type": "text", "angle": 0, "index": 21, "lines": [ { "bbox": [ 88, 328, 330, 339 ], "spans": [ { "bbox": [ 88, 328, 173, 339 ], "type": "text", "content": "（2）表示范围：对于n", "score": 0.99 }, { "bbox": [ 173, 330, 180, 338 ], "type": "inline_equation", "content": "^ +", "score": 0.54 }, { "bbox": [ 180, 328, 330, 339 ], "type": "text", "content": "1位反码机器数×，它所能表示的数据范围为：", "score": 0.978 } ] } ] }, { "bbox": [ 96, 341, 238, 364 ], "type": "list", "angle": 0, "index": 24, "blocks": [ { "bbox": [ 96, 341, 227, 351 ], "type": "text", "angle": 0, "index": 22, "lines": [ { "bbox": [ 97, 340, 229, 352 ], "spans": [ { "bbox": [ 97, 340, 229, 352 ], "type": "text", "content": "定点整数：-(2n-1）≤X≤2n-1", "score": 0.882 } ] } ] }, { "bbox": [ 96, 354, 238, 364 ], "type": "text", "angle": 0, "index": 23, "lines": [ { "bbox": [ 96, 353, 239, 364 ], "spans": [ { "bbox": [ 96, 353, 239, 364 ], "type": "text", "content": "·定点小数:-（1-2-n）≤X≤1-2-n", "score": 0.874 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 86, 375, 111, 386 ], "type": "text", "angle": 0, "index": 25, "lines": [ { "bbox": [ 88, 375, 113, 390 ], "spans": [ { "bbox": [ 88, 375, 113, 390 ], "type": "text", "content": "移码", "score": 1.0 } ] } ] }, { "bbox": [ 112, 394, 143, 428 ], "type": "title", "angle": 0, "index": 26, "lines": [ { "bbox": [ 111, 393, 145, 413 ], "spans": [ { "bbox": [ 111, 393, 145, 413 ], "type": "text", "content": "定点", "score": 0.999 } ] }, { "bbox": [ 111, 411, 145, 430 ], "spans": [ { "bbox": [ 111, 411, 145, 430 ], "type": "text", "content": "整数", "score": 0.999 } ] } ] }, { "bbox": [ 161, 398, 317, 428 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 161, 398, 317, 428 ], "spans": [ { "bbox": [ 161, 398, 317, 428 ], "type": "interline_equation", "content": "[ \\mathrm {X} ] _ {\\text {移}} = 2 ^ {\\mathrm {n}} + \\mathrm {X}", "image_path": "cd099e39b47214cdde721263f19a140f282e4937223b97b0846876b33caae6c2.jpg" } ] } ], "index": 27 }, { "bbox": [ 199, 440, 287, 460 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 199, 440, 287, 460 ], "spans": [ { "bbox": [ 199, 440, 287, 460 ], "type": "interline_equation", "content": "(\\mod 2 ^ {n + 1})", "image_path": "8c3a93fa9528d939a9b2ea2642676792ce251a4879d189806a2c8d5a5bfe087c.jpg" } ] } ], "index": 28 }, { "bbox": [ 86, 468, 321, 481 ], "type": "text", "angle": 0, "index": 29, "lines": [ { "bbox": [ 88, 469, 321, 483 ], "spans": [ { "bbox": [ 88, 469, 321, 483 ], "type": "text", "content": "2、表示方法：最高位为符号位，其他位为数值位。", "score": 1.0 } ] } ] }, { "bbox": [ 87, 484, 424, 513 ], "type": "list", "angle": 0, "index": 32, "blocks": [ { "bbox": [ 87, 484, 230, 497 ], "type": "text", "angle": 0, "index": 30, "lines": [ { "bbox": [ 88, 483, 230, 498 ], "spans": [ { "bbox": [ 88, 483, 230, 498 ], "type": "text", "content": " 符号位：1－正数，0－负数。", "score": 1.0 } ] } ] }, { "bbox": [ 87, 499, 424, 513 ], "type": "text", "angle": 0, "index": 31, "lines": [ { "bbox": [ 87, 498, 426, 515 ], "spans": [ { "bbox": [ 87, 498, 426, 515 ], "type": "text", "content": " 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。", "score": 1.0 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 86, 528, 581, 539 ], "type": "text", "angle": 0, "index": 33, "lines": [ { "bbox": [ 89, 529, 582, 539 ], "spans": [ { "bbox": [ 89, 529, 582, 539 ], "type": "text", "content": "值位，正效的，与绝对值怕问，贝双的，为绝对值耿反旧，不位加", "score": 0.751 } ] } ] }, { "bbox": [ 94, 596, 221, 614 ], "type": "title", "angle": 0, "index": 34, "lines": [ { "bbox": [ 93, 595, 223, 616 ], "spans": [ { "bbox": [ 93, 595, 223, 616 ], "type": "text", "content": "对于定点整数：", "score": 0.99 } ] } ] }, { "bbox": [ 443, 560, 543, 600 ], "type": "text", "angle": 0, "index": 35, "lines": [ { "bbox": [ 440, 558, 545, 582 ], "spans": [ { "bbox": [ 440, 558, 545, 582 ], "type": "text", "content": "移码=补码的", "score": 0.996 } ] }, { "bbox": [ 443, 579, 543, 601 ], "spans": [ { "bbox": [ 443, 579, 543, 601 ], "type": "text", "content": "符号位取反", "score": 0.992 } ] } ] }, { "bbox": [ 117, 629, 536, 690 ], "type": "list", "angle": 0, "index": 38, "blocks": [ { "bbox": [ 117, 629, 483, 653 ], "type": "text", "angle": 0, "index": 36, "lines": [ { "bbox": [ 117, 625, 476, 655 ], "spans": [ { "bbox": [ 117, 625, 159, 655 ], "type": "text", "content": "·若", "score": 0.756 }, { "bbox": [ 160, 629, 282, 653 ], "type": "inline_equation", "content": "\\mathfrak { c } { = } { + } \\mathfrak { X } _ { 1 } \\mathfrak { X } _ { 2 } { \\dots } { \\dots } \\mathfrak { X } _ { n }", "score": 0.58 }, { "bbox": [ 282, 625, 312, 655 ], "type": "text", "content": "，则", "score": 0.996 }, { "bbox": [ 312, 629, 476, 655 ], "type": "inline_equation", "content": "[ \\mathsf { X } ] _ { \\mp \\mathcal { B } } = \\mathsf { 1 } , \\mathsf { X } _ { 1 } \\mathsf { X } _ { 2 } . . . . . . \\mathsf { X } _ { \\mathsf { n } }", "score": 0.56 } ] } ] }, { "bbox": [ 118, 665, 536, 690 ], "type": "text", "angle": 0, "index": 37, "lines": [ { "bbox": [ 117, 663, 539, 692 ], "spans": [ { "bbox": [ 117, 663, 150, 691 ], "type": "text", "content": "·若", "score": 0.814 }, { "bbox": [ 151, 666, 280, 690 ], "type": "inline_equation", "content": "\\mathbf { \\ddot { X } } = - \\mathbf { \\nabla } \\mathbf { X } _ { 1 } \\mathbf { X } _ { 2 } \\ldots \\ldots \\mathbf { X } _ { n }", "score": 0.6 }, { "bbox": [ 281, 663, 318, 691 ], "type": "text", "content": "，则", "score": 0.998 }, { "bbox": [ 318, 665, 383, 692 ], "type": "inline_equation", "content": "[ \\mathbf { X } ] _ { \\mathcal { F B } } = \\mathbf { 0 } ,", "score": 0.78 }, { "bbox": [ 383, 663, 539, 691 ], "type": "text", "content": ",xX Xx.. Xn +1.", "score": 0.686 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 93, 702, 294, 715 ], "type": "text", "angle": 0, "index": 39, "lines": [ { "bbox": [ 95, 701, 295, 716 ], "spans": [ { "bbox": [ 95, 701, 295, 716 ], "type": "text", "content": "（1） 0的表示：0 的移码表示形式是唯一的", "score": 1.0 } ] } ] }, { "bbox": [ 87, 718, 428, 761 ], "type": "list", "angle": 0, "index": 43, "blocks": [ { "bbox": [ 88, 718, 236, 730 ], "type": "text", "angle": 0, "index": 40, "lines": [ { "bbox": [ 88, 717, 238, 733 ], "spans": [ { "bbox": [ 88, 717, 97, 733 ], "type": "text", "content": "", "score": 1.0 }, { "bbox": [ 97, 719, 117, 731 ], "type": "inline_equation", "content": "[ + 0 ]", "score": 0.71 }, { "bbox": [ 117, 717, 238, 733 ], "type": "text", "content": "移＝ 10…0 [-0]移＝ 10…0", "score": 1.0 } ] } ] }, { "bbox": [ 87, 733, 428, 746 ], "type": "text", "angle": 0, "index": 41, "lines": [ { "bbox": [ 88, 734, 430, 748 ], "spans": [ { "bbox": [ 88, 734, 199, 748 ], "type": "text", "content": " （2）表示范围：对于", "score": 1.0 }, { "bbox": [ 199, 734, 224, 746 ], "type": "inline_equation", "content": "\\mathsf { n } + \\mathsf { 1 }", "score": 0.91 }, { "bbox": [ 224, 734, 430, 748 ], "type": "text", "content": "位移码机器数 X，它所能表示的数据范围为：", "score": 1.0 } ] } ] }, { "bbox": [ 88, 749, 232, 761 ], "type": "text", "angle": 0, "index": 42, "lines": [ { "bbox": [ 89, 750, 232, 762 ], "spans": [ { "bbox": [ 89, 750, 149, 762 ], "type": "text", "content": " 定点整数：", "score": 1.0 }, { "bbox": [ 150, 750, 232, 761 ], "type": "inline_equation", "content": "- 2 \\mathsf { n } { \\mathsf { \\leq } } \\mathsf { X } \\leq 2 \\mathsf { n } - 1", "score": 0.85 } ] } ] } ], "sub_type": "text" } ], "discarded_blocks": [], "page_size": [ 595, 841 ], "page_idx": 5 }, { "para_blocks": [ { "type": "image", "bbox": [ 104, 82, 138, 111 ], "blocks": [ { "bbox": [ 104, 82, 138, 111 ], "lines": [ { "bbox": [ 104, 82, 138, 111 ], "spans": [ { "bbox": [ 104, 82, 138, 111 ], "type": "image", "image_path": "17570bda25ff10b972ee9301e89e66c4e3e561a977bba5dfa96f0a63acf2709d.jpg" } ] } ], "index": 0, "angle": 0, "type": "image_body" } ], "index": 0 }, { "bbox": [ 158, 81, 295, 98 ], "type": "title", "angle": 0, "index": 1, "lines": [ { "bbox": [ 156, 82, 296, 99 ], "spans": [ { "bbox": [ 156, 82, 296, 99 ], "type": "text", "content": "四种定点机器数的对比", "score": 0.995 } ] } ] }, { "bbox": [ 329, 84, 406, 99 ], "type": "title", "angle": 0, "index": 2, "lines": [ { "bbox": [ 327, 81, 408, 100 ], "spans": [ { "bbox": [ 327, 81, 408, 100 ], "type": "text", "content": "1、表示方法", "score": 0.997 } ] } ] }, { "bbox": [ 129, 141, 180, 156 ], "type": "title", "angle": 0, "index": 3, "lines": [ { "bbox": [ 130, 142, 180, 157 ], "spans": [ { "bbox": [ 130, 142, 180, 157 ], "type": "text", "content": "定点整数", "score": 0.999 } ] } ] }, { "type": "table", "bbox": [ 182, 103, 493, 196 ], "blocks": [ { "bbox": [ 182, 103, 493, 196 ], "lines": [ { "bbox": [ 182, 103, 493, 196 ], "spans": [ { "bbox": [ 182, 103, 493, 196 ], "type": "table", "html": "
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
", "image_path": "41c63d3523508f4ebc3df1e459527e3c41e3182e257cbced25cee0832cc19663.jpg" } ] } ], "index": 4, "angle": 0, "type": "table_body" } ], "index": 4 }, { "bbox": [ 120, 236, 146, 264 ], "type": "title", "angle": 0, "index": 5, "lines": [ { "bbox": [ 117, 235, 149, 253 ], "spans": [ { "bbox": [ 117, 235, 149, 253 ], "type": "text", "content": "定点", "score": 0.999 } ] }, { "bbox": [ 118, 248, 149, 266 ], "spans": [ { "bbox": [ 118, 248, 149, 266 ], "type": "text", "content": "小数", "score": 0.998 } ] } ] }, { "type": "table", "bbox": [ 152, 200, 495, 301 ], "blocks": [ { "bbox": [ 152, 200, 495, 301 ], "lines": [ { "bbox": [ 152, 200, 495, 301 ], "spans": [ { "bbox": [ 152, 200, 495, 301 ], "type": "table", "html": "
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
", "image_path": "4fb08762fdd2cab463ab29fc4b5ae17c5ee24e9f2245facd4630057aaaa9d5de.jpg" } ] } ], "index": 6, "angle": 0, "type": "table_body" } ], "index": 6 }, { "type": "table", "bbox": [ 88, 333, 577, 522 ], "blocks": [ { "bbox": [ 88, 333, 577, 522 ], "lines": [ { "bbox": [ 88, 333, 577, 522 ], "spans": [ { "bbox": [ 88, 333, 577, 522 ], "type": "table", "html": "
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
", "image_path": "82e974e6af36d2b511be0bfa3d01f84da4b72e86186e1b9275b73b7ee0287a68.jpg" } ] } ], "index": 7, "angle": 0, "type": "table_body" } ], "index": 7 }, { "type": "table", "bbox": [ 92, 569, 307, 665 ], "blocks": [ { "bbox": [ 169, 548, 236, 562 ], "lines": [ { "bbox": [ 169, 548, 237, 563 ], "spans": [ { "bbox": [ 169, 548, 237, 563 ], "type": "text", "content": "n+1位机器数", "score": 0.997 } ] } ], "index": 8, "angle": 0, "type": "table_caption" }, { "bbox": [ 92, 569, 307, 665 ], "lines": [ { "bbox": [ 92, 569, 307, 665 ], "spans": [ { "bbox": [ 92, 569, 307, 665 ], "type": "table", "html": "
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
", "image_path": "12af43b7c38126a6dbfa7217f2e5d569976f2ab0bdb03a07079c2a390a4e7a41.jpg" } ] } ], "index": 9, "angle": 0, "type": "table_body" } ], "index": 9 } ], "discarded_blocks": [], "page_size": [ 595, 841 ], "page_idx": 6 }, { "para_blocks": [ { "bbox": [ 92, 87, 160, 101 ], "type": "text", "angle": 0, "index": 0, "lines": [] }, { "bbox": [ 92, 87, 198, 144 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 92, 87, 198, 144 ], "spans": [ { "bbox": [ 92, 87, 198, 144 ], "type": "interline_equation", "content": "\\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}", "image_path": "1da50c8aec212edaea1e14ff2a3f71cde06fdc87eb3bc5d3dbad1ac89cd8f092.jpg" } ] } ], "index": 1 }, { "bbox": [ 251, 87, 318, 100 ], "type": "text", "angle": 0, "index": 2, "lines": [] }, { "bbox": [ 251, 87, 368, 145 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 251, 87, 368, 145 ], "spans": [ { "bbox": [ 251, 87, 368, 145 ], "type": "interline_equation", "content": "\\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}", "image_path": "ae62b8b8d754b264d256ff236caadf0e2d806f49ee7ecc0c815a1c4a7d249109.jpg" } ] } ], "index": 3 }, { "bbox": [ 92, 164, 158, 178 ], "type": "text", "angle": 0, "index": 4, "lines": [ { "bbox": [ 91, 163, 160, 179 ], "spans": [ { "bbox": [ 91, 163, 160, 179 ], "type": "text", "content": "[X]补→真值？", "score": 0.935 } ] } ] }, { "bbox": [ 92, 180, 230, 222 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 92, 180, 230, 222 ], "spans": [ { "bbox": [ 92, 180, 230, 222 ], "type": "interline_equation", "content": "\\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}", "image_path": "d69a591acdb9451f68a6e46ec957680bccbd3a6fd45b217987c4edbf7b23fa0a.jpg" } ] } ], "index": 5 }, { "bbox": [ 251, 165, 318, 179 ], "type": "text", "angle": 0, "index": 6, "lines": [ { "bbox": [ 250, 166, 319, 180 ], "spans": [ { "bbox": [ 250, 166, 319, 180 ], "type": "text", "content": "[X]移→真值？", "score": 0.952 } ] } ] }, { "bbox": [ 251, 182, 389, 223 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 251, 182, 389, 223 ], "spans": [ { "bbox": [ 251, 182, 389, 223 ], "type": "interline_equation", "content": "\\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}", "image_path": "fc75d670fc1a7c8e7032dcb815495ed2d13766a2f05a75430bb7cffdc06fce16.jpg" } ] } ], "index": 7 }, { "bbox": [ 88, 234, 143, 247 ], "type": "title", "angle": 0, "index": 8, "lines": [ { "bbox": [ 88, 235, 143, 248 ], "spans": [ { "bbox": [ 88, 235, 143, 248 ], "type": "text", "content": "浮点数格式", "score": 1.0 } ] } ] }, { "bbox": [ 89, 254, 158, 266 ], "type": "text", "angle": 0, "index": 9, "lines": [ { "bbox": [ 89, 255, 160, 267 ], "spans": [ { "bbox": [ 89, 255, 160, 267 ], "type": "text", "content": "浮点数N的构成：", "score": 0.984 } ] } ] }, { "bbox": [ 204, 253, 270, 264 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 204, 253, 270, 264 ], "spans": [ { "bbox": [ 204, 253, 270, 264 ], "type": "interline_equation", "content": "N = M \\times R ^ {E}", "image_path": "506b2520b99b0508c9881053fe2005225f52714c4150292ba602b527ab4ec9bb.jpg" } ] } ], "index": 10 }, { "bbox": [ 89, 269, 342, 293 ], "type": "list", "angle": 0, "index": 13, "blocks": [ { "bbox": [ 89, 269, 342, 280 ], "type": "text", "angle": 0, "index": 11, "lines": [ { "bbox": [ 89, 268, 343, 280 ], "spans": [ { "bbox": [ 89, 268, 343, 280 ], "type": "text", "content": "阶码E（Exponent）、尾数M（Mantissa）和阶码的底R（Radix)", "score": 0.959 } ] } ] }, { "bbox": [ 89, 282, 296, 293 ], "type": "text", "angle": 0, "index": 12, "lines": [ { "bbox": [ 89, 282, 297, 293 ], "spans": [ { "bbox": [ 89, 282, 297, 293 ], "type": "text", "content": "阶码的底R：是一个常数，隐含规定，一般为2、8或16", "score": 0.991 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 94, 301, 121, 324 ], "type": "text", "angle": 0, "index": 14, "lines": [ { "bbox": [ 95, 300, 123, 311 ], "spans": [ { "bbox": [ 95, 300, 123, 311 ], "type": "text", "content": "为什么将", "score": 0.999 } ] }, { "bbox": [ 95, 307, 123, 317 ], "spans": [ { "bbox": [ 95, 307, 123, 317 ], "type": "text", "content": "数符放置", "score": 0.983 } ] }, { "bbox": [ 95, 315, 123, 326 ], "spans": [ { "bbox": [ 95, 315, 123, 326 ], "type": "text", "content": "在首位？", "score": 0.969 } ] } ] }, { "bbox": [ 93, 338, 126, 360 ], "type": "text", "angle": 0, "index": 15, "lines": [ { "bbox": [ 93, 337, 126, 347 ], "spans": [ { "bbox": [ 93, 337, 126, 347 ], "type": "text", "content": "将数符放置", "score": 0.994 } ] }, { "bbox": [ 92, 344, 127, 354 ], "spans": [ { "bbox": [ 92, 344, 127, 354 ], "type": "text", "content": "在首位，方", "score": 0.971 } ] }, { "bbox": [ 93, 352, 126, 360 ], "spans": [ { "bbox": [ 93, 352, 126, 360 ], "type": "text", "content": "便比较大小", "score": 0.991 } ] } ] }, { "type": "image", "bbox": [ 166, 301, 345, 337 ], "blocks": [ { "bbox": [ 166, 301, 345, 337 ], "lines": [ { "bbox": [ 166, 301, 345, 337 ], "spans": [ { "bbox": [ 166, 301, 345, 337 ], "type": "image", "image_path": "f318b4e4d2f9ec985b58f83758be6fd1d10255482e3dcd00bc9b8f495c476389.jpg" } ] } ], 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], "type": "title", "angle": 0, "index": 23, "lines": [ { "bbox": [ 98, 421, 190, 434 ], "spans": [ { "bbox": [ 98, 421, 190, 434 ], "type": "text", "content": "尾数M：定点小数", "score": 0.954 } ] } ] }, { "bbox": [ 314, 420, 427, 432 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 314, 420, 427, 432 ], "spans": [ { "bbox": [ 314, 420, 427, 432 ], "type": "interline_equation", "content": "0. 1 0 1 1 1 0 \\times 2 ^ {- 2} = 0. 0 0 1 0 1 1 1", "image_path": "6fed770bf83e60c442d5db60f480c7c5ffa31fbdd84240e62b1e6068aeea5cfd.jpg" } ] } ], "index": 24 }, { "bbox": [ 335, 437, 414, 453 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 335, 437, 414, 453 ], "spans": [ { "bbox": [ 335, 437, 414, 453 ], "type": "interline_equation", "content": "N = M \\times R ^ {E}", "image_path": "4e9024dc16c33bb4143253ad8c32cc6fc3f89030beced0667b59bef5c494f0d6.jpg" } ] } ], "index": 25 }, { "bbox": [ 111, 439, 293, 481 ], "type": "list", "angle": 0, "index": 29, "blocks": [ { 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564 ], "type": "list", "angle": 0, "index": 35, "blocks": [ { "bbox": [ 111, 504, 296, 515 ], "type": "text", "angle": 0, "index": 31, "lines": [ { "bbox": [ 113, 504, 296, 516 ], "spans": [ { "bbox": [ 113, 504, 296, 516 ], "type": "text", "content": "·阶码的位数：多少决定了浮点数的表示范围", "score": 0.976 } ] } ] }, { "bbox": [ 111, 520, 436, 532 ], "type": "text", "angle": 0, "index": 32, "lines": [ { "bbox": [ 113, 520, 437, 532 ], "spans": [ { "bbox": [ 113, 520, 437, 532 ], "type": "text", "content": "·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", "score": 0.991 } ] } ] }, { "bbox": [ 111, 536, 436, 548 ], "type": "text", "angle": 0, "index": 33, "lines": [ { "bbox": [ 112, 536, 437, 549 ], "spans": [ { "bbox": [ 112, 536, 437, 549 ], "type": "text", "content": "·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", "score": 0.993 } ] } ] }, { "bbox": [ 111, 553, 275, 564 ], "type": "text", "angle": 0, "index": 34, "lines": [ { "bbox": [ 113, 553, 276, 565 ], "spans": [ { "bbox": [ 113, 553, 276, 565 ], "type": "text", 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{ "bbox": [ 108, 114, 310, 185 ], "type": "list", "angle": 0, "index": 4, "blocks": [ { "bbox": [ 108, 114, 310, 146 ], "type": "text", "angle": 0, "index": 1, "lines": [ { "bbox": [ 120, 115, 310, 128 ], "spans": [ { "bbox": [ 120, 115, 310, 128 ], "type": "text", "content": "规格化操作：修改阶码和左右移尾数的", "score": 0.995 } ] }, { "bbox": [ 122, 132, 267, 146 ], "spans": [ { "bbox": [ 122, 132, 267, 146 ], "type": "text", "content": "方法来使其变为规格化浮点数", "score": 0.999 } ] } ] }, { "bbox": [ 108, 151, 289, 166 ], "type": "text", "angle": 0, "index": 2, "lines": [ { "bbox": [ 117, 152, 288, 166 ], "spans": [ { "bbox": [ 117, 152, 288, 166 ], "type": "text", "content": "右规：尾数进行右移实现的规格化", "score": 0.998 } ] } ] }, { "bbox": [ 109, 171, 289, 185 ], "type": "text", "angle": 0, "index": 3, "lines": [ { "bbox": [ 116, 172, 289, 185 ], "spans": [ { "bbox": [ 116, 172, 289, 185 ], "type": "text", "content": "左规：尾数进行左移实现的规格化", "score": 0.997 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 313, 93, 480, 108 ], 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302 ], "type": "text", "content": "（3）按照格式写出M和E的规定机器数编码", "score": 0.97 } ] } ] }, { "bbox": [ 115, 306, 257, 322 ], "type": "text", "angle": 0, "index": 18, "lines": [ { "bbox": [ 116, 307, 257, 320 ], "spans": [ { "bbox": [ 116, 307, 257, 320 ], "type": "text", "content": "（4）按照格式要求排列E和M", "score": 0.977 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 86, 343, 451, 372 ], "type": "text", "angle": 0, "index": 20, "lines": [ { "bbox": [ 88, 343, 452, 358 ], "spans": [ { "bbox": [ 88, 343, 452, 358 ], "type": "text", "content": "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。", "score": 1.0 } ] }, { "bbox": [ 88, 359, 158, 373 ], "spans": [ { "bbox": [ 88, 359, 158, 373 ], "type": "text", "content": "右规一次即可。", "score": 1.0 } ] } ] }, { "bbox": [ 87, 375, 258, 387 ], "type": "text", "angle": 0, "index": 21, "lines": [ { "bbox": [ 89, 375, 258, 389 ], "spans": [ { "bbox": [ 89, 375, 258, 389 ], "type": "text", "content": "阶码发生溢出时，浮点数被判为溢出", "score": 1.0 } ] } ] }, { "type": "image", "bbox": [ 503, 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"content": "\\cdot = 2 \\wedge _ { \\mathsf { n } }", "score": 0.88 } ] } ] }, { "bbox": [ 87, 588, 453, 602 ], "type": "text", "angle": 0, "index": 29, "lines": [ { "bbox": [ 88, 589, 455, 604 ], "spans": [ { "bbox": [ 88, 589, 130, 604 ], "type": "text", "content": "Eg.[-2]原", "score": 1.0 }, { "bbox": [ 131, 590, 162, 602 ], "type": "inline_equation", "content": "= 1 0 1 0", "score": 0.81 }, { "bbox": [ 163, 589, 195, 604 ], "type": "text", "content": "；[-2]补", "score": 1.0 }, { "bbox": [ 195, 590, 226, 602 ], "type": "inline_equation", "content": "\\mathord { \\left. \\kern - delimiterspace \\right.} 1 1 0 ", "score": 0.57 }, { "bbox": [ 226, 589, 455, 604 ], "type": "text", "content": "，相加为 1000（当成原码并去掉符号位，就是 8）", "score": 1.0 } ] } ] }, { "bbox": [ 98, 604, 248, 618 ], "type": "text", "angle": 0, "index": 30, "lines": [ { "bbox": [ 100, 605, 248, 618 ], "spans": [ { "bbox": [ 100, 605, 248, 618 ], "type": "text", "content": "负数的补码就是其绝对值的补数", "score": 1.0 } ] } ] }, { "bbox": [ 86, 620, 420, 634 ], "type": "text", "angle": 0, "index": 31, "lines": [ { "bbox": [ 87, 619, 421, 635 ], "spans": [ { "bbox": [ 87, 619, 139, 635 ], "type": "text", "content": "X的绝对值", "score": 1.0 }, { "bbox": [ 139, 621, 158, 634 ], "type": "inline_equation", "content": "+ [ x ]", "score": 0.7 }, { "bbox": [ 158, 619, 373, 635 ], "type": "text", "content": "补但是[x]补当成原码去掉符号位，为10000即", "score": 1.0 }, { "bbox": [ 373, 621, 388, 633 ], "type": "inline_equation", "content": "^ { 2 \\wedge }", "score": 0.64 }, { "bbox": [ 389, 619, 394, 635 ], "type": "text", "content": "（", "score": 1.0 }, { "bbox": [ 395, 621, 418, 634 ], "type": "inline_equation", "content": "( n + 1 )", "score": 0.66 }, { "bbox": [ 418, 619, 421, 635 ], "type": "text", "content": "）", "score": 1.0 } ] } ] }, { "bbox": [ 87, 635, 295, 649 ], "type": "text", "angle": 0, "index": 32, "lines": [ { "bbox": [ 88, 635, 296, 650 ], "spans": [ { "bbox": [ 88, 635, 189, 650 ], "type": "text", "content": "还是上个例子。[-2]补", "score": 1.0 }, { "bbox": [ 189, 637, 238, 649 ], "type": "inline_equation", "content": "= 1 1 1 0 = 1 4", "score": 0.89 }, { "bbox": [ 239, 635, 246, 650 ], "type": "text", "content": "，", "score": 1.0 }, { "bbox": [ 246, 637, 291, 649 ], "type": "inline_equation", "content": "2 + 1 4 = 1 6", "score": 0.88 }, { "bbox": [ 291, 635, 296, 650 ], "type": "text", "content": "；", "score": 1.0 } ] } ] }, { "bbox": [ 87, 651, 304, 664 ], "type": "text", "angle": 0, "index": 33, "lines": [ { "bbox": [ 89, 652, 306, 666 ], "spans": [ { "bbox": [ 89, 652, 306, 666 ], "type": "text", "content": "所以，有符号数和无符号数之间的转换规则是：", "score": 1.0 } ] } ] }, { "bbox": [ 87, 667, 288, 680 ], "type": "text", "angle": 0, "index": 34, "lines": [ { "bbox": [ 89, 667, 289, 682 ], "spans": [ { "bbox": [ 89, 667, 289, 682 ], "type": "text", "content": "位模式不变，但是解释这些位的方式改变了", "score": 1.0 } ] } ] }, { "bbox": [ 87, 682, 163, 695 ], "type": "text", "angle": 0, "index": 35, "lines": [ { "bbox": [ 88, 683, 164, 697 ], "spans": [ { "bbox": [ 88, 683, 164, 697 ], "type": "text", "content": "数值数据的表示", "score": 1.0 } ] } ] }, { "bbox": [ 87, 698, 143, 711 ], "type": "text", "angle": 0, "index": 36, "lines": [ { "bbox": [ 88, 698, 143, 712 ], "spans": [ { "bbox": [ 88, 698, 143, 712 ], "type": "text", "content": "进位计数制", "score": 1.0 } ] } ] }, { "bbox": [ 87, 714, 184, 727 ], "type": "text", "angle": 0, "index": 37, "lines": [ { "bbox": [ 89, 714, 185, 727 ], "spans": [ { "bbox": [ 89, 714, 185, 727 ], "type": "text", "content": "不同数制之间的转换", "score": 1.0 } ] } ] }, { "bbox": [ 87, 729, 152, 742 ], "type": "text", "angle": 0, "index": 38, "lines": [ { "bbox": [ 89, 729, 154, 743 ], "spans": [ { "bbox": [ 89, 729, 154, 743 ], "type": "text", "content": "十进制的编码", "score": 1.0 } ] } ] }, { "bbox": [ 87, 745, 121, 757 ], "type": "text", "angle": 0, "index": 39, "lines": [ { "bbox": [ 88, 745, 123, 760 ], "spans": [ { "bbox": [ 88, 745, 123, 760 ], "type": "text", "content": "机器数", "score": 1.0 } ] } ] } ], "discarded_blocks": [], "page_size": [ 595, 841 ], "page_idx": 8 }, { "para_blocks": [ { "bbox": [ 87, 79, 377, 91 ], "type": "text", "angle": 0, "index": 0, "lines": [ { "bbox": [ 89, 79, 379, 92 ], "spans": [ { "bbox": [ 89, 79, 379, 92 ], "type": "text", "content": "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：", "score": 1.0 } ] } ] }, { "bbox": [ 88, 94, 324, 103 ], "type": "text", "angle": 0, "index": 1, "lines": [ { "bbox": [ 88, 94, 324, 104 ], "spans": [ { "bbox": [ 88, 95, 95, 102 ], "type": "inline_equation", "content": "^ \\ast", "score": 0.57 }, { "bbox": [ 95, 94, 324, 104 ], "type": "text", "content": "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", "score": 0.999 } ] } ] }, { "bbox": [ 96, 105, 323, 145 ], "type": "list", "angle": 0, "index": 6, "blocks": [ { "bbox": [ 96, 105, 323, 113 ], "type": "text", "angle": 0, "index": 2, "lines": [ { "bbox": [ 96, 104, 324, 113 ], "spans": [ { "bbox": [ 96, 104, 324, 113 ], "type": "text", "content": "·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", "score": 0.978 } ] } ] }, { "bbox": [ 96, 115, 235, 123 ], "type": "text", "angle": 0, "index": 3, "lines": [ { "bbox": [ 97, 115, 220, 123 ], "spans": [ { "bbox": [ 97, 115, 220, 123 ], "type": "text", "content": "·机器数的小数点用隐含规定的方式来表达", "score": 0.987 } ] } ] }, { "bbox": [ 96, 126, 207, 135 ], "type": "text", "angle": 0, "index": 4, "lines": [ { "bbox": [ 97, 126, 207, 135 ], "spans": [ { "bbox": [ 97, 126, 207, 135 ], "type": "text", "content": "·表示的数值范围受计算机字长的限制", "score": 0.982 } ] } ] }, { "bbox": [ 96, 137, 285, 145 ], "type": "text", "angle": 0, "index": 5, "lines": [ { "bbox": [ 96, 136, 286, 146 ], "spans": [ { "bbox": [ 96, 136, 286, 146 ], "type": "text", "content": "·编码方法：不同的排列方式，常见的有原码、反码、补码、移码。", "score": 0.99 } ] } ] } ], "sub_type": "text" }, { "type": "image", "bbox": [ 309, 142, 320, 154 ], "blocks": [ { "bbox": [ 309, 142, 320, 154 ], "lines": [ { "bbox": [ 309, 142, 320, 154 ], "spans": [ { "bbox": [ 309, 142, 320, 154 ], "type": "image", "image_path": "c47a7a94827b3662a134a37286e20304c8e0e73f91dd09676afa6229802037f6.jpg" } ] } ], "index": 7, "angle": 0, "type": "image_body" } ], "index": 7 }, { "bbox": [ 87, 174, 250, 193 ], "type": "title", "angle": 0, "index": 8, "lines": [ { "bbox": [ 88, 174, 252, 195 ], "spans": [ { "bbox": [ 88, 174, 252, 195 ], "type": "text", "content": "定点机器数的表示方法", "score": 1.0 } ] } ] }, { "bbox": [ 87, 231, 195, 243 ], "type": "text", "angle": 0, "index": 9, "lines": [ { "bbox": [ 89, 230, 195, 245 ], "spans": [ { "bbox": [ 89, 230, 195, 245 ], "type": "text", "content": "一个字节由 8 个位组成", "score": 1.0 } ] } ] }, { "bbox": [ 87, 246, 331, 259 ], "type": "text", "angle": 0, "index": 10, "lines": [ { "bbox": [ 89, 247, 332, 260 ], "spans": [ { "bbox": [ 89, 247, 332, 260 ], "type": "text", "content": "我们把这种按照一位一位表示数据的方式称为位模式", "score": 1.0 } ] } ] }, { "bbox": [ 87, 262, 174, 275 ], "type": "text", "angle": 0, "index": 11, "lines": [ { "bbox": [ 88, 263, 174, 275 ], "spans": [ { "bbox": [ 88, 263, 174, 275 ], "type": "text", "content": "对于无符号数编码", "score": 1.0 } ] } ] }, { "bbox": [ 87, 277, 272, 290 ], "type": "text", "angle": 0, "index": 12, "lines": [ { "bbox": [ 89, 278, 273, 291 ], "spans": [ { "bbox": [ 89, 278, 273, 291 ], "type": "text", "content": "在机器中的解释，采用原码表示法（？）", "score": 1.0 } ] } ] }, { "type": "image", "bbox": [ 88, 290, 461, 422 ], "blocks": [ { "bbox": [ 88, 290, 461, 422 ], "lines": [ { "bbox": [ 88, 290, 461, 422 ], "spans": [ { "bbox": [ 88, 290, 461, 422 ], "type": "image", "image_path": "29519d3b05891aec898580f89a8b7d69cdc6b6f2666f40bc361510a60e4b8e61.jpg" } ] } ], "index": 13, "angle": 0, "type": "image_body" } ], "index": 13 }, { "bbox": [ 87, 433, 237, 445 ], "type": "text", "angle": 0, "index": 14, "lines": [ { "bbox": [ 89, 434, 238, 446 ], "spans": [ { "bbox": [ 89, 434, 238, 446 ], "type": "text", "content": "对于有符号数的编码，采用补码", "score": 1.0 } ] } ] } ], "discarded_blocks": [], "page_size": [ 595, 841 ], "page_idx": 9 }, { "para_blocks": [ { "type": "image", "bbox": [ 88, 75, 481, 282 ], "blocks": [ { "bbox": [ 88, 75, 481, 282 ], "lines": [ { "bbox": [ 88, 75, 481, 282 ], "spans": [ { "bbox": [ 88, 75, 481, 282 ], "type": "image", "image_path": "3bb2c65a3b93dd5f3ba70445f8e1ac6b1845d70eca6912b30ec7b60296858a1a.jpg" } ] } ], "index": 0, "angle": 0, "type": "image_body" } ], "index": 0 }, { "bbox": [ 86, 296, 379, 310 ], "type": "text", "angle": 0, "index": 1, "lines": [ { "bbox": [ 89, 297, 379, 310 ], "spans": [ { "bbox": [ 89, 297, 379, 310 ], "type": "text", "content": "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：", "score": 1.0 } ] } ] }, { "bbox": [ 93, 312, 383, 326 ], "type": "text", "angle": 0, "index": 2, "lines": [ { "bbox": [ 95, 312, 383, 327 ], "spans": [ { "bbox": [ 95, 312, 383, 327 ], "type": "text", "content": "（这里的 B2U/B2T 是位向量到无符号数和有符号数的函数映射）", "score": 1.0 } ] } ] }, { "bbox": [ 87, 328, 217, 341 ], "type": "text", "angle": 0, "index": 3, "lines": [ { "bbox": [ 88, 327, 217, 343 ], "spans": [ { "bbox": [ 88, 327, 217, 343 ], "type": "text", "content": "最高位理解成负权重-2^w-1", "score": 1.0 } ] } ] }, { "bbox": [ 88, 350, 208, 364 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 88, 350, 208, 364 ], "spans": [ { "bbox": [ 88, 350, 208, 364 ], "type": "interline_equation", "content": "B 2 U _ {w} = x _ {w - 1} \\cdot 2 ^ {w} + B 2 T _ {w}", "image_path": "a4a48fbea7f612dad91bb421ab1b5bca91bc84a9189bcdaefe6f535669af5f99.jpg" } ] } ], "index": 4 }, { "bbox": [ 86, 375, 303, 387 ], "type": "text", "angle": 0, "index": 5, "lines": [ { "bbox": [ 88, 375, 303, 389 ], "spans": [ { "bbox": [ 88, 375, 303, 389 ], "type": "text", "content": "用 T2U 来表示有符号数到无符号数的函数映射", "score": 1.0 } ] } ] }, { "bbox": [ 87, 394, 370, 428 ], "type": "text", "angle": 0, "index": 6, "lines": [ { "bbox": [ 89, 393, 329, 429 ], "spans": [ { "bbox": [ 89, 393, 217, 429 ], "type": "inline_equation", "content": "T 2 U _ { w } ( x ) = \\left\\{ \\begin{array} { c } { { x + 2 ^ { w } , x < 0 } } \\\\ { { x , x > 0 } } \\end{array} \\right.", "score": 0.76 }, { "bbox": [ 238, 402, 329, 417 ], "type": "inline_equation", "content": "T 2 U _ { w } \\left( x \\right) = \\left( x + 2 ^ { w } \\right)", "score": 0.76 } ] } ] }, { "bbox": [ 88, 437, 238, 470 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 88, 437, 238, 470 ], "spans": [ { "bbox": [ 88, 437, 238, 470 ], "type": "interline_equation", "content": "U 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.", "image_path": "bebacba3b43ee8a983eac0873165fc32b0d2ed3fbac2c44949f709c7a6c51d81.jpg" } ] } ], "index": 7 }, { "bbox": [ 86, 484, 265, 497 ], "type": "text", "angle": 0, "index": 8, "lines": [ { "bbox": [ 88, 483, 267, 498 ], "spans": [ { "bbox": [ 88, 483, 267, 498 ], "type": "text", "content": "W位(包含了符号位！)补码表示的数值", "score": 1.0 } ] } ] }, { "bbox": [ 88, 504, 213, 536 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 88, 504, 213, 536 ], "spans": [ { "bbox": [ 88, 504, 213, 536 ], "type": "interline_equation", "content": "\\omega = - x _ {\\omega - 1} 2 ^ {\\omega - 1} + \\sum_ {i = 0} ^ {\\omega - 2} x _ {i} 2 ^ {i}", "image_path": "22c58311fdad6d274129624017c5b47b7d10f3e80e3f2d2a4075e54a8bb0c2f9.jpg" } ] } ], "index": 9 }, { "bbox": [ 86, 546, 379, 560 ], "type": "text", "angle": 0, "index": 10, "lines": [ { "bbox": [ 88, 545, 380, 562 ], "spans": [ { "bbox": [ 88, 545, 227, 562 ], "type": "text", "content": "也就是说，把第一位作为负数-", "score": 1.0 }, { "bbox": [ 227, 547, 249, 559 ], "type": "inline_equation", "content": ". 2 \\land \\mathfrak { n }", "score": 0.87 }, { "bbox": [ 249, 545, 380, 562 ], "type": "text", "content": "来处理；正数为 0,负数为 1；", "score": 1.0 } ] } ] }, { "bbox": [ 86, 561, 493, 605 ], "type": "text", "angle": 0, "index": 11, "lines": [ { "bbox": [ 89, 563, 494, 575 ], "spans": [ { "bbox": [ 89, 563, 494, 575 ], "type": "text", "content": "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，", "score": 1.0 } ] }, { "bbox": [ 89, 578, 489, 591 ], "spans": [ { "bbox": [ 89, 578, 489, 591 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 89, 592, 178, 607 ], "spans": [ { "bbox": [ 89, 592, 178, 607 ], "type": "text", "content": "1”。下面尝试证明。", "score": 1.0 } ] } ] }, { "bbox": [ 86, 608, 494, 637 ], "type": "text", "angle": 0, "index": 12, "lines": [ { "bbox": [ 88, 608, 495, 624 ], "spans": [ { "bbox": [ 88, 608, 323, 624 ], "type": "text", "content": "原命题精确描述为：相对于 w 位的二进制数，整数", "score": 1.0 }, { "bbox": [ 323, 608, 359, 622 ], "type": "inline_equation", "content": "\\mathsf { b } \\in ( 0 , ]", "score": 0.85 }, { "bbox": [ 359, 608, 379, 624 ], "type": "text", "content": "，即", "score": 1.0 }, { "bbox": [ 380, 608, 416, 622 ], "type": "inline_equation", "content": "\\mathsf { b } \\in ( 0 , ]", "score": 0.84 }, { "bbox": [ 416, 608, 448, 624 ], "type": "text", "content": "，等式", "score": 1.0 }, { "bbox": [ 448, 608, 495, 622 ], "type": "inline_equation", "content": "- b = - b + 1", "score": 0.85 } ] }, { "bbox": [ 86, 622, 119, 640 ], "spans": [ { "bbox": [ 86, 622, 119, 640 ], "type": "text", "content": "成立。", "score": 1.0 } ] } ] }, { "bbox": [ 86, 640, 453, 652 ], "type": "text", "angle": 0, "index": 13, "lines": [ { "bbox": [ 88, 640, 452, 653 ], "spans": [ { "bbox": [ 88, 640, 452, 653 ], "type": "text", "content": "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？", "score": 1.0 } ] } ] }, { "bbox": [ 86, 655, 502, 683 ], "type": "text", "angle": 0, "index": 14, "lines": [ { "bbox": [ 89, 655, 501, 668 ], "spans": [ { "bbox": [ 89, 655, 363, 668 ], "type": "text", "content": "反码、补码的真值为负数的时候机器数形式值（符号位作为", "score": 1.0 }, { "bbox": [ 363, 656, 384, 668 ], "type": "inline_equation", "content": "{ 2 } \\Lambda _ { \\mathsf { n } }", "score": 0.89 }, { "bbox": [ 384, 655, 501, 668 ], "type": "text", "content": "而不是正负号）减去对应", "score": 1.0 } ] }, { "bbox": [ 89, 671, 349, 684 ], "spans": [ { "bbox": [ 89, 671, 101, 684 ], "type": "text", "content": "的", "score": 1.0 }, { "bbox": [ 101, 671, 139, 684 ], "type": "inline_equation", "content": "2 \\sim ( \\mathsf { n } + 1 )", "score": 0.91 }, { "bbox": [ 139, 671, 171, 684 ], "type": "text", "content": "或者是", "score": 1.0 }, { "bbox": [ 171, 671, 186, 683 ], "type": "inline_equation", "content": "_ { 2 ^ { \\wedge } }", "score": 0.66 }, { "bbox": [ 186, 671, 222, 684 ], "type": "text", "content": "（n+1）", "score": 1.0 }, { "bbox": [ 222, 671, 236, 683 ], "type": "inline_equation", "content": "+ 1", "score": 0.56 }, { "bbox": [ 236, 671, 349, 684 ], "type": "text", "content": "就是这个机器数的真值。", "score": 1.0 } ] } ] }, { "bbox": [ 86, 687, 245, 700 ], "type": "text", "angle": 0, "index": 15, "lines": [ { "bbox": [ 88, 685, 244, 703 ], "spans": [ { "bbox": [ 88, 685, 205, 703 ], "type": "text", "content": "移码是无论正负直接减去", "score": 1.0 }, { "bbox": [ 205, 687, 244, 700 ], "type": "inline_equation", "content": "2 \\sim ( \\mathsf { n } + 1 )", "score": 0.87 } ] } ] }, { "bbox": [ 87, 702, 195, 715 ], "type": "text", "angle": 0, "index": 16, "lines": [ { "bbox": [ 89, 703, 195, 716 ], "spans": [ { "bbox": [ 89, 703, 195, 716 ], "type": "text", "content": "而原码没有类似的结果", "score": 1.0 } ] } ] } ], "discarded_blocks": [], "page_size": [ 595, 841 ], "page_idx": 10 }, { "para_blocks": [ { "type": "image", "bbox": [ 88, 82, 483, 259 ], "blocks": [ { "bbox": [ 88, 82, 483, 259 ], "lines": [ { "bbox": [ 88, 82, 483, 259 ], "spans": [ { "bbox": [ 88, 82, 483, 259 ], "type": "image", "image_path": "78e6ebe0fa6d18716eca1d48f88e453ca73f8c16ae9fe3c381407ee46ef7c2df.jpg" } ] } ], "index": 0, "angle": 0, "type": "image_body" } ], "index": 0 }, { "bbox": [ 88, 265, 274, 280 ], "type": "text", "angle": 0, "index": 1, "lines": [ { "bbox": [ 88, 265, 274, 280 ], "spans": [ { "bbox": [ 88, 265, 274, 280 ], "type": "text", "content": "有符号数最高位为 0（正数），其余为 1", "score": 1.0 } ] } ] }, { "type": "image", "bbox": [ 88, 301, 477, 477 ], "blocks": [ { "bbox": [ 88, 301, 477, 477 ], "lines": [ { "bbox": [ 88, 301, 477, 477 ], "spans": [ { "bbox": [ 88, 301, 477, 477 ], "type": "image", "image_path": "e3ecdb1331e495f2deeb4e6668c8da5f41e4d66251fb5eee1929cfca02758dec.jpg" } ] } ], "index": 2, "angle": 0, "type": "image_body" } ], "index": 2 }, { "bbox": [ 88, 483, 312, 497 ], "type": "text", "angle": 0, "index": 3, "lines": [ { "bbox": [ 89, 484, 312, 497 ], "spans": [ { "bbox": [ 89, 484, 312, 497 ], "type": "text", "content": "有符号数的-1和无符号数的最大值一样编码表示", "score": 1.0 } ] } ] }, { "type": "image", "bbox": [ 88, 499, 525, 684 ], "blocks": [ { "bbox": [ 88, 499, 525, 684 ], "lines": [ { "bbox": [ 88, 499, 525, 684 ], "spans": [ { "bbox": [ 88, 499, 525, 684 ], "type": "image", "image_path": "d7ebf2a15fdae3ac42d3466cc5c4d421de2dfae73da3be0f75e1620b2f98e562.jpg" } ] } ], "index": 4, "angle": 0, "type": "image_body" } ], "index": 4 } ], "discarded_blocks": [], "page_size": [ 595, 841 ], "page_idx": 11 }, { "para_blocks": [ { "bbox": [ 86, 84, 243, 103 ], "type": "title", "angle": 0, "index": 0, "lines": [ { "bbox": [ 86, 84, 245, 105 ], "spans": [ { "bbox": [ 86, 84, 245, 105 ], "type": "text", "content": "2．真值与补码的转换", "score": 1.0 } ] } ] }, { "bbox": [ 86, 140, 142, 153 ], "type": "title", "angle": 0, "index": 1, "lines": [ { "bbox": [ 88, 140, 142, 154 ], "spans": [ { "bbox": [ 88, 140, 142, 154 ], "type": "text", "content": "真值->补码", "score": 1.0 } ] } ] }, { "bbox": [ 86, 156, 235, 168 ], "type": "text", "angle": 0, "index": 2, "lines": [ { "bbox": [ 88, 155, 235, 170 ], "spans": [ { "bbox": [ 88, 155, 173, 170 ], "type": "text", "content": "正数的补码：去掉", "score": 1.0 }, { "bbox": [ 173, 157, 180, 167 ], "type": "inline_equation", "content": "^ +", "score": 0.76 }, { "bbox": [ 180, 155, 235, 170 ], "type": "text", "content": "号前面加 0。", "score": 1.0 } ] } ] }, { "bbox": [ 86, 171, 440, 184 ], "type": "text", "angle": 0, "index": 3, "lines": [ { "bbox": [ 88, 169, 442, 186 ], "spans": [ { "bbox": [ 88, 169, 442, 186 ], "type": "text", "content": "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。", "score": 1.0 } ] } ] }, { "bbox": [ 86, 186, 469, 199 ], "type": "text", "angle": 0, "index": 4, "lines": [ { "bbox": [ 88, 185, 470, 200 ], "spans": [ { "bbox": [ 88, 185, 470, 200 ], "type": "text", "content": "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;", "score": 1.0 } ] } ] }, { "bbox": [ 86, 202, 294, 215 ], "type": "text", "angle": 0, "index": 5, "lines": [ { "bbox": [ 88, 202, 296, 216 ], "spans": [ { "bbox": [ 88, 202, 296, 216 ], "type": "text", "content": "计算一个负数的补码时，通常遵循以下步骤：", "score": 1.0 } ] } ] }, { "bbox": [ 105, 217, 486, 262 ], "type": "list", "angle": 0, "index": 9, "blocks": [ { "bbox": [ 105, 217, 486, 231 ], "type": "text", "angle": 0, "index": 6, "lines": [ { "bbox": [ 107, 218, 487, 232 ], "spans": [ { "bbox": [ 107, 218, 487, 232 ], "type": "text", "content": "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。", "score": 1.0 } ] } ] }, { "bbox": [ 105, 233, 386, 246 ], "type": "text", "angle": 0, "index": 7, "lines": [ { "bbox": [ 105, 232, 385, 248 ], "spans": [ { "bbox": [ 105, 232, 373, 248 ], "type": "text", "content": "2. 取反：将二进制数的每一位取反，即 0 变为 1，1 变为", "score": 1.0 }, { "bbox": [ 373, 234, 385, 246 ], "type": "inline_equation", "content": "0 _ { \\circ }", "score": 0.64 } ] } ] }, { "bbox": [ 105, 249, 377, 262 ], "type": "text", "angle": 0, "index": 8, "lines": [ { "bbox": [ 105, 248, 379, 264 ], "spans": [ { "bbox": [ 105, 248, 379, 264 ], "type": "text", "content": "3. 加 1：在取反结果的基础上加 1，得到最终的补码表示。", "score": 1.0 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 86, 264, 454, 277 ], "type": "text", "angle": 0, "index": 10, "lines": [ { "bbox": [ 88, 264, 455, 279 ], "spans": [ { "bbox": [ 88, 264, 455, 279 ], "type": "text", "content": "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", "score": 1.0 } ] } ] }, { "bbox": [ 86, 280, 504, 308 ], "type": "text", "angle": 0, "index": 11, "lines": [ { "bbox": [ 89, 280, 505, 293 ], "spans": [ { "bbox": [ 89, 280, 505, 293 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 88, 296, 421, 309 ], "spans": [ { "bbox": [ 88, 296, 337, 309 ], "type": "text", "content": "取反（从0变成1—），不都是符号位为1吗？但参与", "score": 1.0 }, { "bbox": [ 337, 297, 351, 308 ], "type": "inline_equation", "content": "+ 1", "score": 0.82 }, { "bbox": [ 351, 296, 421, 309 ], "type": "text", "content": "运算是必须的。", "score": 1.0 } ] } ] }, { "bbox": [ 86, 312, 142, 324 ], "type": "title", "angle": 0, "index": 12, "lines": [ { "bbox": [ 88, 312, 142, 325 ], "spans": [ { "bbox": [ 88, 312, 112, 325 ], "type": "text", "content": "补码-", "score": 1.0 }, { "bbox": [ 113, 312, 120, 322 ], "type": "inline_equation", "content": "\\cdot >", "score": 0.68 }, { "bbox": [ 121, 312, 142, 325 ], "type": "text", "content": "真值", "score": 1.0 } ] } ] }, { "bbox": [ 86, 327, 289, 339 ], "type": "text", "angle": 0, "index": 13, "lines": [ { "bbox": [ 88, 325, 290, 342 ], "spans": [ { "bbox": [ 88, 325, 267, 342 ], "type": "text", "content": "符号位 0 的补码的真值：去掉 0 前面加", "score": 1.0 }, { "bbox": [ 267, 328, 274, 338 ], "type": "inline_equation", "content": "^ +", "score": 0.7 }, { "bbox": [ 274, 325, 290, 342 ], "type": "text", "content": "号。", "score": 1.0 } ] } ] }, { "bbox": [ 86, 343, 200, 355 ], "type": "text", "angle": 0, "index": 14, "lines": [ { "bbox": [ 89, 343, 200, 356 ], "spans": [ { "bbox": [ 89, 343, 200, 356 ], "type": "text", "content": "符号位1的补码的真值：", "score": 1.0 } ] } ] }, { "bbox": [ 86, 358, 496, 417 ], "type": "list", "angle": 0, "index": 18, "blocks": [ { "bbox": [ 89, 358, 379, 370 ], "type": "text", "angle": 0, "index": 15, "lines": [ { "bbox": [ 92, 357, 379, 373 ], "spans": [ { "bbox": [ 92, 357, 379, 373 ], "type": "text", "content": "1、去掉 1 前面加-号，从右到左找到第一个 1，左边全部取反。", "score": 1.0 } ] } ] }, { "bbox": [ 87, 373, 258, 386 ], "type": "text", "angle": 0, "index": 16, "lines": [ { "bbox": [ 88, 374, 258, 387 ], "spans": [ { "bbox": [ 88, 374, 258, 387 ], "type": "text", "content": "2、负数的原码就是它的补码的补码。", "score": 1.0 } ] } ] }, { "bbox": [ 86, 389, 496, 417 ], "type": "text", "angle": 0, "index": 17, "lines": [ { "bbox": [ 88, 389, 497, 403 ], "spans": [ { "bbox": [ 88, 389, 497, 403 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 88, 404, 133, 419 ], "spans": [ { "bbox": [ 88, 404, 133, 419 ], "type": "text", "content": "各位取反", "score": 1.0 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 105, 470, 404, 489 ], "type": "title", "angle": 0, "index": 19, "lines": [ { "bbox": [ 104, 467, 406, 491 ], "spans": [ { "bbox": [ 104, 467, 153, 491 ], "type": "text", "content": "3.对于", "score": 1.0 }, { "bbox": [ 153, 470, 242, 489 ], "type": "inline_equation", "content": "( X + 2 \\land ( \\mathbf { n } + 1 ) )", "score": 0.69 }, { "bbox": [ 242, 467, 406, 491 ], "type": "text", "content": "mod (2^(n+1))的解释", "score": 1.0 } ] } ] }, { "bbox": [ 86, 540, 489, 570 ], "type": "text", "angle": 0, "index": 20, "lines": [ { "bbox": [ 89, 541, 490, 555 ], "spans": [ { "bbox": [ 89, 541, 272, 555 ], "type": "text", "content": "对某两个整数a，b，若它们除以正整数", "score": 1.0 }, { "bbox": [ 273, 542, 285, 553 ], "type": "inline_equation", "content": "\\mathsf { m }", "score": 0.53 }, { "bbox": [ 285, 541, 490, 555 ], "type": "text", "content": "所得的余数相等，则称a，b对于模m同余，", "score": 1.0 } ] }, { "bbox": [ 89, 557, 247, 570 ], "spans": [ { "bbox": [ 89, 557, 247, 570 ], "type": "text", "content": "也就是严格来说，存在整数k使得", "score": 1.0 } ] } ] }, { "bbox": [ 86, 572, 334, 585 ], "type": "text", "angle": 0, "index": 21, "lines": [ { "bbox": [ 88, 572, 335, 587 ], "spans": [ { "bbox": [ 88, 572, 133, 585 ], "type": "inline_equation", "content": "a - b = k m", "score": 0.88 }, { "bbox": [ 133, 572, 226, 587 ], "type": "text", "content": "，则称 a,b 对于除数", "score": 1.0 }, { "bbox": [ 226, 574, 238, 585 ], "type": "inline_equation", "content": "\\mathsf { m }", "score": 0.65 }, { "bbox": [ 238, 572, 335, 587 ], "type": "text", "content": "是同余的。一般记做", "score": 1.0 } ] } ] }, { "bbox": [ 87, 588, 151, 601 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 87, 588, 151, 601 ], "spans": [ { "bbox": [ 87, 588, 151, 601 ], "type": "interline_equation", "content": "a \\equiv b (\\bmod m)", "image_path": "3b36ee0f04f604f2f8b68ab0a13fcabc79e0b7adb7d4065653ecf97005c7d5cb.jpg" } ] } ], "index": 22 }, { "bbox": [ 86, 603, 454, 616 ], "type": "text", "angle": 0, "index": 23, "lines": [ { "bbox": [ 88, 603, 455, 618 ], "spans": [ { "bbox": [ 88, 603, 455, 618 ], "type": "text", "content": "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", "score": 1.0 } ] } ] }, { "bbox": [ 86, 618, 502, 663 ], "type": "text", "angle": 0, "index": 24, "lines": [ { "bbox": [ 88, 619, 502, 633 ], "spans": [ { "bbox": [ 88, 619, 145, 632 ], "type": "inline_equation", "content": "\\mathsf { A } { = } \\mathsf { B } { + } \\mathsf { K } { \\times } \\mathsf { M } ( \\mathsf { K }", "score": 0.76 }, { "bbox": [ 146, 619, 226, 633 ], "type": "text", "content": "为整数)，则记为", "score": 1.0 }, { "bbox": [ 226, 619, 290, 632 ], "type": "inline_equation", "content": "\\mathsf { A } \\equiv \\mathsf { B } ( \\mathsf { m o d } \\mathsf { M } )", "score": 0.64 }, { "bbox": [ 290, 619, 502, 633 ], "type": "text", "content": ")，即 A、B各除以 M后的余数相同。在补码运", "score": 1.0 } ] }, { "bbox": [ 88, 634, 498, 648 ], "spans": [ { "bbox": [ 88, 634, 203, 648 ], "type": "text", "content": "算中，[A]补-[B]补=[A]补", "score": 1.0 }, { "bbox": [ 203, 635, 224, 647 ], "type": "inline_equation", "content": "+ \\mathsf { M }", "score": 0.58 }, { "bbox": [ 224, 634, 311, 648 ], "type": "text", "content": "-[B]补，而 M-[B]补", "score": 1.0 }, { "bbox": [ 312, 636, 321, 645 ], "type": "inline_equation", "content": "=", "score": 0.72 }, { "bbox": [ 321, 634, 498, 648 ], "type": "text", "content": "[-B]补，因此补码可以借助加法运算来", "score": 1.0 } ] }, { "bbox": [ 88, 650, 379, 665 ], "spans": [ { "bbox": [ 88, 650, 379, 665 ], "type": "text", "content": "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：", "score": 1.0 } ] } ] }, { "bbox": [ 86, 666, 502, 694 ], "type": "text", "angle": 0, "index": 25, "lines": [ { "bbox": [ 88, 666, 504, 680 ], "spans": [ { "bbox": [ 88, 666, 290, 680 ], "type": "text", "content": "模运算的同余性质：对于任意整数 a 和模数", "score": 1.0 }, { "bbox": [ 290, 667, 302, 678 ], "type": "inline_equation", "content": "\\mathsf { m }", "score": 0.63 }, { "bbox": [ 302, 666, 323, 680 ], "type": "text", "content": "，有", "score": 1.0 }, { "bbox": [ 323, 666, 408, 679 ], "type": "inline_equation", "content": "\\mathsf { a } \\equiv \\mathsf { a } + \\mathsf { k m } ( \\mathsf { m o d } \\mathsf { m } )", "score": 0.81 }, { "bbox": [ 409, 666, 504, 680 ], "type": "text", "content": "，其中 k为整数。这", "score": 1.0 } ] }, { "bbox": [ 88, 682, 376, 696 ], "spans": [ { "bbox": [ 88, 682, 143, 696 ], "type": "text", "content": "意味着在模", "score": 1.0 }, { "bbox": [ 143, 682, 155, 694 ], "type": "inline_equation", "content": "\\mathsf { m }", "score": 0.66 }, { "bbox": [ 155, 682, 304, 696 ], "type": "text", "content": "的运算中，数值是循环的，超过", "score": 1.0 }, { "bbox": [ 304, 682, 316, 693 ], "type": "inline_equation", "content": "\\mathsf { m }", "score": 0.66 }, { "bbox": [ 317, 682, 376, 696 ], "type": "text", "content": "会回到起点。", "score": 1.0 } ] } ] }, { "bbox": [ 86, 697, 376, 709 ], "type": "text", "angle": 0, "index": 26, "lines": [ { "bbox": [ 88, 696, 376, 712 ], "spans": [ { "bbox": [ 88, 696, 167, 712 ], "type": "text", "content": "为何常见写法是", "score": 1.0 }, { "bbox": [ 167, 698, 217, 710 ], "type": "inline_equation", "content": "^ { 6 6 } x + 2 \\wedge _ { \\mathsf { n } + 1 }", "score": 0.9 }, { "bbox": [ 217, 696, 244, 712 ], "type": "text", "content": "mod", "score": 1.0 }, { "bbox": [ 244, 698, 271, 709 ], "type": "inline_equation", "content": "\\mathsf { \\pm } \\mathsf { \\Lambda } \\mathsf { n } \\mathsf { \\pm } ^ { \\prime }", "score": 0.82 }, { "bbox": [ 272, 696, 313, 712 ], "type": "text", "content": "1”而不是", "score": 1.0 }, { "bbox": [ 313, 698, 322, 709 ], "type": "inline_equation", "content": "\\pmb { \\times }", "score": 0.52 }, { "bbox": [ 323, 696, 349, 712 ], "type": "text", "content": "mod", "score": 1.0 }, { "bbox": [ 349, 698, 376, 710 ], "type": "inline_equation", "content": "^ { 2 n + 1 }", "score": 0.72 } ] } ] }, { "bbox": [ 86, 712, 324, 725 ], "type": "text", "angle": 0, "index": 27, "lines": [ { "bbox": [ 88, 711, 325, 728 ], "spans": [ { "bbox": [ 88, 711, 136, 728 ], "type": "text", "content": "数论上，", "score": 1.0 }, { "bbox": [ 136, 713, 149, 725 ], "type": "inline_equation", "content": "^ { * } \\times", "score": 0.67 }, { "bbox": [ 149, 711, 161, 728 ], "type": "text", "content": "与", "score": 1.0 }, { "bbox": [ 161, 714, 223, 726 ], "type": "inline_equation", "content": "\\mathsf { x } + 2 \\wedge \\{ \\mathsf { n } + 1 \\} \\times ^ { \\prime \\prime }", "score": 0.9 }, { "bbox": [ 223, 711, 244, 728 ], "type": "text", "content": "在模", "score": 1.0 }, { "bbox": [ 245, 714, 285, 726 ], "type": "inline_equation", "content": "2 \\cdot \\{ \\mathsf { n } + 1 \\}", "score": 0.91 }, { "bbox": [ 286, 711, 325, 728 ], "type": "text", "content": "下等价；", "score": 1.0 } ] } ] }, { "bbox": [ 86, 728, 501, 756 ], "type": "text", "angle": 0, "index": 28, "lines": [ { "bbox": [ 88, 727, 502, 742 ], "spans": [ { "bbox": [ 88, 727, 405, 742 ], "type": "text", "content": "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", "score": 1.0 }, { "bbox": [ 405, 729, 448, 741 ], "type": "inline_equation", "content": "2 \\times \\{ \\mathsf { n } + 1 \\}", "score": 0.89 }, { "bbox": [ 448, 727, 502, 742 ], "type": "text", "content": "更能直观反", "score": 1.0 } ] }, { "bbox": [ 88, 744, 299, 758 ], "spans": [ { "bbox": [ 88, 744, 193, 758 ], "type": "text", "content": "映“负数被搬到了高位", "score": 1.0 }, { "bbox": [ 193, 745, 207, 756 ], "type": "inline_equation", "content": "\\ O = \\uparrow", "score": 0.82 }, { "bbox": [ 207, 744, 299, 758 ], "type": "text", "content": "的区间”这个事实。", "score": 1.0 } ] } ] } ], "discarded_blocks": [], "page_size": [ 595, 841 ], "page_idx": 12 }, { "para_blocks": [ { "bbox": [ 86, 79, 421, 108 ], "type": "list", "angle": 0, "index": 2, "blocks": [ { "bbox": [ 86, 79, 359, 92 ], "type": "text", "angle": 0, "index": 0, "lines": [ { "bbox": [ 87, 76, 360, 95 ], "spans": [ { "bbox": [ 87, 76, 316, 95 ], "type": "text", "content": " 非负数直接写成“它自己” (因为落在小半区间", "score": 1.0 }, { "bbox": [ 317, 79, 352, 92 ], "type": "inline_equation", "content": "[ 0 , 2 \\land \\mathsf { n } ) ]", "score": 0.86 }, { "bbox": [ 352, 76, 360, 95 ], "type": "text", "content": ")；", "score": 1.0 } ] } ] }, { "bbox": [ 86, 95, 421, 108 ], "type": "text", "angle": 0, "index": 1, "lines": [ { "bbox": [ 87, 93, 420, 111 ], "spans": [ { "bbox": [ 87, 93, 148, 111 ], "type": "text", "content": " 负数写成", "score": 1.0 }, { "bbox": [ 148, 95, 215, 108 ], "type": "inline_equation", "content": "^ { \\mathfrak { a } } \\mathsf { X } + 2 ^ { \\wedge } \\{ \\mathsf { n } + 1 \\} ^ { \\prime \\prime }", "score": 0.91 }, { "bbox": [ 215, 93, 336, 111 ], "type": "text", "content": "(因为这样就落在大半区间", "score": 1.0 }, { "bbox": [ 336, 95, 420, 108 ], "type": "inline_equation", "content": "[ 2 \\land \\neg , 2 \\land \\{ \\mathsf { n } + 1 \\} - 1 ] ) _ { \\circ }", "score": 0.86 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 86, 110, 473, 122 ], "type": "text", "angle": 0, "index": 3, "lines": [ { "bbox": [ 88, 109, 474, 124 ], "spans": [ { "bbox": [ 88, 109, 171, 124 ], "type": "text", "content": "在计算机系统中，", "score": 1.0 }, { "bbox": [ 172, 111, 181, 122 ], "type": "inline_equation", "content": "\\mathsf { n }", "score": 0.67 }, { "bbox": [ 182, 109, 393, 124 ], "type": "text", "content": "位定点整数（包括符号位）补码的取值范围是", "score": 1.0 }, { "bbox": [ 393, 111, 420, 122 ], "type": "inline_equation", "content": "- 2 \\land \\mathsf { n }", "score": 0.91 }, { "bbox": [ 421, 109, 433, 124 ], "type": "text", "content": "到", "score": 1.0 }, { "bbox": [ 433, 111, 468, 122 ], "type": "inline_equation", "content": "2 \\ n _ { \\mathsf { n } } - 1", "score": 0.87 }, { "bbox": [ 468, 109, 474, 124 ], "type": "text", "content": "。", "score": 1.0 } ] } ] }, { "bbox": [ 86, 125, 502, 154 ], "type": "text", "angle": 0, "index": 4, "lines": [ { "bbox": [ 88, 125, 503, 139 ], "spans": [ { "bbox": [ 88, 125, 164, 139 ], "type": "text", "content": "这意味着总共有", "score": 1.0 }, { "bbox": [ 164, 126, 205, 138 ], "type": "inline_equation", "content": "2 \\cdot \\{ \\mathsf { n } + 1 \\}", "score": 0.92 }, { "bbox": [ 205, 125, 375, 139 ], "type": "text", "content": "个不同的数值可以表示。因此，模数", "score": 1.0 }, { "bbox": [ 376, 126, 416, 138 ], "type": "inline_equation", "content": "2 \\cdot \\{ \\mathsf { n } + 1 \\}", "score": 0.92 }, { "bbox": [ 417, 125, 503, 139 ], "type": "text", "content": "对应于这些数值的", "score": 1.0 } ] }, { "bbox": [ 88, 141, 128, 156 ], "spans": [ { "bbox": [ 88, 141, 128, 156 ], "type": "text", "content": "总数量。", "score": 1.0 } ] } ] }, { "bbox": [ 86, 157, 497, 185 ], "type": "text", "angle": 0, "index": 5, "lines": [ { "bbox": [ 88, 156, 498, 171 ], "spans": [ { "bbox": [ 88, 156, 174, 171 ], "type": "text", "content": "负数的表示：在模", "score": 1.0 }, { "bbox": [ 174, 157, 214, 170 ], "type": "inline_equation", "content": "2 \\cdot \\{ \\mathsf { n } + 1 \\}", "score": 0.86 }, { "bbox": [ 214, 156, 351, 171 ], "type": "text", "content": "的系统中，负数 X 可以表示为", "score": 1.0 }, { "bbox": [ 351, 157, 411, 170 ], "type": "inline_equation", "content": "2 \\wedge \\{ \\mathsf { n } + 1 \\} + \\mathsf { X } ,", "score": 0.92 }, { "bbox": [ 411, 156, 498, 171 ], "type": "text", "content": ",因为 X 为负数，会", "score": 1.0 } ] }, { "bbox": [ 89, 173, 381, 186 ], "spans": [ { "bbox": [ 89, 173, 111, 186 ], "type": "text", "content": "落在", "score": 1.0 }, { "bbox": [ 111, 173, 138, 185 ], "type": "inline_equation", "content": "2 \\land ( \\mathsf { n } )", "score": 0.87 }, { "bbox": [ 138, 173, 151, 186 ], "type": "text", "content": "到", "score": 1.0 }, { "bbox": [ 151, 173, 207, 185 ], "type": "inline_equation", "content": "2 \\cdot \\{ \\mathsf { n } + 1 \\} - 1", "score": 0.91 }, { "bbox": [ 207, 173, 381, 186 ], "type": "text", "content": "的范围内，符合无符号数的表示范围。", "score": 1.0 } ] } ] }, { "bbox": [ 86, 188, 483, 201 ], "type": "text", "angle": 0, "index": 6, "lines": [ { "bbox": [ 88, 185, 480, 206 ], "spans": [ { "bbox": [ 88, 185, 132, 206 ], "type": "text", "content": "因为模为", "score": 1.0 }, { "bbox": [ 133, 188, 194, 201 ], "type": "inline_equation", "content": "2 \\cdot ( n + 1 ) , k = 1", "score": 0.77 }, { "bbox": [ 174, 189, 193, 200 ], "type": "inline_equation", "content": "k = 1", "score": 0.6 }, { "bbox": [ 195, 185, 268, 206 ], "type": "text", "content": "，那么就可以将-", "score": 1.0 }, { "bbox": [ 269, 188, 320, 200 ], "type": "inline_equation", "content": "2 ^ { \\wedge } \\mathsf { n } - 2 ^ { \\wedge } \\mathsf { n } - 1", "score": 0.88 }, { "bbox": [ 321, 185, 354, 206 ], "type": "text", "content": "统一成", "score": 1.0 }, { "bbox": [ 354, 189, 408, 201 ], "type": "inline_equation", "content": "( X { + } 2 ^ { \\wedge } ( \\mathsf { n } { + } 1 ) )", "score": 0.79 }, { "bbox": [ 408, 185, 437, 206 ], "type": "text", "content": ") mod", "score": 1.0 }, { "bbox": [ 437, 189, 480, 201 ], "type": "inline_equation", "content": "( 2 \\land ( \\mathsf { n } + 1 ) )", "score": 0.81 } ] } ] }, { "bbox": [ 86, 203, 498, 232 ], "type": "text", "angle": 0, "index": 7, "lines": [ { "bbox": [ 88, 203, 499, 217 ], "spans": [ { "bbox": [ 88, 203, 499, 217 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 88, 219, 148, 233 ], "spans": [ { "bbox": [ 88, 219, 148, 233 ], "type": "text", "content": "模的同余数。", "score": 1.0 } ] } ] }, { "bbox": [ 86, 234, 495, 263 ], "type": "text", "angle": 0, "index": 8, "lines": [ { "bbox": [ 95, 233, 497, 249 ], "spans": [ { "bbox": [ 95, 233, 340, 249 ], "type": "text", "content": "（这里的取模运算，请让我们抛弃符号数，eg.-2 mod", "score": 1.0 }, { "bbox": [ 340, 235, 360, 248 ], "type": "inline_equation", "content": "8 { = } 6", "score": 0.8 }, { "bbox": [ 361, 233, 364, 249 ], "type": "text", "content": ",", "score": 1.0 }, { "bbox": [ 365, 235, 403, 248 ], "type": "inline_equation", "content": "[ 6 ] { = } 1 1 0", "score": 0.58 }, { "bbox": [ 403, 233, 443, 249 ], "type": "text", "content": ",而 [-2]补", "score": 1.0 }, { "bbox": [ 444, 235, 475, 248 ], "type": "inline_equation", "content": "\\mathord { = } 1 1 1 0", "score": 0.63 }, { "bbox": [ 476, 233, 497, 249 ], "type": "text", "content": "，当", "score": 1.0 } ] }, { "bbox": [ 89, 250, 189, 264 ], "spans": [ { "bbox": [ 89, 250, 189, 264 ], "type": "text", "content": "成原码，去掉符号位）", "score": 1.0 } ] } ] }, { "bbox": [ 86, 265, 495, 294 ], "type": "text", "angle": 0, "index": 9, "lines": [ { "bbox": [ 89, 266, 496, 279 ], "spans": [ { "bbox": [ 89, 266, 214, 279 ], "type": "text", "content": "规定：把0当成正数，也即", "score": 1.0 }, { "bbox": [ 214, 266, 227, 278 ], "type": "inline_equation", "content": "+ 0", "score": 0.85 }, { "bbox": [ 228, 266, 496, 279 ], "type": "text", "content": "，这样0的编码就变成：0，0000000。那8位二进制表示", "score": 1.0 } ] }, { "bbox": [ 88, 281, 255, 295 ], "spans": [ { "bbox": [ 88, 281, 184, 295 ], "type": "text", "content": "的正数范围仍然是：", "score": 1.0 }, { "bbox": [ 185, 282, 250, 294 ], "type": "inline_equation", "content": "+ 0 -- + 1 2 7 _ { \\mathrm { { ( } } }", "score": 0.73 }, { "bbox": [ 251, 281, 255, 295 ], "type": "text", "content": "。", "score": 1.0 } ] } ] }, { "bbox": [ 86, 296, 492, 341 ], "type": "text", "angle": 0, "index": 10, "lines": [ { "bbox": [ 89, 297, 491, 310 ], "spans": [ { "bbox": [ 89, 297, 491, 310 ], "type": "text", "content": "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-", "score": 1.0 } ] }, { "bbox": [ 89, 313, 493, 326 ], "spans": [ { "bbox": [ 89, 313, 493, 326 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 93, 329, 313, 341 ], "spans": [ { "bbox": [ 93, 329, 313, 341 ], "type": "text", "content": "—— -0变成：-128 —— -1，就能成功解决问题。", "score": 1.0 } ] } ] }, { "bbox": [ 86, 343, 498, 371 ], "type": "text", "angle": 0, "index": 11, "lines": [ { "bbox": [ 88, 343, 499, 358 ], "spans": [ { "bbox": [ 88, 343, 143, 358 ], "type": "text", "content": "-0 的补数是", "score": 1.0 }, { "bbox": [ 144, 344, 233, 357 ], "type": "inline_equation", "content": "2 5 6 - 0 = 2 5 6 = 0 \\times 1 0 0", "score": 0.92 }, { "bbox": [ 233, 343, 441, 358 ], "type": "text", "content": "，由于是“8 位二进制数”，所以-0 的补数是", "score": 1.0 }, { "bbox": [ 441, 343, 467, 357 ], "type": "inline_equation", "content": "0 \\times 0 0", "score": 0.64 }, { "bbox": [ 467, 343, 499, 358 ], "type": "text", "content": "；‘我", "score": 1.0 } ] }, { "bbox": [ 88, 359, 199, 373 ], "spans": [ { "bbox": [ 88, 359, 134, 373 ], "type": "text", "content": "们知道“-", "score": 1.0 }, { "bbox": [ 134, 359, 167, 371 ], "type": "inline_equation", "content": "\\cdot 1 = 0 - 1 \\prime", "score": 0.85 }, { "bbox": [ 167, 359, 199, 373 ], "type": "text", "content": "，所以", "score": 1.0 } ] } ] }, { "bbox": [ 86, 375, 498, 403 ], "type": "text", "angle": 0, "index": 12, "lines": [ { "bbox": [ 88, 375, 499, 389 ], "spans": [ { "bbox": [ 88, 375, 143, 389 ], "type": "text", "content": "-1 的补数是", "score": 1.0 }, { "bbox": [ 143, 375, 226, 388 ], "type": "inline_equation", "content": "2 5 6 - 1 = 2 5 5 = 0 \\times 1 =", "score": 0.89 }, { "bbox": [ 226, 375, 499, 389 ], "type": "text", "content": "；这就好比是\"0-1\"不够减，\"借 256\"得到的（这里借的是模", "score": 1.0 } ] }, { "bbox": [ 86, 388, 130, 406 ], "spans": [ { "bbox": [ 86, 388, 130, 406 ], "type": "text", "content": "数值）。", "score": 1.0 } ] } ] }, { "bbox": [ 86, 406, 217, 418 ], "type": "text", "angle": 0, "index": 13, "lines": [ { "bbox": [ 88, 406, 218, 420 ], "spans": [ { "bbox": [ 88, 406, 218, 420 ], "type": "text", "content": "同理，可以-2~-127的补数；", "score": 1.0 } ] } ] }, { "bbox": [ 86, 422, 293, 434 ], "type": "text", "angle": 0, "index": 14, "lines": [ { "bbox": [ 88, 421, 294, 436 ], "spans": [ { "bbox": [ 88, 421, 294, 436 ], "type": "text", "content": "注意：这里的补数，就是计算机所讲的补码。", "score": 1.0 } ] } ] }, { "bbox": [ 86, 438, 255, 450 ], "type": "text", "angle": 0, "index": 15, "lines": [ { "bbox": [ 88, 435, 250, 454 ], "spans": [ { "bbox": [ 88, 435, 155, 454 ], "type": "text", "content": "-127 的补数是", "score": 1.0 }, { "bbox": [ 156, 438, 250, 450 ], "type": "inline_equation", "content": "2 5 6 - 1 2 7 = 1 2 9 = 0 \\times 8 1", "score": 0.89 } ] } ] }, { "bbox": [ 86, 454, 248, 465 ], "type": "text", "angle": 0, "index": 16, "lines": [ { "bbox": [ 88, 451, 243, 468 ], "spans": [ { "bbox": [ 88, 451, 190, 468 ], "type": "text", "content": "-1~-127 的补码范围：", "score": 1.0 }, { "bbox": [ 190, 454, 243, 466 ], "type": "inline_equation", "content": "0 { \\times } \\mathsf { F F } { \\sim } 0 { \\times } 8 1", "score": 0.68 } ] } ] }, { "bbox": [ 86, 469, 170, 481 ], "type": "text", "angle": 0, "index": 17, "lines": [ { "bbox": [ 88, 468, 171, 482 ], "spans": [ { "bbox": [ 88, 468, 171, 482 ], "type": "text", "content": "负数-128的补码：", "score": 1.0 } ] } ] }, { "bbox": [ 86, 484, 314, 497 ], "type": "text", "angle": 0, "index": 18, "lines": [ { "bbox": [ 87, 481, 315, 500 ], "spans": [ { "bbox": [ 87, 481, 143, 500 ], "type": "text", "content": "我们知道“-", "score": 1.0 }, { "bbox": [ 143, 484, 202, 497 ], "type": "inline_equation", "content": "\\cdot 1 2 8 = 0 - 1 2 8 ^ { \\prime \\prime }", "score": 0.86 }, { "bbox": [ 202, 481, 224, 500 ], "type": "text", "content": "，“", "score": 1.0 }, { "bbox": [ 224, 484, 292, 497 ], "type": "inline_equation", "content": "- 1 2 8 = - 1 + - 1 2 7 ^ { \\prime \\prime }", "score": 0.82 }, { "bbox": [ 293, 481, 315, 500 ], "type": "text", "content": "所以", "score": 1.0 } ] } ] }, { "bbox": [ 86, 499, 505, 528 ], "type": "text", "angle": 0, "index": 19, "lines": [ { "bbox": [ 88, 499, 507, 514 ], "spans": [ { "bbox": [ 88, 499, 155, 514 ], "type": "text", "content": "-128 的补数是", "score": 1.0 }, { "bbox": [ 155, 500, 251, 513 ], "type": "inline_equation", "content": "2 5 6 - 1 2 8 = 1 2 8 = 0 \\times 8 0", "score": 0.9 }, { "bbox": [ 251, 499, 507, 514 ], "type": "text", "content": "；所以-128 的补码为 0x80，但是-128 没有原码和反码。", "score": 1.0 } ] }, { "bbox": [ 88, 515, 259, 529 ], "spans": [ { "bbox": [ 88, 515, 259, 529 ], "type": "text", "content": "所以人为地规定 10000000 表示-128", "score": 1.0 } ] } ] }, { "bbox": [ 87, 531, 115, 543 ], "type": "text", "angle": 0, "index": 20, "lines": [ { "bbox": [ 88, 529, 119, 546 ], "spans": [ { "bbox": [ 88, 529, 119, 546 ], "type": "text", "content": "总结：", "score": 1.0 } ] } ] }, { "bbox": [ 86, 546, 279, 559 ], "type": "text", "angle": 0, "index": 21, "lines": [ { "bbox": [ 89, 547, 279, 560 ], "spans": [ { "bbox": [ 89, 547, 279, 560 ], "type": "text", "content": "补码补码，就是补上去一个模对应的补数", "score": 1.0 } ] } ] }, { "bbox": [ 87, 580, 122, 597 ], "type": "title", "angle": 0, "index": 22, "lines": [ { "bbox": [ 85, 577, 126, 602 ], "spans": [ { "bbox": [ 85, 577, 126, 602 ], "type": "text", "content": "小结", "score": 1.0 } ] } ] }, { "bbox": [ 86, 636, 325, 649 ], "type": "text", "angle": 0, "index": 23, "lines": [ { "bbox": [ 88, 635, 326, 651 ], "spans": [ { "bbox": [ 88, 635, 326, 651 ], "type": "text", "content": "在一个区间长度为 M 内，统一正负数的常用方法是", "score": 1.0 } ] } ] }, { "bbox": [ 86, 651, 181, 663 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 86, 651, 181, 663 ], "spans": [ { "bbox": [ 86, 651, 181, 663 ], "type": "interline_equation", "content": "X ^ {\\prime} = (X + M) \\mod M", "image_path": "beafd15c2870a35bf6caf29e5deeb098a0a9e02a3d35c6c8cf34e7d138c7fa7d.jpg" } ] } ], "index": 24 }, { "bbox": [ 86, 666, 502, 710 ], "type": "text", "angle": 0, "index": 25, "lines": [ { "bbox": [ 88, 666, 503, 681 ], "spans": [ { "bbox": [ 88, 666, 371, 681 ], "type": "text", "content": "其中 M 就是模数。如果你换成一个非 M 的倍数 N，则只有在", "score": 1.0 }, { "bbox": [ 371, 667, 396, 679 ], "type": "inline_equation", "content": "\\Nu \\equiv 0", "score": 0.85 }, { "bbox": [ 396, 666, 503, 681 ], "type": "text", "content": "(mod M)的情况下才能", "score": 1.0 } ] }, { "bbox": [ 88, 684, 498, 696 ], "spans": [ { "bbox": [ 88, 684, 498, 696 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 88, 701, 107, 713 ], "spans": [ { "bbox": [ 88, 701, 107, 713 ], "type": "text", "content": "一。", "score": 1.0 } ] } ] }, { "bbox": [ 86, 714, 497, 742 ], "type": "text", "angle": 0, "index": 26, "lines": [ { "bbox": [ 89, 714, 498, 726 ], "spans": [ { "bbox": [ 89, 714, 321, 726 ], "type": "text", "content": "可以这么理解：如果一个区间（或集合）恰好包含", "score": 1.0 }, { "bbox": [ 321, 715, 334, 726 ], "type": "inline_equation", "content": "\\mathsf { m }", "score": 0.51 }, { "bbox": [ 334, 714, 409, 726 ], "type": "text", "content": "个整数，并且这", "score": 1.0 }, { "bbox": [ 409, 714, 422, 726 ], "type": "inline_equation", "content": "\\mathsf { m }", "score": 0.5 }, { "bbox": [ 422, 714, 498, 726 ], "type": "text", "content": "个整数构成了一", "score": 1.0 } ] }, { "bbox": [ 88, 729, 303, 743 ], "spans": [ { "bbox": [ 88, 729, 111, 743 ], "type": "text", "content": "个模", "score": 1.0 }, { "bbox": [ 111, 730, 124, 742 ], "type": "inline_equation", "content": "\\mathsf { m }", "score": 0.56 }, { "bbox": [ 124, 729, 303, 743 ], "type": "text", "content": "的完全剩余系，那么对任意整数 X，用", "score": 1.0 } ] } ] }, { "bbox": [ 87, 745, 133, 756 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 87, 745, 133, 756 ], "spans": [ { "bbox": [ 87, 745, 133, 756 ], "type": "interline_equation", "content": "X \\bmod m", "image_path": "b7fa56ca12cf469ff5d4d066afb576e47268073ab4fc06cc30d6109b3342fda2.jpg" } ] } ], "index": 27 } ], "discarded_blocks": [], "page_size": [ 595, 841 ], "page_idx": 13 }, { "para_blocks": [ { "bbox": [ 86, 79, 501, 107 ], "type": "text", "angle": 0, "index": 0, "lines": [ { "bbox": [ 89, 79, 500, 92 ], "spans": [ { "bbox": [ 89, 79, 500, 92 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 89, 95, 321, 108 ], "spans": [ { "bbox": [ 89, 95, 321, 108 ], "type": "text", "content": "且互不同余），那么无论 X是正数还是负数，都有", "score": 1.0 } ] } ] }, { "bbox": [ 87, 111, 148, 121 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 87, 111, 148, 121 ], "spans": [ { "bbox": [ 87, 111, 148, 121 ], "type": "interline_equation", "content": "X \\equiv X \\bmod m", "image_path": "92ff28ad2ac2d39604ac401c45d8fdc10fe10ad7aa4d8cebca64fb6437194e65.jpg" } ] } ], "index": 1 }, { "bbox": [ 86, 125, 301, 138 ], "type": "text", "angle": 0, "index": 2, "lines": [ { "bbox": [ 88, 125, 302, 141 ], "spans": [ { "bbox": [ 88, 125, 302, 141 ], "type": "text", "content": "而且 Xmodm 就是该模 m 意义下的标准表示。", "score": 1.0 } ] } ] }, { "bbox": [ 87, 147, 255, 165 ], "type": "title", "angle": 0, "index": 3, "lines": [ { "bbox": [ 88, 146, 257, 167 ], "spans": [ { "bbox": [ 88, 146, 257, 167 ], "type": "text", "content": "为什么定点小数的模 2？", "score": 1.0 } ] } ] }, { "bbox": [ 86, 172, 508, 232 ], "type": "text", "angle": 0, "index": 4, "lines": [ { "bbox": [ 89, 172, 505, 185 ], "spans": [ { "bbox": [ 89, 172, 459, 185 ], "type": "text", "content": "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", "score": 1.0 }, { "bbox": [ 460, 173, 505, 185 ], "type": "inline_equation", "content": "1 - 2 \\land ( - \\mathsf { n } )", "score": 0.83 } ] }, { "bbox": [ 88, 188, 509, 202 ], "spans": [ { "bbox": [ 88, 188, 174, 202 ], "type": "text", "content": "之间的差值正好是", "score": 1.0 }, { "bbox": [ 174, 189, 219, 201 ], "type": "inline_equation", "content": "2 - 2 \\land ( - \\mathsf { n } )", "score": 0.81 }, { "bbox": [ 220, 188, 509, 202 ], "type": "text", "content": "，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。", "score": 1.0 } ] }, { "bbox": [ 88, 204, 496, 216 ], "spans": [ { "bbox": [ 88, 204, 122, 216 ], "type": "inline_equation", "content": "- 2 \\land ( - \\mathsf { n } )", "score": 0.62 }, { "bbox": [ 122, 204, 380, 216 ], "type": "text", "content": "并没有被省略，而是补码表示的范围已经包含了从 -1 到", "score": 1.0 }, { "bbox": [ 381, 204, 426, 216 ], "type": "inline_equation", "content": "1 - 2 \\land ( - \\mathsf { n } )", "score": 0.8 }, { "bbox": [ 426, 204, 496, 216 ], "type": "text", "content": "的所有可能值。", "score": 1.0 } ] }, { "bbox": [ 88, 219, 440, 232 ], "spans": [ { "bbox": [ 88, 219, 440, 232 ], "type": "text", "content": "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。", "score": 1.0 } ] } ] }, { "bbox": [ 87, 269, 187, 287 ], "type": "title", "angle": 0, "index": 5, "lines": [ { "bbox": [ 88, 268, 188, 290 ], "spans": [ { "bbox": [ 88, 268, 188, 290 ], "type": "text", "content": "关于数的扩展", "score": 1.0 } ] } ] }, { "bbox": [ 86, 324, 242, 337 ], "type": "text", "angle": 0, "index": 6, "lines": [ { "bbox": [ 89, 324, 243, 338 ], "spans": [ { "bbox": [ 89, 324, 243, 338 ], "type": "text", "content": "基本上是这样的。对两类数来说：", "score": 1.0 } ] } ] }, { "bbox": [ 105, 339, 236, 368 ], "type": "list", "angle": 0, "index": 9, "blocks": [ { "bbox": [ 105, 339, 236, 352 ], "type": "text", "angle": 0, "index": 7, "lines": [ { "bbox": [ 122, 339, 238, 353 ], "spans": [ { "bbox": [ 122, 339, 238, 353 ], "type": "text", "content": "高位扩展（符号扩展）：", "score": 1.0 } ] } ] }, { "bbox": [ 105, 355, 236, 368 ], "type": "text", "angle": 0, "index": 8, "lines": [ { "bbox": [ 122, 355, 238, 369 ], "spans": [ { "bbox": [ 122, 355, 238, 369 ], "type": "text", "content": "低位扩展（增加精度）：", "score": 1.0 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 87, 386, 189, 399 ], "type": "title", "angle": 0, "index": 10, "lines": [ { "bbox": [ 89, 387, 189, 399 ], "spans": [ { "bbox": [ 89, 387, 189, 399 ], "type": "text", "content": "定点整数的符号扩展：", "score": 1.0 } ] } ] }, { "bbox": [ 86, 402, 218, 415 ], "type": "text", "angle": 0, "index": 11, "lines": [ { "bbox": [ 89, 403, 217, 417 ], "spans": [ { "bbox": [ 89, 403, 217, 417 ], "type": "text", "content": "对于无符号数，称为零扩展", "score": 1.0 } ] } ] }, { "bbox": [ 86, 417, 238, 430 ], "type": "text", "angle": 0, "index": 12, "lines": [ { "bbox": [ 89, 418, 238, 431 ], "spans": [ { "bbox": [ 89, 418, 238, 431 ], "type": "text", "content": "对于有符号数，称为符号位扩展", "score": 1.0 } ] } ] }, { "bbox": [ 86, 433, 494, 461 ], "type": "text", "angle": 0, "index": 13, "lines": [ { "bbox": [ 89, 433, 495, 446 ], "spans": [ { "bbox": [ 89, 433, 495, 446 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 88, 449, 102, 465 ], "spans": [ { "bbox": [ 88, 449, 102, 465 ], "type": "text", "content": "1。", "score": 1.0 } ] } ] }, { "bbox": [ 88, 467, 276, 518 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 88, 467, 276, 518 ], "spans": [ { "bbox": [ 88, 467, 276, 518 ], "type": "interline_equation", "content": "\\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}", "image_path": "aed113e2721cf447af94ac7c3d992bb566d046b88cda848b052ccf30d002f3c4.jpg" } ] } ], "index": 14 }, { "bbox": [ 87, 527, 189, 539 ], "type": "title", "angle": 0, "index": 15, "lines": [ { "bbox": [ 89, 528, 189, 539 ], "spans": [ { "bbox": [ 89, 528, 189, 539 ], "type": "text", "content": "定点小数的符号扩展：", "score": 1.0 } ] } ] }, { "bbox": [ 86, 542, 494, 570 ], "type": "text", "angle": 0, "index": 16, "lines": [ { "bbox": [ 89, 543, 495, 555 ], "spans": [ { "bbox": [ 89, 543, 495, 555 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 88, 558, 102, 574 ], "spans": [ { "bbox": [ 88, 558, 102, 574 ], "type": "text", "content": "1。", "score": 1.0 } ] } ] }, { "bbox": [ 87, 573, 132, 586 ], "type": "title", "angle": 0, "index": 17, "lines": [ { "bbox": [ 88, 573, 133, 588 ], "spans": [ { "bbox": [ 88, 573, 133, 588 ], "type": "text", "content": "低位截断", "score": 1.0 } ] } ] }, { "bbox": [ 86, 589, 326, 602 ], "type": "text", "angle": 0, "index": 18, "lines": [ { "bbox": [ 88, 589, 326, 604 ], "spans": [ { "bbox": [ 88, 589, 326, 604 ], "type": "text", "content": "将 int 类型强制转换为 short 类型，高 16 位被丢弃", "score": 1.0 } ] } ] }, { "bbox": [ 86, 604, 503, 633 ], "type": "text", "angle": 0, "index": 19, "lines": [ { "bbox": [ 88, 603, 505, 618 ], "spans": [ { "bbox": [ 88, 603, 121, 618 ], "type": "text", "content": "将一个", "score": 1.0 }, { "bbox": [ 122, 606, 133, 617 ], "type": "inline_equation", "content": "\\pmb { \\mathsf { W } }", "score": 0.53 }, { "bbox": [ 134, 603, 505, 618 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 88, 618, 138, 634 ], "spans": [ { "bbox": [ 88, 618, 138, 634 ], "type": "text", "content": "取模运算。", "score": 1.0 } ] } ] }, { "bbox": [ 88, 642, 371, 656 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 88, 642, 371, 656 ], "spans": [ { "bbox": [ 88, 642, 371, 656 ], "type": "interline_equation", "content": "B 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)", "image_path": "8319129a0d5fe876e86a131988b6e7ba39efdfa539360f865dc676c3b6d6bff7.jpg" } ] } ], "index": 20 }, { "bbox": [ 87, 666, 154, 679 ], "type": "title", "angle": 0, "index": 21, "lines": [ { "bbox": [ 88, 667, 154, 681 ], "spans": [ { "bbox": [ 88, 667, 154, 681 ], "type": "text", "content": "截断有符号数", "score": 1.0 } ] } ] }, { "bbox": [ 86, 682, 311, 695 ], "type": "text", "angle": 0, "index": 22, "lines": [ { "bbox": [ 89, 682, 311, 697 ], "spans": [ { "bbox": [ 89, 682, 311, 697 ], "type": "text", "content": "先转换成无符号数，再截断，再转换成有符号数", "score": 1.0 } ] } ] }, { "bbox": [ 87, 698, 101, 710 ], "type": "text", "angle": 0, "index": 23, "lines": [ { "bbox": [ 88, 698, 102, 714 ], "spans": [ { "bbox": [ 88, 698, 102, 714 ], "type": "text", "content": "即", "score": 1.0 } ] } ] }, { "bbox": [ 179, 717, 357, 739 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 179, 717, 357, 739 ], "spans": [ { "bbox": [ 179, 717, 357, 739 ], "type": "interline_equation", "content": "T ^ {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}", "image_path": "f1c88bc310fe1e2e37ba83dd693b9624742a44553e7d967fccfd571cc58dd954.jpg" } ] } ], "index": 24 }, { "bbox": [ 88, 742, 449, 754 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 88, 742, 449, 754 ], "spans": [ { "bbox": [ 88, 742, 449, 754 ], "type": "interline_equation", "content": "B 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)", "image_path": "01e4f66698ba2ac43fa05920478fcf77b0dd4053bffd5595316e9249499cf7e7.jpg" } ] } ], "index": 25 } ], "discarded_blocks": [], "page_size": [ 595, 841 ], "page_idx": 14 }, { "para_blocks": [ { "bbox": [ 86, 143, 196, 164 ], "type": "title", "angle": 0, "index": 0, "lines": [ { "bbox": [ 86, 142, 197, 165 ], "spans": [ { "bbox": [ 86, 142, 197, 165 ], "type": "text", "content": "4、其他运算符", "score": 1.0 } ] } ] }, { "bbox": [ 86, 205, 242, 225 ], "type": "title", "angle": 0, "index": 1, "lines": [ { "bbox": [ 88, 204, 242, 226 ], "spans": [ { "bbox": [ 88, 204, 242, 226 ], "type": "text", "content": "布尔运算（位级运算）", "score": 1.0 } ] } ] }, { "bbox": [ 86, 260, 236, 274 ], "type": "text", "angle": 0, "index": 2, "lines": [ { "bbox": [ 88, 260, 236, 275 ], "spans": [ { "bbox": [ 88, 260, 236, 275 ], "type": "text", "content": "~/NOT 非（取反）（单目运算）", "score": 1.0 } ] } ] }, { "bbox": [ 88, 276, 137, 289 ], "type": "text", "angle": 0, "index": 3, "lines": [ { "bbox": [ 88, 275, 139, 291 ], "spans": [ { "bbox": [ 88, 275, 139, 291 ], "type": "text", "content": "&/AND 与", "score": 1.0 } ] } ] }, { "bbox": [ 89, 291, 129, 305 ], "type": "text", "angle": 0, "index": 4, "lines": [ { "bbox": [ 88, 290, 130, 309 ], "spans": [ { "bbox": [ 88, 290, 130, 309 ], "type": "text", "content": "|/OR 或", "score": 1.0 } ] } ] }, { "bbox": [ 88, 307, 195, 320 ], "type": "text", "angle": 0, "index": 5, "lines": [ { "bbox": [ 88, 307, 196, 322 ], "spans": [ { "bbox": [ 88, 307, 196, 322 ], "type": "text", "content": "^/EXCLUSIVE-OR 异或", "score": 1.0 } ] } ] }, { "bbox": [ 88, 322, 147, 336 ], "type": "text", "angle": 0, "index": 6, "lines": [ { "bbox": [ 88, 322, 149, 337 ], "spans": [ { "bbox": [ 88, 322, 149, 337 ], "type": "text", "content": "取反的时候：", "score": 1.0 } ] } ] }, { "bbox": [ 88, 338, 348, 352 ], "type": "text", "angle": 0, "index": 7, "lines": [ { "bbox": [ 88, 337, 348, 354 ], "spans": [ { "bbox": [ 88, 337, 293, 354 ], "type": "text", "content": "因此，可以总结出~按位取反的计算结论是：", "score": 1.0 }, { "bbox": [ 293, 339, 348, 352 ], "type": "inline_equation", "content": "\\sim \\mathsf { n } = - ( \\mathsf { n } + 1 )", "score": 0.83 } ] } ] }, { "bbox": [ 88, 354, 259, 367 ], "type": "text", "angle": 0, "index": 8, "lines": [ { "bbox": [ 88, 354, 258, 369 ], "spans": [ { "bbox": [ 88, 354, 151, 369 ], "type": "text", "content": "例如本例中，", "score": 1.0 }, { "bbox": [ 151, 354, 204, 367 ], "type": "inline_equation", "content": "\\mathord { \\sim } 5 = - ( 5 + 1 )", "score": 0.9 }, { "bbox": [ 204, 354, 226, 369 ], "type": "text", "content": "，即", "score": 1.0 }, { "bbox": [ 226, 354, 258, 367 ], "type": "inline_equation", "content": "\\mathord { \\sim } 5 = - 6", "score": 0.86 } ] } ] }, { "bbox": [ 87, 388, 154, 407 ], "type": "title", "angle": 0, "index": 9, "lines": [ { "bbox": [ 86, 386, 156, 409 ], "spans": [ { "bbox": [ 86, 386, 156, 409 ], "type": "text", "content": "逻辑运算", "score": 1.0 } ] } ] }, { "bbox": [ 86, 444, 275, 457 ], "type": "text", "angle": 0, "index": 10, "lines": [ { "bbox": [ 88, 442, 275, 459 ], "spans": [ { "bbox": [ 88, 442, 275, 459 ], "type": "text", "content": "所有非零参数为 true，参数 0 表示 false", "score": 1.0 } ] } ] }, { "bbox": [ 88, 459, 267, 472 ], "type": "text", "angle": 0, "index": 11, "lines": [ { "bbox": [ 88, 459, 267, 473 ], "spans": [ { "bbox": [ 88, 459, 267, 473 ], "type": "text", "content": "结果只有两个，true与false 惰性运算", "score": 1.0 } ] } ] }, { "bbox": [ 89, 475, 120, 487 ], "type": "text", "angle": 0, "index": 12, "lines": [ { "bbox": [ 88, 473, 121, 491 ], "spans": [ { "bbox": [ 88, 473, 121, 491 ], "type": "text", "content": "|| OR", "score": 1.0 } ] } ] }, { "bbox": [ 88, 491, 130, 502 ], "type": "text", "angle": 0, "index": 13, "lines": [ { "bbox": [ 88, 491, 131, 503 ], "spans": [ { "bbox": [ 88, 491, 131, 503 ], "type": "text", "content": "&& AND", "score": 1.0 } ] } ] }, { "bbox": [ 88, 507, 117, 518 ], "type": "text", "angle": 0, "index": 14, "lines": [ { "bbox": [ 86, 506, 119, 521 ], "spans": [ { "bbox": [ 86, 506, 119, 521 ], "type": "text", "content": "! NOT", "score": 1.0 } ] } ] }, { "bbox": [ 86, 539, 154, 559 ], "type": "title", "angle": 0, "index": 15, "lines": [ { "bbox": [ 86, 538, 157, 561 ], "spans": [ { "bbox": [ 86, 538, 157, 561 ], "type": "text", "content": "移位运算", "score": 1.0 } ] } ] }, { "bbox": [ 86, 595, 506, 624 ], "type": "text", "angle": 0, "index": 16, "lines": [ { "bbox": [ 89, 596, 504, 608 ], "spans": [ { "bbox": [ 89, 596, 504, 608 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 88, 611, 293, 624 ], "spans": [ { "bbox": [ 88, 611, 293, 624 ], "type": "text", "content": "数据位一般置入CF标志位(进位、借位 标志)", "score": 1.0 } ] } ] }, { "bbox": [ 86, 626, 504, 640 ], "type": "text", "angle": 0, "index": 17, "lines": [ { "bbox": [ 88, 627, 504, 640 ], "spans": [ { "bbox": [ 88, 627, 504, 640 ], "type": "text", "content": "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。", "score": 1.0 } ] } ] }, { "bbox": [ 88, 642, 314, 655 ], "type": "text", "angle": 0, "index": 18, "lines": [ { "bbox": [ 89, 643, 313, 655 ], "spans": [ { "bbox": [ 89, 643, 313, 655 ], "type": "text", "content": "计算机的算术移位指令大多采用补码的 移位规则", "score": 1.0 } ] } ] }, { "bbox": [ 86, 657, 509, 687 ], "type": "text", "angle": 0, "index": 19, "lines": [ { "bbox": [ 89, 659, 510, 671 ], "spans": [ { "bbox": [ 89, 659, 510, 671 ], "type": "text", "content": "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，", "score": 1.0 } ] }, { "bbox": [ 89, 674, 217, 687 ], "spans": [ { "bbox": [ 89, 674, 217, 687 ], "type": "text", "content": "则称为大循环，否则小循环", "score": 1.0 } ] } ] }, { "bbox": [ 86, 689, 267, 702 ], "type": "text", "angle": 0, "index": 20, "lines": [ { "bbox": [ 89, 689, 267, 703 ], "spans": [ { "bbox": [ 89, 689, 267, 703 ], "type": "text", "content": "左移相当于乘以2，右移相当于除以二", "score": 1.0 } ] } ] }, { "bbox": [ 86, 704, 506, 750 ], "type": "text", "angle": 0, "index": 21, "lines": [ { "bbox": [ 89, 705, 505, 718 ], "spans": [ { "bbox": [ 89, 705, 505, 718 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 88, 719, 506, 734 ], "spans": [ { "bbox": [ 88, 719, 133, 734 ], "type": "text", "content": "法运算时", "score": 1.0 }, { "bbox": [ 133, 721, 153, 733 ], "type": "inline_equation", "content": "\\textstyle \\sum = 1", "score": 0.87 }, { "bbox": [ 154, 719, 313, 734 ], "type": "text", "content": ",则CF置1表示进位；减法运算时", "score": 1.0 }, { "bbox": [ 314, 720, 349, 734 ], "type": "inline_equation", "content": "C { = } 0 , C F", "score": 0.58 }, { "bbox": [ 349, 719, 506, 734 ], "type": "text", "content": "置1表示借位。CF只对无符号数", "score": 1.0 } ] }, { "bbox": [ 88, 735, 148, 751 ], "spans": [ { "bbox": [ 88, 735, 148, 751 ], "type": "text", "content": "运算有意义。", "score": 1.0 } ] } ] } ], "discarded_blocks": [], "page_size": [ 595, 841 ], "page_idx": 15 }, { "para_blocks": [ { "bbox": [ 86, 79, 503, 169 ], "type": "list", "angle": 0, "index": 4, "blocks": [ { "bbox": [ 86, 79, 364, 90 ], "type": "text", "angle": 0, "index": 0, "lines": [ { "bbox": [ 88, 79, 365, 93 ], "spans": [ { "bbox": [ 88, 79, 365, 93 ], "type": "text", "content": "ZF: 零标志。最近的操作得出的结果为 0（全零）则 ZF 置 1。", "score": 1.0 } ] } ] }, { "bbox": [ 86, 95, 503, 121 ], "type": "text", "angle": 0, "index": 1, "lines": [ { "bbox": [ 89, 95, 504, 107 ], "spans": [ { "bbox": [ 89, 95, 504, 107 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 88, 110, 216, 123 ], "spans": [ { "bbox": [ 88, 110, 216, 123 ], "type": "text", "content": "结果为正数置0，负数置1。", "score": 1.0 } ] } ] }, { "bbox": [ 86, 125, 503, 153 ], "type": "text", "angle": 0, "index": 2, "lines": [ { "bbox": [ 89, 126, 505, 138 ], "spans": [ { "bbox": [ 89, 126, 505, 138 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 89, 141, 196, 154 ], "spans": [ { "bbox": [ 89, 141, 196, 154 ], "type": "text", "content": "溢出则置1，否则置0；", "score": 1.0 } ] } ] }, { "bbox": [ 86, 157, 345, 169 ], "type": "text", "angle": 0, "index": 3, "lines": [ { "bbox": [ 88, 156, 346, 171 ], "spans": [ { "bbox": [ 88, 156, 346, 171 ], "type": "text", "content": "PF:奇偶标志位。操作数 1 的个数为偶数置 1，否则置 0；", "score": 1.0 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 87, 193, 119, 208 ], "type": "title", "angle": 0, "index": 5, "lines": [ { "bbox": [ 87, 191, 120, 212 ], "spans": [ { "bbox": [ 87, 191, 120, 212 ], "type": "text", "content": "左移", "score": 1.0 } ] } ] }, { "bbox": [ 86, 243, 235, 255 ], "type": "text", "angle": 0, "index": 6, "lines": [ { "bbox": [ 89, 244, 235, 256 ], "spans": [ { "bbox": [ 89, 244, 235, 256 ], "type": "text", "content": "逻辑左移，高位移出，低位补0", "score": 1.0 } ] } ] }, { "bbox": [ 86, 259, 205, 270 ], "type": "text", "angle": 0, "index": 7, "lines": [ { "bbox": [ 89, 259, 205, 272 ], "spans": [ { "bbox": [ 89, 259, 205, 272 ], "type": "text", "content": "左移不区分算术还是逻辑", "score": 1.0 } ] } ] }, { "bbox": [ 86, 275, 354, 286 ], "type": "text", "angle": 0, "index": 8, "lines": [ { "bbox": [ 88, 274, 356, 289 ], "spans": [ { "bbox": [ 88, 274, 356, 289 ], "type": "text", "content": "对于原码的算术左移，符号位不变，高位移出，低位补 0；", "score": 1.0 } ] } ] }, { "bbox": [ 87, 290, 282, 301 ], "type": "text", "angle": 0, "index": 9, "lines": [ { "bbox": [ 89, 290, 283, 303 ], "spans": [ { "bbox": [ 89, 290, 283, 303 ], "type": "text", "content": "当左移移出的数据位为“1”时，发生溢出。", "score": 1.0 } ] } ] }, { "bbox": [ 86, 306, 497, 349 ], "type": "text", "angle": 0, "index": 10, "lines": [ { "bbox": [ 89, 306, 495, 318 ], "spans": [ { "bbox": [ 89, 306, 495, 318 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 89, 322, 498, 334 ], "spans": [ { "bbox": [ 89, 322, 498, 334 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 89, 337, 248, 349 ], "spans": [ { "bbox": [ 89, 337, 248, 349 ], "type": "text", "content": "据的最高有效位必须与符号位相同", "score": 1.0 } ] } ] }, { "bbox": [ 86, 352, 498, 380 ], "type": "text", "angle": 0, "index": 11, "lines": [ { "bbox": [ 89, 352, 499, 364 ], "spans": [ { "bbox": [ 89, 352, 499, 364 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 89, 368, 215, 380 ], "spans": [ { "bbox": [ 89, 368, 215, 380 ], "type": "text", "content": "时，不会改变机器数的符号", "score": 1.0 } ] } ] }, { "bbox": [ 87, 419, 119, 435 ], "type": "title", "angle": 0, "index": 12, "lines": [ { "bbox": [ 85, 417, 121, 439 ], "spans": [ { "bbox": [ 85, 417, 121, 439 ], "type": "text", "content": "右移", "score": 1.0 } ] } ] }, { "bbox": [ 86, 470, 235, 481 ], "type": "text", "angle": 0, "index": 13, "lines": [ { "bbox": [ 89, 470, 235, 483 ], "spans": [ { "bbox": [ 89, 470, 235, 483 ], "type": "text", "content": "逻辑右移，低位移出，高位补0", "score": 1.0 } ] } ] }, { "bbox": [ 86, 486, 349, 497 ], "type": "text", "angle": 0, "index": 14, "lines": [ { "bbox": [ 88, 486, 351, 499 ], "spans": [ { "bbox": [ 88, 486, 351, 499 ], "type": "text", "content": "对于原码的算数右移，符号位不变，低位移出，高位补0", "score": 1.0 } ] } ] }, { "bbox": [ 87, 501, 132, 513 ], "type": "text", "angle": 0, "index": 15, "lines": [ { "bbox": [ 88, 501, 133, 514 ], "spans": [ { "bbox": [ 88, 501, 133, 514 ], "type": "text", "content": "算数右移", "score": 1.0 } ] } ] }, { "bbox": [ 86, 517, 320, 528 ], "type": "text", "angle": 0, "index": 16, "lines": [ { "bbox": [ 89, 518, 321, 530 ], "spans": [ { "bbox": [ 89, 518, 321, 530 ], "type": "text", "content": "对于补码，符号位不变，低位移出，高位补符号位", "score": 1.0 } ] } ] }, { "bbox": [ 86, 533, 297, 544 ], "type": "text", "angle": 0, "index": 17, "lines": [ { "bbox": [ 88, 533, 298, 546 ], "spans": [ { "bbox": [ 88, 533, 298, 546 ], "type": "text", "content": "对于原码，符号位不变，低位移出，高位补0", "score": 1.0 } ] } ] }, { "bbox": [ 86, 579, 343, 591 ], "type": "text", "angle": 0, "index": 18, "lines": [ { "bbox": [ 89, 580, 344, 592 ], "spans": [ { "bbox": [ 89, 580, 344, 592 ], "type": "text", "content": "C语言中一个特性就是支持按位进行布尔运算（位运算）", "score": 1.0 } ] } ] }, { "bbox": [ 87, 595, 236, 607 ], "type": "text", "angle": 0, "index": 19, "lines": [ { "bbox": [ 89, 596, 236, 608 ], "spans": [ { "bbox": [ 89, 596, 236, 608 ], "type": "text", "content": "位运算的用法就是实现掩码运算", "score": 1.0 } ] } ] }, { "bbox": [ 87, 610, 152, 622 ], "type": "text", "angle": 0, "index": 20, "lines": [ { "bbox": [ 89, 611, 154, 624 ], "spans": [ { "bbox": [ 89, 611, 154, 624 ], "type": "text", "content": "特定的位序列", "score": 1.0 } ] } ] }, { "bbox": [ 87, 626, 281, 638 ], "type": "text", "angle": 0, "index": 21, "lines": [ { "bbox": [ 89, 627, 282, 640 ], "spans": [ { "bbox": [ 89, 627, 282, 640 ], "type": "text", "content": "比如说和0xFF，进行与运算，就是其本身", "score": 1.0 } ] } ] }, { "bbox": [ 86, 676, 243, 693 ], "type": "title", "angle": 0, "index": 22, "lines": [ { "bbox": [ 86, 674, 245, 696 ], "spans": [ { "bbox": [ 86, 674, 245, 696 ], "type": "text", "content": "5、机器数编码与真值", "score": 1.0 } ] } ] }, { "bbox": [ 86, 731, 412, 743 ], "type": "text", "angle": 0, "index": 23, "lines": [ { "bbox": [ 89, 731, 412, 745 ], "spans": [ { "bbox": [ 89, 731, 386, 745 ], "type": "text", "content": "为什么原码、补码、反码、移码 作为机器数的时候，符号位算作", "score": 1.0 }, { "bbox": [ 387, 731, 412, 744 ], "type": "inline_equation", "content": "2 \\land \\mathsf { n ? }", "score": 0.76 } ] } ] }, { "bbox": [ 87, 746, 132, 759 ], "type": "text", "angle": 0, "index": 24, "lines": [ { "bbox": [ 88, 746, 133, 761 ], "spans": [ { "bbox": [ 88, 746, 133, 761 ], "type": "text", "content": "关于移码", "score": 1.0 } ] } ] } ], "discarded_blocks": [], "page_size": [ 595, 841 ], "page_idx": 16 }, { "para_blocks": [ { "bbox": [ 86, 79, 504, 107 ], "type": "text", "angle": 0, "index": 0, "lines": [ { "bbox": [ 90, 80, 504, 91 ], "spans": [ { "bbox": [ 90, 80, 504, 91 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 95, 95, 468, 108 ], "spans": [ { "bbox": [ 95, 95, 468, 108 ], "type": "text", "content": "（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。", "score": 1.0 } ] } ] }, { "bbox": [ 86, 110, 504, 139 ], "type": "text", "angle": 0, "index": 1, "lines": [ { "bbox": [ 88, 111, 505, 123 ], "spans": [ { "bbox": [ 88, 111, 505, 123 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 96, 126, 230, 138 ], "spans": [ { "bbox": [ 96, 126, 230, 138 ], "type": "text", "content": "（如判断是最小值或者最大值）", "score": 1.0 } ] } ] }, { "bbox": [ 86, 141, 418, 154 ], "type": "text", "angle": 0, "index": 2, "lines": [ { "bbox": [ 88, 141, 420, 155 ], "spans": [ { "bbox": [ 88, 141, 420, 155 ], "type": "text", "content": "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", "score": 1.0 } ] } ] }, { "bbox": [ 86, 157, 383, 170 ], "type": "text", "angle": 0, "index": 3, "lines": [ { "bbox": [ 88, 156, 384, 171 ], "spans": [ { "bbox": [ 88, 156, 384, 171 ], "type": "text", "content": "Long 在 64 位机器上占 8 个字节 32 位机器上，long 占 4 个字节", "score": 1.0 } ] } ] }, { "bbox": [ 86, 172, 311, 185 ], "type": "text", "angle": 0, "index": 4, "lines": [ { "bbox": [ 88, 172, 311, 186 ], "spans": [ { "bbox": [ 88, 172, 311, 186 ], "type": "text", "content": "Unsigned关键字 数字只能为非负数，无符号数", "score": 1.0 } ] } ] }, { "type": "table", "bbox": [ 83, 186, 595, 491 ], "blocks": [ { "bbox": [ 83, 186, 595, 491 ], "lines": [ { "bbox": [ 83, 186, 595, 491 ], "spans": [ { "bbox": [ 83, 186, 595, 491 ], "type": "table", "html": "
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
", "image_path": "d4b7fb7f45843a9c1fd0ec69762e3eee3776f4c1067cb3e72e15e7fcb0f4a688.jpg" } ] } ], "index": 5, "angle": 0, "type": "table_body" } ], "index": 5 }, { "type": "image", "bbox": [ 88, 506, 462, 696 ], "blocks": [ { "bbox": [ 88, 506, 462, 696 ], "lines": [ { "bbox": [ 88, 506, 462, 696 ], "spans": [ { "bbox": [ 88, 506, 462, 696 ], "type": "image", "image_path": "1a41381584803073f6746fb38769bedaa0499f690915a2f9652a86f1e498a1d5.jpg" } ] } ], "index": 6, "angle": 0, "type": "image_body" } ], "index": 6 }, { "bbox": [ 86, 711, 312, 724 ], "type": "text", "angle": 0, "index": 7, "lines": [ { "bbox": [ 89, 712, 312, 724 ], "spans": [ { "bbox": [ 89, 712, 312, 724 ], "type": "text", "content": "假设一个整数的数据类型有w位，用向量x表示", "score": 1.0 } ] } ] }, { "bbox": [ 87, 732, 244, 749 ], "type": "text", "angle": 0, "index": 8, "lines": [ { "bbox": [ 87, 726, 244, 751 ], "spans": [ { "bbox": [ 87, 726, 141, 751 ], "type": "text", "content": "For vector", "score": 1.0 }, { "bbox": [ 141, 731, 244, 748 ], "type": "inline_equation", "content": "\\vec { x } = [ x _ { w - 1 } , x _ { w - 2 } , \\cdots , x _ { 0 } ]", "score": 0.8 } ] } ] } ], "discarded_blocks": [], "page_size": [ 595, 841 ], "page_idx": 17 }, { "para_blocks": [ { "bbox": [ 88, 77, 267, 91 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 88, 77, 267, 91 ], "spans": [ { "bbox": [ 88, 77, 267, 91 ], "type": "interline_equation", "content": "B 2 U _ {w} (\\vec {x}) \\doteq x _ {w - 1} \\cdot 2 ^ {w - 1} + x _ {w - 2} \\cdot 2 ^ {w - 2} \\dots", "image_path": "de3c46b45a0ebed828429b94f86f6fe59c6e34673c3717d5ce1a39510700d598.jpg" } ] } ], "index": 0 }, { "bbox": [ 86, 110, 250, 123 ], "type": "text", "angle": 0, "index": 1, "lines": [ { "bbox": [ 88, 109, 251, 126 ], "spans": [ { "bbox": [ 88, 109, 251, 126 ], "type": "text", "content": "B2U 的意思是 binary to unsigned", "score": 1.0 } ] } ] }, { "bbox": [ 87, 126, 258, 138 ], "type": "text", "angle": 0, "index": 2, "lines": [ { "bbox": [ 89, 126, 258, 139 ], "spans": [ { "bbox": [ 89, 126, 258, 139 ], "type": "text", "content": "对于有符号数的编码采取补码的方式", "score": 1.0 } ] } ] }, { "bbox": [ 88, 140, 277, 153 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 88, 140, 277, 153 ], "spans": [ { "bbox": [ 88, 140, 277, 153 ], "type": "interline_equation", "content": "B 2 T _ {w} (\\vec {x}) \\dot {=} x _ {w - 1} \\cdot - 2 ^ {w - 1} + x _ {w - 2} \\cdot 2 ^ {w - 2} \\dots", "image_path": "48f6fa4f5c81ae014437f8ab7922d9f65073a33216929d86a90f64b6ad571642.jpg" } ] } ], "index": 3 }, { "bbox": [ 86, 172, 342, 185 ], "type": "text", "angle": 0, "index": 4, "lines": [ { "bbox": [ 89, 172, 342, 185 ], "spans": [ { "bbox": [ 89, 172, 342, 185 ], "type": "text", "content": "这里最高位为1时表示负数，最高位为0时表示非负数", "score": 1.0 } ] } ] }, { "bbox": [ 87, 188, 185, 200 ], "type": "text", "angle": 0, "index": 5, "lines": [ { "bbox": [ 89, 188, 185, 201 ], "spans": [ { "bbox": [ 89, 188, 185, 201 ], "type": "text", "content": "最高位也叫做符号位", "score": 1.0 } ] } ] }, { "bbox": [ 86, 203, 394, 216 ], "type": "text", "angle": 0, "index": 6, "lines": [ { "bbox": [ 89, 204, 395, 217 ], "spans": [ { "bbox": [ 89, 204, 395, 217 ], "type": "text", "content": "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", "score": 1.0 } ] } ] }, { "bbox": [ 87, 219, 310, 232 ], "type": "text", "angle": 0, "index": 7, "lines": [ { "bbox": [ 89, 220, 310, 232 ], "spans": [ { "bbox": [ 89, 220, 310, 232 ], "type": "text", "content": "记住对于无符号数，最高位的1表示的不是权重", "score": 1.0 } ] } ] }, { "bbox": [ 87, 235, 182, 248 ], "type": "text", "angle": 0, "index": 8, "lines": [ { "bbox": [ 88, 232, 179, 250 ], "spans": [ { "bbox": [ 88, 232, 140, 250 ], "type": "text", "content": "也就是说，", "score": 1.0 }, { "bbox": [ 140, 235, 179, 248 ], "type": "inline_equation", "content": "- 2 \\land 3 = - 8", "score": 0.86 } ] } ] }, { "bbox": [ 87, 250, 299, 263 ], "type": "text", "angle": 0, "index": 9, "lines": [ { "bbox": [ 89, 250, 299, 264 ], "spans": [ { "bbox": [ 89, 250, 299, 264 ], "type": "text", "content": "-1在有符号数全为1，但在无符号数为最大值", "score": 1.0 } ] } ] }, { "bbox": [ 86, 266, 335, 280 ], "type": "text", "angle": 0, "index": 10, "lines": [ { "bbox": [ 89, 266, 336, 280 ], "spans": [ { "bbox": [ 89, 266, 336, 280 ], "type": "text", "content": "如果在计算的时候一个是有符号数，一个是无符号数，", "score": 1.0 } ] } ] }, { "bbox": [ 86, 281, 287, 294 ], "type": "text", "angle": 0, "index": 11, "lines": [ { "bbox": [ 89, 282, 288, 295 ], "spans": [ { "bbox": [ 89, 282, 288, 295 ], "type": "text", "content": "C语言会隐式地将有符号数转换为无符号数", "score": 1.0 } ] } ] }, { "bbox": [ 86, 346, 307, 365 ], "type": "title", "angle": 0, "index": 12, "lines": [ { "bbox": [ 87, 345, 308, 367 ], "spans": [ { "bbox": [ 87, 345, 308, 367 ], "type": "text", "content": "6、溢出与取模运算的数学关系", "score": 1.0 } ] } ] }, { "bbox": [ 86, 401, 331, 415 ], "type": "text", "angle": 0, "index": 13, "lines": [ { "bbox": [ 89, 401, 331, 417 ], "spans": [ { "bbox": [ 89, 401, 331, 417 ], "type": "text", "content": "设我们有两个 w 位无符号整数 a 和 b，其和为 S，即", "score": 1.0 } ] } ] }, { "bbox": [ 87, 418, 132, 429 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 87, 418, 132, 429 ], "spans": [ { "bbox": [ 87, 418, 132, 429 ], "type": "interline_equation", "content": "S = a + b", "image_path": "9f132641c8488ca004b4e1ba029ef363bff54e9952cd7d821c7e8188ecf11372.jpg" } ] } ], "index": 14 }, { "bbox": [ 86, 433, 504, 461 ], "type": "text", "angle": 0, "index": 15, "lines": [ { "bbox": [ 89, 433, 504, 446 ], "spans": [ { "bbox": [ 89, 433, 504, 446 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 88, 449, 406, 462 ], "spans": [ { "bbox": [ 88, 449, 406, 462 ], "type": "text", "content": "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", "score": 1.0 } ] } ] }, { "bbox": [ 87, 465, 158, 476 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 87, 465, 158, 476 ], "spans": [ { "bbox": [ 87, 465, 158, 476 ], "type": "interline_equation", "content": "R = S \\bmod 2 ^ {\\wedge} w", "image_path": "c08c9bb2aee4c18808b8b0e6863e5d4dbb6b96d59beb5873e6fdc6f526fd4ba1.jpg" } ] } ], "index": 16 }, { "bbox": [ 86, 480, 504, 507 ], "type": "text", "angle": 0, "index": 17, "lines": [ { "bbox": [ 89, 481, 505, 493 ], "spans": [ { "bbox": [ 89, 481, 374, 493 ], "type": "text", "content": "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", "score": 1.0 }, { "bbox": [ 375, 481, 398, 493 ], "type": "inline_equation", "content": "_ { 2 } \\wedge _ { \\mathsf { W } }", "score": 0.89 }, { "bbox": [ 398, 481, 505, 493 ], "type": "text", "content": "取模。这正是计算机硬", "score": 1.0 } ] }, { "bbox": [ 89, 497, 238, 508 ], "spans": [ { "bbox": [ 89, 497, 238, 508 ], "type": "text", "content": "件中处理无符号整数溢出的方式", "score": 1.0 } ] } ] }, { "bbox": [ 86, 511, 504, 539 ], "type": "text", "angle": 0, "index": 18, "lines": [ { "bbox": [ 88, 511, 505, 524 ], "spans": [ { "bbox": [ 88, 511, 377, 523 ], "type": "text", "content": "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", "score": 1.0 }, { "bbox": [ 378, 511, 428, 524 ], "type": "inline_equation", "content": "2 ^ { \\wedge } 7 = 1 2 8", "score": 0.85 }, { "bbox": [ 428, 511, 505, 523 ], "type": "text", "content": "作为偏移量？原", "score": 1.0 } ] }, { "bbox": [ 88, 527, 128, 541 ], "spans": [ { "bbox": [ 88, 527, 128, 541 ], "type": "text", "content": "因在于：", "score": 1.0 } ] } ] }, { "bbox": [ 104, 542, 504, 693 ], "type": "list", "angle": 0, "index": 22, "blocks": [ { "bbox": [ 104, 542, 503, 585 ], "type": "text", "angle": 0, "index": 19, "lines": [ { "bbox": [ 124, 543, 499, 555 ], "spans": [ { "bbox": [ 124, 543, 499, 555 ], "type": "text", "content": "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。", "score": 1.0 } ] }, { "bbox": [ 124, 559, 504, 571 ], "spans": [ { "bbox": [ 124, 559, 504, 571 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 124, 573, 143, 587 ], "spans": [ { "bbox": [ 124, 573, 143, 587 ], "type": "text", "content": "计。", "score": 1.0 } ] } ] }, { "bbox": [ 104, 589, 504, 631 ], "type": "text", "angle": 0, "index": 20, "lines": [ { "bbox": [ 124, 590, 505, 602 ], "spans": [ { "bbox": [ 124, 590, 505, 602 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 125, 605, 505, 618 ], "spans": [ { "bbox": [ 125, 605, 505, 618 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 126, 622, 341, 632 ], "spans": [ { "bbox": [ 126, 622, 341, 632 ], "type": "text", "content": "的过程更加简便，同时避免了 0 不对称的问题。", "score": 1.0 } ] } ] }, { "bbox": [ 104, 636, 504, 693 ], "type": "text", "angle": 0, "index": 21, "lines": [ { "bbox": [ 124, 637, 505, 649 ], "spans": [ { "bbox": [ 124, 637, 505, 649 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 124, 652, 505, 665 ], "spans": [ { "bbox": [ 124, 652, 505, 665 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 124, 667, 506, 680 ], "spans": [ { "bbox": [ 124, 667, 506, 680 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 124, 682, 468, 695 ], "spans": [ { "bbox": [ 124, 682, 468, 695 ], "type": "text", "content": "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。", "score": 1.0 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 86, 698, 242, 710 ], "type": "title", "angle": 0, "index": 23, "lines": [ { "bbox": [ 89, 699, 242, 712 ], "spans": [ { "bbox": [ 89, 699, 242, 712 ], "type": "text", "content": "5.3. 关于阶码真值为 -127 和 128", "score": 1.0 } ] } ] }, { "bbox": [ 86, 714, 498, 742 ], "type": "text", "angle": 0, "index": 24, "lines": [ { "bbox": [ 88, 714, 500, 728 ], "spans": [ { "bbox": [ 88, 714, 242, 728 ], "type": "text", "content": "一般我们正常探讨的阶码区间是", "score": 1.0 }, { "bbox": [ 243, 714, 314, 727 ], "type": "inline_equation", "content": "- 1 2 6 \\mathsf { D } \\sim 1 2 7 \\mathsf { D }", "score": 0.55 }, { "bbox": [ 314, 714, 500, 728 ], "type": "text", "content": "，而真值 -127D 的阶码为 0000 0000B，", "score": 1.0 } ] }, { "bbox": [ 88, 729, 249, 744 ], "spans": [ { "bbox": [ 88, 729, 249, 744 ], "type": "text", "content": "真值 128D 的阶码为 1111 1111B。", "score": 1.0 } ] } ] } ], "discarded_blocks": [], "page_size": [ 595, 841 ], "page_idx": 18 }, { "para_blocks": [ { "bbox": [ 86, 79, 196, 91 ], "type": "title", "angle": 0, "index": 0, "lines": [ { "bbox": [ 88, 79, 196, 93 ], "spans": [ { "bbox": [ 88, 79, 196, 93 ], "type": "text", "content": "5.3.1. 阶码真值为 -127", "score": 1.0 } ] } ] }, { "bbox": [ 86, 95, 498, 121 ], "type": "text", "angle": 0, "index": 1, "lines": [ { "bbox": [ 89, 94, 499, 109 ], "spans": [ { "bbox": [ 89, 94, 499, 109 ], "type": "text", "content": "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，", "score": 1.0 } ] }, { "bbox": [ 87, 109, 102, 125 ], "spans": [ { "bbox": [ 87, 109, 102, 125 ], "type": "text", "content": "即", "score": 1.0 } ] } ] }, { "bbox": [ 86, 125, 260, 138 ], "type": "text", "angle": 0, "index": 2, "lines": [ { "bbox": [ 88, 124, 262, 140 ], "spans": [ { "bbox": [ 88, 124, 262, 140 ], "type": "text", "content": "尾数码 隐含的最高位不是 1，而是 0；", "score": 1.0 } ] } ] }, { "bbox": [ 86, 142, 250, 154 ], "type": "text", "angle": 0, "index": 3, "lines": [ { "bbox": [ 88, 141, 251, 157 ], "spans": [ { "bbox": [ 88, 141, 251, 157 ], "type": "text", "content": "阶码真值 固定为 -126，而非 -127；", "score": 1.0 } ] } ] }, { "bbox": [ 86, 157, 301, 169 ], "type": "text", "angle": 0, "index": 4, "lines": [ { "bbox": [ 89, 154, 295, 173 ], "spans": [ { "bbox": [ 89, 154, 269, 173 ], "type": "text", "content": "当阶码全为 0 ，尾数全为 0，表示 真值", "score": 1.0 }, { "bbox": [ 270, 157, 295, 169 ], "type": "inline_equation", "content": "+ / - 0", "score": 0.82 } ] } ] }, { "bbox": [ 86, 172, 193, 185 ], "type": "title", "angle": 0, "index": 5, "lines": [ { "bbox": [ 88, 173, 193, 187 ], "spans": [ { "bbox": [ 88, 173, 193, 187 ], "type": "text", "content": "5.3.2. 阶码真值为 128", "score": 1.0 } ] } ] }, { "bbox": [ 104, 188, 433, 216 ], "type": "list", "angle": 0, "index": 8, "blocks": [ { "bbox": [ 105, 188, 364, 200 ], "type": "text", "angle": 0, "index": 6, "lines": [ { "bbox": [ 107, 187, 365, 203 ], "spans": [ { "bbox": [ 107, 187, 365, 203 ], "type": "text", "content": "1. 当阶码全为 1 ，尾数全为 0，表示 正负无穷大 +/- ∞", "score": 1.0 } ] } ] }, { "bbox": [ 104, 203, 433, 216 ], "type": "text", "angle": 0, "index": 7, "lines": [ { "bbox": [ 105, 203, 434, 218 ], "spans": [ { "bbox": [ 105, 203, 434, 218 ], "type": "text", "content": "2. 当阶码全为 1 ，尾数不全为 0，表示非数值 NaN（Not a Number）", "score": 1.0 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 86, 219, 285, 232 ], "type": "text", "angle": 0, "index": 9, "lines": [ { "bbox": [ 88, 218, 285, 233 ], "spans": [ { "bbox": [ 88, 218, 126, 233 ], "type": "text", "content": "如 0/0，", "score": 1.0 }, { "bbox": [ 127, 220, 152, 231 ], "type": "inline_equation", "content": "\\infty - \\infty", "score": 0.7 }, { "bbox": [ 152, 218, 285, 233 ], "type": "text", "content": "等非法运算的结果即为 NaN", "score": 1.0 } ] } ] }, { "bbox": [ 86, 234, 332, 248 ], "type": "text", "angle": 0, "index": 10, "lines": [ { "bbox": [ 89, 235, 332, 248 ], "spans": [ { "bbox": [ 89, 235, 332, 248 ], "type": "text", "content": "汉字输入法程序：将汉字输入计算机转换成汉字内码", "score": 1.0 } ] } ] }, { "bbox": [ 86, 250, 508, 341 ], "type": "list", "angle": 0, "index": 15, "blocks": [ { "bbox": [ 87, 250, 481, 263 ], "type": "text", "angle": 0, "index": 11, "lines": [ { "bbox": [ 89, 249, 481, 264 ], "spans": [ { "bbox": [ 89, 249, 481, 264 ], "type": "text", "content": "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）", "score": 1.0 } ] } ] }, { "bbox": [ 86, 265, 508, 294 ], "type": "text", "angle": 0, "index": 12, "lines": [ { "bbox": [ 88, 266, 510, 279 ], "spans": [ { "bbox": [ 88, 266, 510, 279 ], "type": "text", "content": "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、", "score": 1.0 } ] }, { "bbox": [ 106, 281, 311, 295 ], "spans": [ { "bbox": [ 106, 281, 311, 295 ], "type": "text", "content": "国标码、汉字内码2个字节最高位均为“1”）", "score": 1.0 } ] } ] }, { "bbox": [ 86, 296, 502, 325 ], "type": "text", "angle": 0, "index": 13, "lines": [ { "bbox": [ 88, 297, 503, 310 ], "spans": [ { "bbox": [ 88, 297, 503, 310 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 106, 312, 167, 327 ], "spans": [ { "bbox": [ 106, 312, 167, 327 ], "type": "text", "content": "的代码标准。", "score": 1.0 } ] } ] }, { "bbox": [ 86, 328, 386, 341 ], "type": "text", "angle": 0, "index": 14, "lines": [ { "bbox": [ 88, 327, 387, 343 ], "spans": [ { "bbox": [ 88, 327, 387, 343 ], "type": "text", "content": "4、输出——字形码 点阵表示法 字模码：用于汉字的显示和打印", "score": 1.0 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 104, 343, 433, 356 ], "type": "text", "angle": 0, "index": 16, "lines": [ { "bbox": [ 105, 343, 434, 358 ], "spans": [ { "bbox": [ 105, 343, 152, 358 ], "type": "text", "content": "汉字字库———", "score": 1.0 }, { "bbox": [ 179, 344, 434, 357 ], "type": "text", "content": "所有汉字的字模点阵代码按顺序集中存放根据内码查表", "score": 1.0 } ] } ] }, { "bbox": [ 104, 359, 359, 372 ], "type": "text", "angle": 0, "index": 17, "lines": [ { "bbox": [ 107, 360, 359, 374 ], "spans": [ { "bbox": [ 107, 360, 359, 374 ], "type": "text", "content": "字形检索程序：将汉字的机内代码转化为汉字的字形码", "score": 1.0 } ] } ] }, { "bbox": [ 87, 390, 142, 402 ], "type": "title", "angle": 0, "index": 18, "lines": [ { "bbox": [ 88, 391, 143, 404 ], "spans": [ { "bbox": [ 88, 391, 143, 404 ], "type": "text", "content": "整数的运算", "score": 1.0 } ] } ] }, { "bbox": [ 87, 406, 149, 419 ], "type": "text", "angle": 0, "index": 19, "lines": [ { "bbox": [ 88, 404, 150, 422 ], "spans": [ { "bbox": [ 88, 404, 129, 422 ], "type": "text", "content": "计算值：", "score": 1.0 }, { "bbox": [ 129, 407, 150, 419 ], "type": "inline_equation", "content": "x { + } y", "score": 0.82 } ] } ] }, { "bbox": [ 86, 422, 258, 434 ], "type": "text", "angle": 0, "index": 20, "lines": [ { "bbox": [ 89, 423, 258, 435 ], "spans": [ { "bbox": [ 89, 423, 258, 435 ], "type": "text", "content": "实际值：计算机中实际上保存的结果", "score": 1.0 } ] } ] }, { "bbox": [ 86, 453, 487, 486 ], "type": "text", "angle": 0, "index": 21, "lines": [ { "bbox": [ 367, 465, 410, 476 ], "spans": [ { "bbox": [ 367, 465, 379, 476 ], "type": "inline_equation", "content": "{ } _ { w y } ^ { w }", "score": 0.7 }, { "bbox": [ 402, 465, 410, 475 ], "type": "inline_equation", "content": "w", "score": 0.68 } ] } ] }, { "bbox": [ 86, 499, 336, 513 ], "type": "text", "angle": 0, "index": 22, "lines": [ { "bbox": [ 89, 499, 337, 514 ], "spans": [ { "bbox": [ 89, 499, 162, 514 ], "type": "text", "content": "溢出时，计算值", "score": 1.0 }, { "bbox": [ 162, 501, 170, 511 ], "type": "inline_equation", "content": "\\mathop { }", "score": 0.73 }, { "bbox": [ 170, 499, 199, 514 ], "type": "text", "content": "实际值", "score": 1.0 }, { "bbox": [ 200, 500, 229, 513 ], "type": "inline_equation", "content": "\\pm 2 \\land \\_", "score": 0.91 }, { "bbox": [ 229, 499, 337, 514 ], "type": "text", "content": "（这里相当于是原码！）", "score": 1.0 } ] } ] }, { "bbox": [ 87, 515, 247, 528 ], "type": "text", "angle": 0, "index": 23, "lines": [ { "bbox": [ 89, 516, 247, 528 ], "spans": [ { "bbox": [ 89, 516, 247, 528 ], "type": "text", "content": "如何判定运算结果是否发生了溢出", "score": 1.0 } ] } ] }, { "type": "code", "bbox": [ 86, 533, 263, 655 ], "blocks": [ { "bbox": [ 86, 533, 263, 655 ], "lines": [ { "bbox": [ 86, 533, 263, 655 ], "spans": [ { "bbox": [ 86, 533, 263, 655 ], "type": "text", "content": "Int uadd.ok(unsigned x,unsigned y) \n{ unsigned sum " }, { "bbox": [ 86, 533, 263, 655 ], "type": "inline_equation", "content": "\\equiv" }, { "bbox": [ 86, 533, 263, 655 ], "type": "text", "content": " x+y; If (sum " }, { "bbox": [ 86, 533, 263, 655 ], "type": "inline_equation", "content": "\\rightharpoondown" }, { "bbox": [ 86, 533, 263, 655 ], "type": "text", "content": " x) \nReturn 1; else return 0; \n}" } ] } ], "index": 24, "angle": 0, "type": "code_body" } ], "index": 24, "sub_type": "algorithm" }, { "bbox": [ 87, 661, 142, 673 ], "type": "title", "angle": 0, "index": 25, "lines": [ { "bbox": [ 88, 661, 143, 674 ], "spans": [ { "bbox": [ 88, 661, 143, 674 ], "type": "text", "content": "有符号整数", "score": 1.0 } ] } ] }, { "bbox": [ 86, 677, 449, 705 ], "type": "text", "angle": 0, "index": 26, "lines": [ { "bbox": [ 89, 677, 451, 690 ], "spans": [ { "bbox": [ 89, 677, 451, 690 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 89, 692, 226, 705 ], "spans": [ { "bbox": [ 89, 692, 226, 705 ], "type": "text", "content": "两个异号的数字肯定不会溢出", "score": 1.0 } ] } ] }, { "bbox": [ 87, 708, 205, 720 ], "type": "text", "angle": 0, "index": 27, "lines": [ { "bbox": [ 89, 708, 205, 721 ], "spans": [ { "bbox": [ 89, 708, 205, 721 ], "type": "text", "content": "两个同号的才有可能溢出", "score": 1.0 } ] } ] } ], "discarded_blocks": [], "page_size": [ 595, 841 ], "page_idx": 19 }, { "para_blocks": [ { "type": "image", "bbox": [ 88, 75, 406, 263 ], "blocks": [ { "bbox": [ 88, 75, 406, 263 ], "lines": [ { "bbox": [ 88, 75, 406, 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"bbox": [ 88, 327, 199, 342 ], "spans": [ { "bbox": [ 88, 327, 199, 342 ], "type": "inline_equation", "content": "x - y = x + (-y) = x + (-y + 1)" } ] } ], "index": 4, "angle": 0, "type": "code_body" } ], "index": 4, "sub_type": "algorithm" }, { "type": "image", "bbox": [ 88, 342, 403, 507 ], "blocks": [ { "bbox": [ 88, 342, 403, 507 ], "lines": [ { "bbox": [ 88, 342, 403, 507 ], "spans": [ { "bbox": [ 88, 342, 403, 507 ], "type": "image", "image_path": "28aaa54c06c24037d9b1537962c7c3302913f8ecd66b2e073b85e38b433cb4c3.jpg" } ] } ], "index": 5, "angle": 0, "type": "image_body" } ], "index": 5 }, { "bbox": [ 88, 577, 455, 626 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 88, 577, 455, 626 ], "spans": [ { "bbox": [ 88, 577, 455, 626 ], "type": "interline_equation", "content": "F 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.", "image_path": "f17b1400a5437fc9428c98f60b2bf7260bea9e983f048508ff4ff0d48ababef6.jpg" } ] } ], "index": 6 }, { "bbox": [ 86, 640, 505, 684 ], "type": "text", "angle": 0, "index": 7, "lines": [ { "bbox": [ 89, 640, 505, 653 ], "spans": [ { "bbox": [ 89, 640, 362, 653 ], "type": "text", "content": "对于正溢出，正溢出实际上是让符号位从 1变成0，计算值", "score": 1.0 }, { "bbox": [ 362, 641, 370, 651 ], "type": "inline_equation", "content": "\\equiv", "score": 0.78 }, { "bbox": [ 370, 640, 401, 653 ], "type": "text", "content": "实际值", "score": 1.0 }, { "bbox": [ 401, 640, 429, 652 ], "type": "inline_equation", "content": "+ 2 \\land _ { \\mathsf { W } , }", "score": 0.91 }, { "bbox": [ 429, 640, 505, 653 ], "type": "text", "content": ",它没被截断，最", "score": 1.0 } ] }, { "bbox": [ 89, 656, 505, 669 ], "spans": [ { "bbox": [ 89, 656, 279, 669 ], "type": "text", "content": "高位由0变成了1，这两个数本来就没有-", "score": 1.0 }, { "bbox": [ 280, 656, 294, 668 ], "type": "inline_equation", "content": "\\mathbf { \\mathcal { Z } ^ { \\wedge } }", "score": 0.84 }, { "bbox": [ 295, 656, 505, 669 ], "type": "text", "content": "（w-1)的权重结果有了，那么实际值就要加上", "score": 1.0 } ] }, { "bbox": [ 88, 670, 327, 686 ], "spans": [ { "bbox": [ 88, 670, 287, 686 ], "type": "text", "content": "2^（w-1），又因为补码的定义，又得减去", "score": 1.0 }, { "bbox": [ 287, 671, 325, 684 ], "type": "inline_equation", "content": "2 \\setminus ( \\mathsf { w } - 1 )", "score": 0.64 }, { "bbox": [ 325, 670, 327, 686 ], "type": "text", "content": "", "score": 1.0 } ] } ] }, { "bbox": [ 86, 687, 505, 715 ], "type": "text", "angle": 0, "index": 8, "lines": [ { "bbox": [ 89, 687, 505, 699 ], "spans": [ { "bbox": [ 89, 688, 185, 699 ], "type": "text", "content": "对于负溢出，计算值", "score": 1.0 }, { "bbox": [ 186, 688, 193, 698 ], "type": "inline_equation", "content": "=", "score": 0.78 }, { "bbox": [ 193, 688, 227, 699 ], "type": "text", "content": "实际值-", "score": 1.0 }, { "bbox": [ 227, 687, 249, 699 ], "type": "inline_equation", "content": "{ \\mathcal { 2 } } ^ { \\wedge } \\mathsf { w }", "score": 0.88 }, { "bbox": [ 250, 688, 505, 699 ], "type": "text", "content": "，这里因为原来两个最高位符号位从 1变成0，两个数", "score": 1.0 } ] }, { "bbox": [ 88, 702, 363, 717 ], "spans": [ { "bbox": [ 88, 702, 123, 717 ], "type": "text", "content": "本来有-", "score": 1.0 }, { "bbox": [ 123, 703, 145, 714 ], "type": "inline_equation", "content": "{ \\mathcal { 2 } } ^ { \\wedge } \\mathsf { w }", "score": 0.83 }, { "bbox": [ 146, 702, 337, 717 ], "type": "text", "content": "的权重结果没了。那么实际值就要减去个-", "score": 1.0 }, { "bbox": [ 338, 703, 360, 714 ], "type": "inline_equation", "content": ". 2 \\land _ { \\mathsf { W } }", "score": 0.85 }, { "bbox": [ 361, 702, 363, 717 ], "type": "text", "content": "", "score": 1.0 } ] } ] }, { "bbox": [ 87, 717, 158, 730 ], "type": "text", "angle": 0, "index": 9, "lines": [ { "bbox": [ 88, 718, 159, 731 ], "spans": [ { "bbox": [ 88, 718, 159, 731 ], "type": "text", "content": "如何判断溢出？", "score": 1.0 } ] } ] }, { "bbox": [ 86, 733, 268, 746 ], "type": "text", "angle": 0, "index": 10, "lines": [ { "bbox": [ 89, 734, 268, 747 ], "spans": [ { "bbox": [ 89, 734, 268, 747 ], "type": "text", "content": "两个正数相加，得到结果为负，正溢出", "score": 1.0 } ] } ] }, { "bbox": [ 87, 749, 264, 761 ], "type": "text", "angle": 0, "index": 11, "lines": [ { "bbox": [ 89, 750, 264, 762 ], "spans": [ { "bbox": [ 89, 750, 204, 762 ], "type": "text", "content": "两个负数相加，得到结果", "score": 1.0 }, { "bbox": [ 205, 750, 222, 761 ], "type": "inline_equation", "content": "\\geqslant 0", "score": 0.88 }, { "bbox": [ 223, 750, 264, 762 ], "type": "text", "content": "，负溢出", "score": 1.0 } ] } ] } ], "discarded_blocks": [], "page_size": [ 595, 841 ], "page_idx": 20 }, { "para_blocks": [ { "bbox": [ 86, 79, 132, 91 ], "type": "text", "angle": 0, "index": 0, "lines": [ { "bbox": [ 88, 79, 133, 94 ], "spans": [ { "bbox": [ 88, 79, 133, 94 ], "type": "text", "content": "加法逆元", "score": 1.0 } ] } ] }, { "bbox": [ 88, 93, 260, 106 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 88, 93, 260, 106 ], "spans": [ { "bbox": [ 88, 93, 260, 106 ], "type": "interline_equation", "content": "F o r x, 0 \\leq x < 2 ^ {w}, x + x ^ {\\prime} = x ^ {\\prime} + x = 0", "image_path": "2029c22c026c4fa30e7e761fb82f81e61eaa09fee23c12b123a8799e763f16e8.jpg" } ] } ], "index": 1 }, { "bbox": [ 86, 126, 135, 139 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 86, 126, 135, 139 ], "spans": [ { "bbox": [ 86, 126, 135, 139 ], "type": "interline_equation", "content": "y - x - > y + x ^ {\\prime}.", "image_path": "598b78d35c62d0ae336bf7c134154459802dc823a2167e0142f6b811df97facd.jpg" } ] } ], "index": 2 }, { "bbox": [ 86, 141, 252, 154 ], "type": "text", "angle": 0, "index": 3, "lines": [ { "bbox": [ 88, 141, 253, 156 ], "spans": [ { "bbox": [ 88, 141, 192, 156 ], "type": "text", "content": "对于无符号整型来说，", "score": 1.0 }, { "bbox": [ 193, 142, 253, 154 ], "type": "inline_equation", "content": "\\mathsf { x } + \\mathsf { x } ^ { \\prime } { = } 2 \\mathsf { \\Lambda } \\mathsf { w } { = } 0", "score": 0.81 } ] } ] }, { "bbox": [ 88, 157, 182, 190 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 88, 157, 182, 190 ], "spans": [ { "bbox": [ 88, 157, 182, 190 ], "type": "interline_equation", "content": "x ^ {\\prime} = \\left\\{ \\begin{array}{l} x, x = 0 \\\\ 2 ^ {w} - x, x > 0 \\end{array} \\right.", "image_path": "6404e5f3b47c1aa33ac05ac957a5d74af45e51c64c456cbee4abb38e221f6f20.jpg" } ] } ], "index": 4 }, { "bbox": [ 86, 203, 279, 216 ], "type": "text", "angle": 0, "index": 5, "lines": [ { "bbox": [ 89, 203, 279, 217 ], "spans": [ { "bbox": [ 89, 203, 279, 217 ], "type": "text", "content": "对于补码表示的有符号数的逆元比较简单", "score": 1.0 } ] } ] }, { "bbox": [ 88, 219, 208, 253 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 88, 219, 208, 253 ], "spans": [ { "bbox": [ 88, 219, 208, 253 ], "type": "interline_equation", "content": "x ^ {\\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.", "image_path": "25d619fbd5211e844c40d4c1cf83b0b73bf6e4be6171c18abfbfcbbb6121a54b.jpg" } ] } ], "index": 6 }, { "bbox": [ 86, 265, 269, 279 ], "type": "text", "angle": 0, "index": 7, "lines": [ { "bbox": [ 89, 267, 269, 280 ], "spans": [ { "bbox": [ 89, 267, 269, 280 ], "type": "text", "content": "由于补码最大值比最小值的绝对值要小", "score": 1.0 } ] } ] }, { "bbox": [ 87, 281, 157, 293 ], "type": "text", "angle": 0, "index": 8, "lines": [ { "bbox": [ 88, 281, 157, 296 ], "spans": [ { "bbox": [ 88, 281, 100, 296 ], "type": "text", "content": "即", "score": 1.0 }, { "bbox": [ 101, 282, 157, 294 ], "type": "inline_equation", "content": "0 1 1 1 < 1 0 0 0", "score": 0.84 } ] } ] }, { "bbox": [ 86, 296, 307, 310 ], "type": "text", "angle": 0, "index": 9, "lines": [ { "bbox": [ 89, 297, 307, 311 ], "spans": [ { "bbox": [ 89, 297, 307, 311 ], "type": "text", "content": "关于 最小值的逆元要通过负溢出 的方法来实现", "score": 1.0 } ] } ] }, { "bbox": [ 88, 312, 101, 324 ], "type": "text", "angle": 0, "index": 10, "lines": [ { "bbox": [ 88, 313, 102, 327 ], "spans": [ { "bbox": [ 88, 313, 102, 327 ], "type": "text", "content": "即", "score": 1.0 } ] } ] }, { "bbox": [ 88, 327, 221, 340 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 88, 327, 221, 340 ], "spans": [ { "bbox": [ 88, 327, 221, 340 ], "type": "interline_equation", "content": "T \\min _ {w} + T \\min _ {w} = - 2 ^ {w} = 0", "image_path": "3e4a3262de20fec5fe5b778f9103bd42c979de6c88ad08934a7fa4929cc139ab.jpg" } ] } ], "index": 11 }, { "bbox": [ 86, 359, 490, 388 ], "type": "text", "angle": 0, "index": 12, "lines": [ { "bbox": [ 87, 358, 491, 374 ], "spans": [ { "bbox": [ 87, 358, 491, 374 ], "type": "text", "content": "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", "score": 1.0 } ] }, { "bbox": [ 88, 374, 192, 391 ], "spans": [ { "bbox": [ 88, 374, 169, 391 ], "type": "text", "content": "因此，z=xy mod", "score": 1.0 }, { "bbox": [ 170, 376, 192, 387 ], "type": "inline_equation", "content": "_ { 2 } \\wedge _ { \\mathsf { W } }", "score": 0.82 } ] } ] }, { "bbox": [ 87, 391, 288, 404 ], "type": "text", "angle": 0, "index": 13, "lines": [ { "bbox": [ 88, 388, 289, 407 ], "spans": [ { "bbox": [ 88, 388, 289, 407 ], "type": "text", "content": "对于有符号数，我们有 z=U2T(xymod2^w)", "score": 1.0 } ] } ] }, { "bbox": [ 86, 406, 501, 434 ], "type": "text", "angle": 0, "index": 14, "lines": [ { "bbox": [ 88, 407, 502, 419 ], "spans": [ { "bbox": [ 88, 407, 203, 419 ], "type": "text", "content": "X’y’ mod 2^w=(xy) mod", "score": 1.0 }, { "bbox": [ 203, 407, 226, 418 ], "type": "inline_equation", "content": "{ 2 } ^ { \\wedge } \\mathsf { w } .", "score": 0.78 }, { "bbox": [ 226, 407, 502, 419 ], "type": "text", "content": ".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", "score": 1.0 } ] }, { "bbox": [ 89, 423, 389, 435 ], "spans": [ { "bbox": [ 89, 423, 300, 435 ], "type": "text", "content": "整数的乘法往往利用移位运算（拆解成与多个", "score": 1.0 }, { "bbox": [ 300, 423, 320, 434 ], "type": "inline_equation", "content": "2 ^ { \\land } \\mathsf { k }", "score": 0.88 }, { "bbox": [ 320, 423, 389, 435 ], "type": "text", "content": "相乘再相加减）", "score": 1.0 } ] } ] }, { "bbox": [ 87, 437, 301, 450 ], "type": "text", "angle": 0, "index": 15, "lines": [ { "bbox": [ 89, 438, 300, 451 ], "spans": [ { "bbox": [ 89, 438, 300, 451 ], "type": "text", "content": "整数的除法遇到除不尽的情况，总是向0舍入", "score": 1.0 } ] } ] }, { "bbox": [ 87, 453, 420, 465 ], "type": "text", "angle": 0, "index": 16, "lines": [ { "bbox": [ 88, 453, 420, 467 ], "spans": [ { "bbox": [ 88, 453, 420, 467 ], "type": "text", "content": "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。", "score": 1.0 } ] } ] }, { "bbox": [ 86, 468, 464, 481 ], "type": "text", "angle": 0, "index": 17, "lines": [ { "bbox": [ 88, 469, 464, 483 ], "spans": [ { "bbox": [ 88, 469, 246, 483 ], "type": "text", "content": "即如果要右移 k 位，在低 k 位加上", "score": 1.0 }, { "bbox": [ 246, 469, 274, 481 ], "type": "inline_equation", "content": "2 \\land k - 1", "score": 0.87 }, { "bbox": [ 275, 469, 291, 483 ], "type": "text", "content": ", 向", "score": 1.0 }, { "bbox": [ 291, 469, 310, 481 ], "type": "inline_equation", "content": "k { + 1 }", "score": 0.89 }, { "bbox": [ 311, 469, 464, 483 ], "type": "text", "content": "产生一个进位，实现了向 0 取整。", "score": 1.0 } ] } ] }, { "bbox": [ 87, 484, 206, 497 ], "type": "text", "angle": 0, "index": 18, "lines": [ { "bbox": [ 89, 485, 205, 497 ], "spans": [ { "bbox": [ 89, 485, 205, 497 ], "type": "text", "content": "即用整除实现了向上取整", "score": 1.0 } ] } ] }, { "bbox": [ 87, 499, 136, 512 ], "type": "text", "angle": 0, "index": 19, "lines": [ { "bbox": [ 88, 499, 139, 513 ], "spans": [ { "bbox": [ 88, 499, 139, 513 ], "type": "text", "content": "举个例子：", "score": 1.0 } ] } ] }, { "bbox": [ 88, 515, 109, 527 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 88, 515, 109, 527 ], "spans": [ { "bbox": [ 88, 515, 109, 527 ], "type": "interline_equation", "content": "K = 0", "image_path": "a29db2a794701a100c0b44039aed46a131e1a905155a3365fed051fc4e450f80.jpg" } ] } ], "index": 20 }, { "bbox": [ 88, 530, 223, 542 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 88, 530, 223, 542 ], "spans": [ { "bbox": [ 88, 530, 223, 542 ], "type": "interline_equation", "content": "1 1 0 0 1 1 1 1 1 1 0 0 1 1 0 0 - 1 2 3 4 0", "image_path": "ae2b079a304117ba6b2332725c7f682d79ef921b7df0b701b11aa92650856927.jpg" } ] } ], "index": 21 }, { "bbox": [ 87, 546, 343, 560 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 87, 546, 343, 560 ], "spans": [ { "bbox": [ 87, 546, 343, 560 ], "type": "interline_equation", "content": "K = 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;", "image_path": "91c104b874db5721d63a7201467a2bcf161076331b50f00aebbf8e09535e4b20.jpg" } ] } ], "index": 22 }, { "bbox": [ 86, 561, 439, 575 ], "type": "text", "angle": 0, "index": 23, "lines": [ { "bbox": [ 88, 561, 440, 576 ], "spans": [ { "bbox": [ 88, 561, 440, 576 ], "type": "text", "content": "加上偏置，1100111111011011，右移四位有 1111110011111101,即-771。", "score": 1.0 } ] } ] }, { "bbox": [ 110, 576, 227, 589 ], "type": "text", "angle": 0, "index": 24, "lines": [ { "bbox": [ 110, 574, 228, 591 ], "spans": [ { "bbox": [ 110, 574, 228, 591 ], "type": "text", "content": "division by a power of 2", "score": 0.957 } ] } ] }, { "bbox": [ 88, 593, 248, 608 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 88, 593, 248, 608 ], "spans": [ { "bbox": [ 88, 593, 248, 608 ], "type": "interline_equation", "content": "(x < 0? x + (1 < < k) - 1: x) > > K", "image_path": "ec86c5a0179520e72388c0b2997a88bf941d1d67f2002173a8e06d37b94f8f02.jpg" } ] } ], "index": 25 }, { "bbox": [ 86, 624, 268, 653 ], "type": "text", "angle": 0, "index": 26, "lines": [ { "bbox": [ 88, 624, 268, 637 ], "spans": [ { "bbox": [ 88, 624, 268, 637 ], "type": "text", "content": "但是，除以2不能推广到除以任意整数", "score": 1.0 } ] }, { "bbox": [ 88, 640, 124, 655 ], "spans": [ { "bbox": [ 88, 640, 124, 655 ], "type": "text", "content": "浮点数", "score": 1.0 } ] } ] } ], "discarded_blocks": [], "page_size": [ 595, 841 ], "page_idx": 21 }, { "para_blocks": [ { "type": "table", "bbox": [ 82, 130, 511, 257 ], "blocks": [ { "bbox": [ 82, 130, 511, 257 ], "lines": [ { "bbox": [ 82, 130, 511, 257 ], "spans": [ { "bbox": [ 82, 130, 511, 257 ], "type": "table", "html": "
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
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"bbox": [ 101, 305, 379, 320 ], "type": "text", "content": "规格化：确保尾数的最高位非0数位刚好在小数点之前", "score": 0.997 } ] } ] }, { "bbox": [ 88, 327, 153, 341 ], "type": "text", "angle": 0, "index": 13, "lines": [ { "bbox": [ 89, 328, 154, 342 ], "spans": [ { "bbox": [ 89, 328, 154, 342 ], "type": "text", "content": "阶码确定范围", "score": 1.0 } ] } ] }, { "bbox": [ 88, 343, 153, 356 ], "type": "text", "angle": 0, "index": 14, "lines": [ { "bbox": [ 88, 344, 154, 356 ], "spans": [ { "bbox": [ 88, 344, 154, 356 ], "type": "text", "content": "尾数影响精度", "score": 1.0 } ] } ] }, { "type": "image", "bbox": [ 88, 370, 419, 457 ], "blocks": [ { "bbox": [ 88, 370, 419, 457 ], "lines": [ { "bbox": [ 88, 370, 419, 457 ], "spans": [ { "bbox": [ 88, 370, 419, 457 ], "type": "image", "image_path": "79f181b47490d71aa33641df7b5c4485f39a62657deff27543ee4ad27dd2b53e.jpg" } ] } ], "index": 15, "angle": 0, "type": "image_body" } ], "index": 15 }, { "bbox": [ 88, 513, 183, 528 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 88, 513, 183, 528 ], "spans": [ { "bbox": [ 88, 513, 183, 528 ], "type": "interline_equation", "content": "V = (- 1) ^ {S} \\times M \\times 2 ^ {E}", "image_path": "5d840cc43b3cb748816ef8c0a608d069f3cfb943c1eba1242c7308d12b963ba2.jpg" } ] } ], "index": 16 }, { "bbox": [ 86, 546, 207, 560 ], "type": "text", "angle": 0, "index": 17, "lines": [ { "bbox": [ 89, 547, 206, 560 ], "spans": [ { "bbox": [ 89, 547, 206, 560 ], "type": "text", "content": "尾数用原码定点小数表示", "score": 1.0 } ] } ] }, { "bbox": [ 86, 561, 236, 575 ], "type": "text", "angle": 0, "index": 18, "lines": [ { "bbox": [ 89, 562, 236, 576 ], "spans": [ { "bbox": [ 89, 562, 236, 576 ], "type": "text", "content": "阶码用移码，规定偏置值为127", "score": 1.0 } ] } ] }, { "bbox": [ 86, 577, 473, 591 ], "type": "text", "angle": 0, "index": 19, "lines": [ { "bbox": [ 88, 575, 475, 594 ], "spans": [ { "bbox": [ 88, 578, 107, 590 ], "type": "inline_equation", "content": "\\mathsf { S } { = } 0 _ { - }", "score": 0.86 }, { "bbox": [ 108, 575, 139, 594 ], "type": "text", "content": ",正数；", "score": 1.0 }, { "bbox": [ 139, 578, 158, 590 ], "type": "inline_equation", "content": "s { = } 1", "score": 0.88 }, { "bbox": [ 158, 575, 475, 594 ], "type": "text", "content": "负数；M 为小数部分，尾数部分，frac。E 为指数部分，阶码，exp。", "score": 1.0 } ] } ] }, { "bbox": [ 87, 593, 345, 606 ], "type": "text", "angle": 0, "index": 20, "lines": [ { "bbox": [ 88, 593, 346, 608 ], "spans": [ { "bbox": [ 88, 593, 155, 608 ], "type": "text", "content": "Emin=1.emax", "score": 1.0 }, { "bbox": [ 155, 594, 180, 606 ], "type": "inline_equation", "content": "= 2 5 4", "score": 0.72 }, { "bbox": [ 181, 593, 286, 608 ], "type": "text", "content": "，对半分，所以要减去", "score": 1.0 }, { "bbox": [ 286, 593, 340, 606 ], "type": "inline_equation", "content": "2 5 4 / 2 { = } 1 2 7", "score": 0.88 }, { "bbox": [ 340, 593, 346, 608 ], "type": "text", "content": "；", "score": 1.0 } ] } ] }, { "bbox": [ 88, 608, 357, 621 ], "type": "text", "angle": 0, "index": 21, "lines": [ { "bbox": [ 89, 608, 358, 623 ], "spans": [ { "bbox": [ 89, 608, 358, 623 ], "type": "text", "content": "第一位总是1，因此没必要显示出来，所以尾数部分要加1", "score": 1.0 } ] } ] }, { "type": "image", "bbox": [ 89, 623, 291, 721 ], "blocks": [ { "bbox": [ 89, 623, 291, 721 ], "lines": [ { "bbox": [ 89, 623, 291, 721 ], "spans": [ { "bbox": [ 89, 623, 291, 721 ], "type": "image", "image_path": "e50dc1d79cdffb23905de3ed3b7c0658a8254a152177a16d4d0e0392f652513b.jpg" } ] } ], "index": 22, "angle": 0, "type": "image_body" } ], "index": 22 } ], "discarded_blocks": [], "page_size": [ 595, 841 ], "page_idx": 23 }, { "para_blocks": [ { "type": "image", "bbox": [ 88, 121, 405, 280 ], "blocks": [ { "bbox": [ 88, 121, 405, 280 ], "lines": [ { "bbox": [ 88, 121, 405, 280 ], "spans": [ { "bbox": [ 88, 121, 405, 280 ], "type": "image", "image_path": "bd23b66fa0ae5d5aa0cccc7dda113d13d37aca406c550155e1c82dd36201b0e2.jpg" } ] } ], "index": 1, "angle": 0, "type": "image_body" } ], "index": 1 }, { "bbox": [ 110, 285, 340, 300 ], "type": "text", "angle": 0, "index": 2, "lines": [ { "bbox": [ 111, 285, 342, 301 ], "spans": [ { "bbox": [ 111, 285, 342, 301 ], "type": "text", "content": "如何将十进制真值转换为偏置值为M的移码？", "score": 0.995 } ] } ] }, { "bbox": [ 111, 313, 325, 341 ], "type": "list", "angle": 0, "index": 5, "blocks": [ { "bbox": [ 111, 313, 244, 327 ], "type": "text", "angle": 0, "index": 3, "lines": [] }, { "bbox": [ 111, 327, 325, 341 ], "type": "text", "angle": 0, "index": 4, "lines": [ { "bbox": [ 111, 325, 327, 343 ], "spans": [ { "bbox": [ 111, 325, 327, 343 ], "type": "text", "content": "②按“无符号整数”规则转换为指定位数", "score": 0.991 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 87, 375, 238, 387 ], "type": "title", "angle": 0, "index": 6, "lines": [ { "bbox": [ 89, 375, 238, 389 ], "spans": [ { "bbox": [ 89, 375, 238, 389 ], "type": "text", "content": "小数点前的 1 省略了（隐藏了 1）", "score": 1.0 } ] } ] }, { "type": "image", "bbox": [ 88, 388, 511, 593 ], "blocks": [ { "bbox": [ 88, 388, 511, 593 ], "lines": [ { "bbox": [ 88, 388, 511, 593 ], "spans": [ { "bbox": [ 88, 388, 511, 593 ], "type": "image", "image_path": "d598243f6708b4a1a023068860747b875a9ef2e74e3149a5cb201ad75a8e9e35.jpg" } ] } ], "index": 7, "angle": 0, "type": "image_body" } ], "index": 7 }, { "bbox": [ 86, 624, 503, 668 ], "type": "list", "angle": 0, "index": 10, "blocks": [ { "bbox": [ 86, 624, 428, 637 ], "type": "text", "angle": 0, "index": 8, "lines": [ { "bbox": [ 89, 624, 428, 639 ], "spans": [ { "bbox": [ 89, 624, 428, 639 ], "type": "text", "content": "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", "score": 1.0 } ] } ] }, { "bbox": [ 86, 640, 503, 668 ], "type": "text", "angle": 0, "index": 9, "lines": [ { "bbox": [ 86, 639, 506, 655 ], "spans": [ { "bbox": [ 86, 639, 383, 655 ], "type": "text", "content": "2、当阶码字段全为 0，非规格化.1、尾数部分也全为 0，则当", "score": 1.0 }, { "bbox": [ 383, 640, 403, 653 ], "type": "inline_equation", "content": "\\mathsf { S } { = } 0", "score": 0.89 }, { "bbox": [ 403, 639, 463, 655 ], "type": "text", "content": "，表示正 0，", "score": 1.0 }, { "bbox": [ 463, 640, 483, 653 ], "type": "inline_equation", "content": "s { = } 1", "score": 0.86 }, { "bbox": [ 483, 639, 506, 655 ], "type": "text", "content": "，负", "score": 1.0 } ] }, { "bbox": [ 86, 655, 103, 671 ], "spans": [ { "bbox": [ 86, 655, 103, 671 ], "type": "text", "content": "0；", "score": 1.0 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 87, 671, 390, 684 ], "type": "text", "angle": 0, "index": 11, "lines": [ { "bbox": [ 88, 670, 391, 686 ], "spans": [ { "bbox": [ 88, 670, 286, 686 ], "type": "text", "content": "表示非常接近 0 的数；如果尾数不为 0，则", "score": 1.0 }, { "bbox": [ 287, 671, 306, 683 ], "type": "inline_equation", "content": "\\mathsf { E } { = } \\mathsf { 1 }", "score": 0.85 }, { "bbox": [ 307, 670, 338, 686 ], "type": "text", "content": "-bias，", "score": 1.0 }, { "bbox": [ 339, 671, 361, 684 ], "type": "inline_equation", "content": "\\mathsf { M } = \\mathsf { f }", "score": 0.78 }, { "bbox": [ 361, 670, 391, 686 ], "type": "text", "content": "不加 1", "score": 1.0 } ] } ] } ], "discarded_blocks": [ { "bbox": [ 88, 79, 214, 91 ], "type": "header", "angle": 0, "index": 0, "lines": [ { "bbox": [ 89, 78, 214, 94 ], "spans": [ { "bbox": [ 89, 78, 214, 94 ], "type": "text", "content": "单精度记得减去 127e-bias", "score": 1.0 } ] } ] } ], "page_size": [ 595, 841 ], "page_idx": 24 }, { "para_blocks": [ { "type": "image", "bbox": [ 88, 75, 465, 257 ], "blocks": [ { "bbox": [ 88, 75, 465, 257 ], "lines": [ { "bbox": [ 88, 75, 465, 257 ], "spans": [ { "bbox": [ 88, 75, 465, 257 ], "type": "image", "image_path": "650d5305479445f75aede3bdffbb25a65884bf601e7cfc1f140fcc4261742161.jpg" } ] } ], "index": 0, "angle": 0, "type": "image_body" } ], "index": 0 }, { "bbox": [ 87, 265, 505, 293 ], "type": "text", "angle": 0, "index": 1, "lines": [ { "bbox": [ 88, 265, 505, 280 ], "spans": [ { "bbox": [ 88, 265, 317, 280 ], "type": "text", "content": "3、当阶码字段全为 1，特殊值；当尾数为 0 时，", "score": 1.0 }, { "bbox": [ 317, 266, 337, 279 ], "type": "inline_equation", "content": "\\mathsf { S } { = } 0", "score": 0.87 }, { "bbox": [ 337, 265, 388, 280 ], "type": "text", "content": "，正无穷；", "score": 1.0 }, { "bbox": [ 389, 266, 408, 279 ], "type": "inline_equation", "content": "s { = } 1", "score": 0.89 }, { "bbox": [ 408, 265, 505, 280 ], "type": "text", "content": "，负无穷；当尾数不", "score": 1.0 } ] }, { "bbox": [ 88, 281, 253, 295 ], "spans": [ { "bbox": [ 88, 281, 253, 295 ], "type": "text", "content": "为0时，表示NaN表示不是一个数", "score": 1.0 } ] } ] }, { "type": "image", "bbox": [ 88, 294, 462, 462 ], "blocks": [ { "bbox": [ 88, 294, 462, 462 ], "lines": [ { "bbox": [ 88, 294, 462, 462 ], "spans": [ { "bbox": [ 88, 294, 462, 462 ], "type": "image", "image_path": "c7544ae05a23243dd7e02061d4e04648f67639f1185b2a400c3cdfb32356d57d.jpg" } ] } ], "index": 2, "angle": 0, "type": "image_body" } ], "index": 2 }, { "type": "table", "bbox": [ 101, 484, 284, 599 ], "blocks": [ { "bbox": [ 105, 472, 152, 483 ], "lines": [ { "bbox": [ 105, 472, 153, 484 ], "spans": [ { "bbox": [ 105, 472, 153, 484 ], "type": "text", "content": "单精度为例", "score": 0.999 } ] } ], "index": 3, "angle": 0, "type": "table_caption" }, { "bbox": [ 101, 484, 284, 599 ], "lines": [ { "bbox": [ 101, 484, 284, 599 ], "spans": [ { "bbox": [ 101, 484, 284, 599 ], "type": "table", "html": "
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
", "image_path": "14c33bdab70e592aaf0ccde21c71194aa3140aa51f19aa17576c208ea689fdc7.jpg" } ] } ], "index": 4, "angle": 0, "type": "table_body" }, { "bbox": [ 293, 583, 404, 594 ], "lines": [ { "bbox": [ 293, 582, 405, 595 ], "spans": [ { "bbox": [ 293, 582, 405, 595 ], "type": "text", "content": "NaN:非数 (not a number)", "score": 0.941 } ] } ], "index": 5, "angle": 0, "type": "table_footnote" } ], "index": 4 }, { "type": "table", "bbox": [ 99, 626, 247, 751 ], "blocks": [ { "bbox": [ 99, 626, 247, 751 ], "lines": [ { "bbox": [ 99, 626, 247, 751 ], "spans": [ { "bbox": [ 99, 626, 247, 751 ], "type": "table", "html": "
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
", "image_path": "905041adb2aacd5eb3288df88fa734e9d7f1bbccff80e53ea0dcd1c85fb214b7.jpg" } ] } ], "index": 6, "angle": 0, "type": "table_body" } ], "index": 6 }, { "type": "table", "bbox": [ 257, 624, 404, 751 ], "blocks": [ { "bbox": [ 257, 624, 404, 751 ], "lines": [ { "bbox": [ 257, 624, 404, 751 ], "spans": [ { "bbox": [ 257, 624, 404, 751 ], "type": "table", "html": "
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
", "image_path": "c4d438acd9a66d9110bfe24f582ea5e1e5761d34adbaaf54d1ddda5ab8206457.jpg" } ] } ], "index": 7, "angle": 0, "type": "table_body" } ], "index": 7 } ], "discarded_blocks": [], "page_size": [ 595, 841 ], "page_idx": 25 }, { "para_blocks": [ { "bbox": [ 89, 77, 390, 131 ], "type": "list", "angle": 0, "index": 3, "blocks": [ { "bbox": [ 89, 77, 268, 89 ], "type": "text", "angle": 0, "index": 0, "lines": [ { "bbox": [ 90, 76, 269, 89 ], "spans": [ { "bbox": [ 90, 76, 186, 89 ], "type": "text", "content": "·阶码：是2n-1的移码，", "score": 0.937 }, { "bbox": [ 186, 78, 200, 89 ], "type": "inline_equation", "content": "\\mathtt { E } =", "score": 0.62 }, { "bbox": [ 201, 76, 269, 89 ], "type": "text", "content": "[E']移=2n-1+E'", "score": 0.892 } ] } ] }, { "bbox": [ 89, 91, 390, 116 ], "type": "text", "angle": 0, "index": 1, "lines": [ { "bbox": [ 89, 90, 391, 104 ], "spans": [ { "bbox": [ 89, 90, 391, 104 ], "type": "text", "content": "·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", "score": 0.993 } ] }, { "bbox": [ 98, 105, 196, 116 ], "spans": [ { "bbox": [ 98, 105, 196, 116 ], "type": "text", "content": "隐藏；临时实数无隐藏位", "score": 0.989 } ] } ] }, { "bbox": [ 89, 119, 238, 131 ], "type": "text", "angle": 0, "index": 2, "lines": [ { "bbox": [ 90, 119, 238, 131 ], "spans": [ { "bbox": [ 90, 119, 238, 131 ], "type": "text", "content": "■符号位：尾数的符号位Ms在最高位", "score": 0.968 } ] } ] } ], "sub_type": "text" }, { "type": "table", "bbox": [ 121, 138, 364, 214 ], "blocks": [ { "bbox": [ 121, 138, 364, 214 ], "lines": [ { "bbox": [ 121, 138, 364, 214 ], "spans": [ { "bbox": [ 121, 138, 364, 214 ], "type": "table", "html": "
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}} \\)
", "image_path": "a8de82aae0dab15c57a2a4b539d59e65ebc8094ec0467130528b436ab139841c.jpg" } ] } ], "index": 4, "angle": 0, "type": "table_body" } ], "index": 4 }, { "bbox": [ 98, 236, 327, 248 ], "type": "text", "angle": 0, "index": 5, "lines": [ { "bbox": [ 97, 235, 327, 249 ], "spans": [ { "bbox": [ 97, 235, 327, 249 ], "type": "text", "content": "例3.10若X和Y均是IEEE754标准的单精度浮点数。", "score": 0.991 } ] } ] }, { "bbox": [ 110, 251, 359, 278 ], "type": "list", "angle": 0, "index": 8, "blocks": [ { "bbox": [ 110, 251, 327, 263 ], "type": "text", "angle": 0, "index": 6, "lines": [ { "bbox": [ 122, 250, 328, 264 ], "spans": [ { "bbox": [ 122, 250, 167, 264 ], "type": "text", "content": "（1）若×", "score": 0.818 }, { "bbox": [ 167, 252, 176, 261 ], "type": "inline_equation", "content": "=", "score": 0.52 }, { "bbox": [ 176, 250, 328, 264 ], "type": "text", "content": "-135.625，求X的规格化浮点数表示。", "score": 0.986 } ] } ] }, { "bbox": [ 110, 265, 359, 278 ], "type": "text", "angle": 0, "index": 7, "lines": [ { "bbox": [ 123, 264, 360, 280 ], "spans": [ { "bbox": [ 123, 264, 360, 280 ], "type": "text", "content": "(2）若浮点数Y的存储形式为41360000H，求Y的真值。", "score": 0.991 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 94, 282, 281, 295 ], "type": "text", "angle": 0, "index": 9, "lines": [ { "bbox": [ 94, 282, 281, 295 ], "spans": [ { "bbox": [ 94, 282, 281, 295 ], "type": "text", "content": "（1）真值→IEEE754规格化单精度浮点数", "score": 0.991 } ] } ] }, { "bbox": [ 94, 296, 340, 323 ], "type": "list", "angle": 0, "index": 12, "blocks": [ { "bbox": [ 94, 296, 340, 310 ], "type": "text", "angle": 0, "index": 10, "lines": [ { "bbox": [ 95, 295, 340, 311 ], "spans": [ { "bbox": [ 95, 297, 105, 308 ], "type": "text", "content": "", "score": 0.0 }, { "bbox": [ 105, 297, 116, 309 ], "type": "inline_equation", "content": "\\textcircled{1}", "score": 0.78 }, { "bbox": [ 116, 297, 209, 308 ], "type": "text", "content": "写出数据的二进制真值", "score": 0.999 }, { "bbox": [ 232, 297, 249, 308 ], "type": "inline_equation", "content": "\\mathbf { x } =", "score": 0.78 }, { "bbox": [ 250, 295, 340, 311 ], "type": "text", "content": "(-10000111.101） 2", "score": 0.924 } ] } ] }, { "bbox": [ 94, 311, 332, 323 ], "type": "text", "angle": 0, "index": 11, "lines": [ { "bbox": [ 95, 311, 332, 323 ], "spans": [ { "bbox": [ 95, 311, 105, 323 ], "type": "text", "content": "", "score": 0.0 }, { "bbox": [ 105, 312, 116, 323 ], "type": "inline_equation", "content": "\\textcircled{2}", "score": 0.71 }, { "bbox": [ 116, 311, 155, 323 ], "type": "text", "content": "转换为M", "score": 0.996 }, { "bbox": [ 155, 312, 173, 322 ], "type": "inline_equation", "content": "\\times 2 ^ { E }", "score": 0.76 }, { "bbox": [ 174, 311, 231, 323 ], "type": "text", "content": "的形式：M'", "score": 0.89 }, { "bbox": [ 232, 312, 287, 322 ], "type": "inline_equation", "content": "{ \\bf \\delta } = \\pm 1 . \\times { \\bf x } \\ldots \\times", "score": 0.79 }, { "bbox": [ 287, 311, 332, 323 ], "type": "text", "content": "，E'为整数", "score": 0.956 } ] } ] } 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"text", "angle": 0, "index": 1, "lines": [ { "bbox": [ 88, 93, 313, 110 ], "spans": [ { "bbox": [ 88, 93, 313, 110 ], "type": "text", "content": "• 一级常用汉字：3755 个，按拼音字母顺序排列", "score": 1.0 } ] } ] }, { "bbox": [ 87, 110, 302, 122 ], "type": "text", "angle": 0, "index": 2, "lines": [ { "bbox": [ 89, 110, 302, 124 ], "spans": [ { "bbox": [ 89, 110, 302, 124 ], "type": "text", "content": "• 二级次常用汉字：3008 个，按偏旁部首排列", "score": 1.0 } ] } ] }, { "bbox": [ 87, 125, 436, 138 ], "type": "text", "angle": 0, "index": 3, "lines": [ { "bbox": [ 88, 125, 437, 140 ], "spans": [ { "bbox": [ 88, 125, 318, 140 ], "type": "text", "content": " 两个字节编码汉字，每个字节各取 7 位，可编码", "score": 1.0 }, { "bbox": [ 318, 126, 403, 138 ], "type": "inline_equation", "content": "1 2 8 \\times 1 2 8 = 1 6 3 8 4", "score": 0.84 }, { "bbox": [ 403, 125, 437, 140 ], "type": "text", "content": "个字符", "score": 1.0 } ] } ] }, { "bbox": [ 87, 141, 420, 154 ], "type": "text", "angle": 0, "index": 4, "lines": [ { "bbox": [ 88, 139, 420, 157 ], "spans": [ { "bbox": [ 88, 139, 234, 157 ], "type": "text", "content": " 将所有的汉字及符号组成一个", "score": 1.0 }, { "bbox": [ 235, 142, 267, 153 ], "type": "inline_equation", "content": "9 4 \\times 9 4", "score": 0.87 }, { "bbox": [ 267, 139, 320, 157 ], "type": "text", "content": "的方阵，行", "score": 1.0 }, { "bbox": [ 333, 139, 383, 157 ], "type": "text", "content": "“区”，列", "score": 1.0 }, { "bbox": [ 396, 139, 420, 157 ], "type": "text", "content": "“位”", "score": 1.0 } ] } ] }, { "bbox": [ 87, 157, 406, 169 ], "type": "text", "angle": 0, "index": 5, "lines": [ { "bbox": [ 86, 155, 408, 173 ], "spans": [ { "bbox": [ 86, 155, 348, 173 ], "type": "text", "content": " 每个汉字与符号都位于某个区的某个位上，区号和位号", "score": 1.0 }, { "bbox": [ 362, 155, 408, 173 ], "type": "text", "content": "“区位码”", "score": 1.0 } ] } ] }, { "bbox": [ 87, 172, 473, 185 ], "type": "text", "angle": 0, "index": 6, "lines": [ { "bbox": [ 87, 170, 473, 188 ], "spans": [ { "bbox": [ 87, 170, 244, 188 ], "type": "text", "content": " 例如：“中”字位于 54 区 48 位", "score": 1.0 }, { "bbox": [ 258, 170, 473, 188 ], "type": "text", "content": "“中”字的区位码即为“5448  （2）国标码", "score": 1.0 } ] } ] }, { "bbox": [ 87, 188, 278, 200 ], "type": "text", "angle": 0, "index": 7, "lines": [ { "bbox": [ 88, 188, 279, 202 ], "spans": [ { "bbox": [ 88, 188, 127, 202 ], "type": "text", "content": " 国标码", "score": 1.0 }, { "bbox": [ 127, 189, 135, 199 ], "type": "inline_equation", "content": "\\mid =", "score": 0.72 }, { "bbox": [ 136, 188, 165, 202 ], "type": "text", "content": "区位码", "score": 1.0 }, { "bbox": [ 166, 188, 205, 200 ], "type": "inline_equation", "content": "+ 2 0 2 0 \\mathsf { H }", "score": 0.87 }, { "bbox": [ 205, 188, 279, 202 ], "type": "text", "content": "，占用两个字节", "score": 1.0 } ] } ] }, { "bbox": [ 87, 203, 233, 216 ], "type": "text", "angle": 0, "index": 8, "lines": [ { "bbox": [ 88, 201, 233, 218 ], "spans": [ { "bbox": [ 88, 201, 201, 218 ], "type": "text", "content": " 例如“中”字：区位码", "score": 1.0 }, { "bbox": [ 201, 204, 233, 216 ], "type": "inline_equation", "content": "\\mathbf { = } 5 4 4 8", "score": 0.68 } ] } ] }, { "bbox": [ 87, 219, 266, 232 ], "type": "text", "angle": 0, "index": 9, "lines": [ { "bbox": [ 88, 217, 267, 234 ], "spans": [ { "bbox": [ 88, 217, 226, 234 ], "type": "text", "content": "• 区码和位码转化为 16 进制，", "score": 1.0 }, { "bbox": [ 226, 219, 267, 232 ], "type": "inline_equation", "content": "{ \\bf = 3 6 3 0 H }", "score": 0.77 } ] } ] }, { "bbox": [ 87, 235, 242, 247 ], "type": "text", "angle": 0, "index": 10, "lines": [ { "bbox": [ 88, 235, 242, 249 ], "spans": [ { "bbox": [ 88, 235, 126, 249 ], "type": "text", "content": "• 国标码", "score": 1.0 }, { "bbox": [ 126, 235, 242, 248 ], "type": "inline_equation", "content": "\\lvert = 3 6 3 0 \\rvert + 2 0 2 0 \\ H = 5 6 5 0 \\ H", "score": 0.84 } ] } ] }, { "bbox": [ 87, 250, 172, 263 ], "type": "text", "angle": 0, "index": 11, "lines": [ { "bbox": [ 89, 248, 173, 265 ], "spans": [ { "bbox": [ 89, 248, 173, 265 ], "type": "text", "content": " （3）汉字内码", "score": 1.0 } ] } ] }, { "bbox": [ 87, 265, 403, 279 ], "type": "text", "angle": 0, "index": 12, "lines": [ { "bbox": [ 87, 264, 404, 281 ], "spans": [ { "bbox": [ 87, 264, 404, 281 ], "type": "text", "content": " 西文字符：七位的 ASCII 码，当用一个字节表示时，最高位为“0”", "score": 1.0 } ] } ] }, { "bbox": [ 87, 281, 433, 294 ], "type": "text", "angle": 0, "index": 13, "lines": [ { "bbox": [ 87, 280, 435, 296 ], "spans": [ { "bbox": [ 87, 280, 191, 296 ], "type": "text", "content": " 汉字内码：汉字内码", "score": 1.0 }, { "bbox": [ 192, 283, 202, 293 ], "type": "inline_equation", "content": "=", "score": 0.85 }, { "bbox": [ 202, 280, 255, 296 ], "type": "text", "content": "汉字国标码", "score": 1.0 }, { "bbox": [ 255, 282, 299, 294 ], "type": "inline_equation", "content": "\\pm 8 0 8 0 \\mathsf { H }", "score": 0.85 }, { "bbox": [ 299, 280, 435, 296 ], "type": "text", "content": "，2 个字节的最高位均为“1”", "score": 1.0 } ] } ] }, { "bbox": [ 87, 297, 320, 310 ], "type": "text", "angle": 0, "index": 14, "lines": [ { "bbox": [ 87, 295, 320, 312 ], "spans": [ { "bbox": [ 87, 295, 199, 312 ], "type": "text", "content": "• 例如“中”字的机内码", "score": 1.0 }, { "bbox": [ 200, 297, 320, 310 ], "type": "inline_equation", "content": "\\lvert = 5 6 5 0 \\rvert + 8 0 8 0 \\ H = \\mathrm { D } 6 \\mathrm { D } 0 \\mathsf { H }", "score": 0.83 } ] } ] }, { "bbox": [ 87, 312, 234, 325 ], "type": "text", "angle": 0, "index": 15, "lines": [ { "bbox": [ 89, 312, 235, 328 ], "spans": [ { "bbox": [ 89, 312, 235, 328 ], "type": "text", "content": " 文本文件中储存的是汉字内码", "score": 1.0 } ] } ] }, { "bbox": [ 87, 328, 450, 341 ], "type": "text", "angle": 0, "index": 16, "lines": [ { "bbox": [ 88, 328, 452, 343 ], "spans": [ { "bbox": [ 88, 328, 214, 343 ], "type": "text", "content": "汉字处理系统中字形信息：", "score": 1.0 }, { "bbox": [ 214, 328, 226, 341 ], "type": "inline_equation", "content": "\\textcircled{1}", "score": 0.85 }, { "bbox": [ 226, 328, 381, 343 ], "type": "text", "content": "用活字或文字版的母体字形形式；", "score": 1.0 }, { "bbox": [ 382, 328, 394, 341 ], "type": "inline_equation", "content": "\\textcircled{2}", "score": 0.86 }, { "bbox": [ 395, 328, 452, 343 ], "type": "text", "content": "点阵表示法、", "score": 1.0 } ] } ] }, { "bbox": [ 87, 343, 352, 356 ], "type": "text", "angle": 0, "index": 17, "lines": [ { "bbox": [ 88, 343, 353, 359 ], "spans": [ { "bbox": [ 88, 343, 353, 359 ], "type": "text", "content": "矢量表示法等形式，最基本的，应用也最广泛的是字模码", "score": 1.0 } ] } ] }, { "bbox": [ 87, 359, 433, 387 ], "type": "text", "angle": 0, "index": 18, "lines": [ { "bbox": [ 88, 359, 433, 373 ], "spans": [ { "bbox": [ 88, 359, 433, 373 ], "type": "text", "content": " 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", "score": 1.0 } ] }, { "bbox": [ 89, 375, 185, 389 ], "spans": [ { "bbox": [ 89, 375, 185, 389 ], "type": "text", "content": "于汉字的显示和打印", "score": 1.0 } ] } ] }, { "bbox": [ 87, 391, 312, 403 ], "type": "text", "angle": 0, "index": 19, "lines": [ { "bbox": [ 88, 391, 313, 405 ], "spans": [ { "bbox": [ 88, 391, 313, 405 ], "type": "text", "content": " 根据汉字输出的要求不同，点阵的规模也不同：", "score": 1.0 } ] } ] }, { "bbox": [ 87, 407, 263, 418 ], "type": "text", "angle": 0, "index": 20, "lines": [ { "bbox": [ 87, 405, 264, 421 ], "spans": [ { "bbox": [ 87, 405, 157, 421 ], "type": "text", "content": "• 简易型汉字：", "score": 1.0 }, { "bbox": [ 158, 407, 190, 419 ], "type": "inline_equation", "content": "1 6 \\times 1 6", "score": 0.87 }, { "bbox": [ 190, 405, 264, 421 ], "type": "text", "content": "， 32 字节/汉字", "score": 1.0 } ] } ] }, { "bbox": [ 87, 422, 263, 434 ], "type": "text", "angle": 0, "index": 21, "lines": [ { "bbox": [ 87, 420, 264, 437 ], "spans": [ { "bbox": [ 87, 420, 157, 437 ], "type": "text", "content": "• 普及型汉字：", "score": 1.0 }, { "bbox": [ 157, 422, 190, 434 ], "type": "inline_equation", "content": "2 4 \\times 2 4", "score": 0.87 }, { "bbox": [ 190, 420, 264, 437 ], "type": "text", "content": "， 72 字节/汉字", "score": 1.0 } ] } ] }, { "bbox": [ 87, 438, 266, 449 ], "type": "text", "angle": 0, "index": 22, "lines": [ { "bbox": [ 88, 437, 267, 452 ], "spans": [ { "bbox": [ 88, 437, 157, 452 ], "type": "text", "content": "• 提高型汉字：", "score": 1.0 }, { "bbox": [ 157, 438, 190, 450 ], "type": "inline_equation", "content": "3 2 \\times 3 2", "score": 0.88 }, { "bbox": [ 190, 437, 267, 452 ], "type": "text", "content": "，128 字节/汉字", "score": 1.0 } ] } ] }, { "bbox": [ 87, 453, 266, 465 ], "type": "text", "angle": 0, "index": 23, "lines": [ { "bbox": [ 88, 451, 267, 468 ], "spans": [ { "bbox": [ 88, 451, 157, 468 ], "type": "text", "content": "• 精密型汉字：", "score": 1.0 }, { "bbox": [ 157, 454, 190, 465 ], "type": "inline_equation", "content": "4 8 \\times 4 8", "score": 0.89 }, { "bbox": [ 190, 451, 267, 468 ], "type": "text", "content": "，288 字节/汉字", "score": 1.0 } ] } ] }, { "bbox": [ 87, 468, 423, 481 ], "type": "text", "angle": 0, "index": 24, "lines": [ { "bbox": [ 88, 469, 423, 483 ], "spans": [ { "bbox": [ 88, 469, 423, 483 ], "type": "text", "content": " 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", "score": 1.0 } ] } ] }, { "bbox": [ 87, 484, 308, 497 ], "type": "text", "angle": 0, "index": 25, "lines": [ { "bbox": [ 88, 484, 308, 498 ], "spans": [ { "bbox": [ 88, 484, 308, 498 ], "type": "text", "content": " 字形检索程序：将汉字的机内代码转化为汉字", "score": 1.0 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 87, 515, 132, 528 ], "type": "title", "angle": 0, "index": 27, "lines": [ { "bbox": [ 88, 515, 133, 530 ], "spans": [ { "bbox": [ 88, 515, 133, 530 ], "type": "text", "content": "补码加减", "score": 1.0 } ] } ] }, { "bbox": [ 105, 534, 214, 547 ], "type": "text", "angle": 0, "index": 28, "lines": [ { "bbox": [ 107, 535, 215, 547 ], "spans": [ { "bbox": [ 107, 535, 215, 547 ], "type": "text", "content": "补码的加法运算公式：", "score": 0.991 } ] } ] }, { "bbox": [ 117, 550, 214, 564 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 117, 550, 214, 564 ], "spans": [ { "bbox": [ 117, 550, 214, 564 ], "type": "interline_equation", "content": "= [ X + Y ] _ {\\text {补}} = [ X ] _ {\\text {补}} + [ Y ] _ {\\text {补}}", "image_path": "16152e56ad039c3a60e7e161d0186a30d2a31b140d8d3a52512fcda2f04b72f0.jpg" } ] } ], "index": 29 }, { "bbox": [ 260, 533, 368, 545 ], "type": "text", "angle": 0, "index": 30, "lines": [ { "bbox": [ 260, 533, 370, 545 ], "spans": [ { "bbox": [ 260, 533, 370, 545 ], "type": "text", "content": "补码的减法运算公式：", "score": 0.996 } ] } ] }, { "bbox": [ 272, 549, 378, 576 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 272, 549, 378, 576 ], "spans": [ { "bbox": [ 272, 549, 378, 576 ], "type": "interline_equation", "content": "\\begin{array}{l} - [ X - Y ] _ {\\text {补}} = [ X + (- Y) ] _ {\\text {补}} \\\\ = [ \\mathrm {X} ] _ {\\text {补}} + [ - \\mathrm {Y} ] _ {\\text {补}} \\\\ \\end{array}", "image_path": "d601aad040f3da0f676d517a595008665e004685db26eaaf694f8007a33844ca.jpg" } ] } ], "index": 31 }, { "bbox": [ 112, 569, 136, 580 ], "type": "text", "angle": 0, "index": 32, "lines": [ { "bbox": [ 112, 570, 138, 581 ], "spans": [ { "bbox": [ 112, 570, 138, 581 ], "type": "text", "content": "证明：", "score": 0.995 } ] } ] }, { "bbox": [ 116, 581, 251, 594 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 116, 581, 251, 594 ], "spans": [ { "bbox": [ 116, 581, 251, 594 ], "type": "interline_equation", "content": "[ X ] _ {\\text {补}} = 2 ^ {n + 1} + X \\quad (\\mathrm {m o d} 2 ^ {n + 1})", "image_path": "ff07a017411944f1ae1e23f721fcfef0a5d4879e94c43f42bb91ae4076b0e5de.jpg" } ] } ], "index": 33 }, { "bbox": [ 116, 598, 251, 611 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 116, 598, 251, 611 ], "spans": [ { "bbox": [ 116, 598, 251, 611 ], "type": "interline_equation", "content": "[ Y ] _ {\\text {补}} = 2 ^ {n + 1} + Y \\quad (\\mathrm {m o d} 2 ^ {n + 1})", "image_path": "cbd22d9a28cb9f43bd443474b627349e6b3ccbfd0e59579155d7e55217c64159.jpg" } ] } ], "index": 34 }, { "bbox": [ 116, 614, 336, 662 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 116, 614, 336, 662 ], "spans": [ { "bbox": [ 116, 614, 336, 662 ], "type": "interline_equation", "content": "\\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}", "image_path": "6aad23c4096e7f809a235f33ef7d754f099269ccb0889185b7dffeae6ca74b1b.jpg" } ] } ], "index": 35 }, { "bbox": [ 99, 672, 362, 698 ], "type": "list", "angle": 0, "index": 38, "blocks": [ { "bbox": [ 99, 672, 271, 684 ], "type": "text", "angle": 0, "index": 36, "lines": [ { "bbox": [ 101, 673, 271, 684 ], "spans": [ { "bbox": [ 101, 673, 194, 684 ], "type": "text", "content": "任意两数之和的补码", "score": 0.998 }, { "bbox": [ 195, 673, 205, 683 ], "type": "inline_equation", "content": "=", "score": 0.83 }, { "bbox": [ 205, 673, 271, 684 ], "type": "text", "content": "两数的补码之和", "score": 0.999 } ] } ] }, { "bbox": [ 99, 687, 362, 698 ], "type": "text", "angle": 0, "index": 37, "lines": [ { "bbox": [ 101, 687, 362, 698 ], "spans": [ { "bbox": [ 101, 687, 194, 698 ], "type": "text", "content": "任意两数之差的补码", "score": 0.998 }, { "bbox": [ 195, 687, 205, 697 ], "type": "inline_equation", "content": "=", "score": 0.83 }, { "bbox": [ 205, 687, 362, 698 ], "type": "text", "content": "被减数的补码与减数相反数的补码之和", "score": 0.997 } ] } ] } ], "sub_type": "text" } ], "discarded_blocks": [], "page_size": [ 595, 841 ], "page_idx": 29 }, { "para_blocks": [ { "bbox": [ 123, 96, 270, 116 ], "type": "title", "angle": 0, "index": 0, "lines": [ { "bbox": [ 121, 94, 272, 117 ], "spans": [ { "bbox": [ 121, 94, 272, 117 ], "type": "text", "content": "求补运算：[Y]补→[-Y]补", "score": 0.92 } ] } ] }, { "bbox": [ 94, 125, 396, 141 ], "type": "text", "angle": 0, "index": 1, "lines": [ { "bbox": [ 95, 125, 396, 142 ], "spans": [ { "bbox": [ 95, 125, 176, 141 ], "type": "text", "content": "求补规则：将", "score": 0.993 }, { "bbox": [ 176, 125, 199, 142 ], "type": "inline_equation", "content": "[ Y ] _ { \\ast \\mathrm { h } }", "score": 0.67 }, { "bbox": [ 200, 125, 396, 141 ], "type": "text", "content": "包括符号位在内每一位取反，末位加1。", "score": 0.999 } ] } ] }, { "bbox": [ 94, 145, 261, 161 ], "type": "text", "angle": 0, "index": 2, "lines": [ { "bbox": [ 94, 142, 264, 163 ], "spans": [ { "bbox": [ 94, 142, 118, 163 ], "type": "text", "content": "若", "score": 0.998 }, { "bbox": [ 119, 144, 169, 162 ], "type": "inline_equation", "content": "[ \\boldsymbol { \\Upsilon } _ { \\sharp \\flat } = \\boldsymbol { \\Upsilon } _ { \\mathsf { s } }", "score": 0.85 }, { "bbox": [ 179, 145, 231, 161 ], "type": "inline_equation", "content": "\\mathsf { Y } _ { 1 } . . . . . \\mathsf { Y } _ { \\mathsf { n } }", "score": 0.79 }, { "bbox": [ 231, 142, 264, 163 ], "type": "text", "content": "，则：", "score": 0.917 } ] } ] }, { "bbox": [ 108, 165, 255, 182 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 108, 165, 255, 182 ], "spans": [ { "bbox": [ 108, 165, 255, 182 ], "type": "interline_equation", "content": "- [ - Y ] _ {\\text {补}} = \\overline {{Y _ {S}}} \\overline {{Y _ {1}}} \\dots \\dots \\overline {{Y _ {n}}} + 1", "image_path": "2682be6a595e12b8bb9a0fa345e503fc16b8eea8df3305199ff85fa6c2d16fd2.jpg" } ] } ], "index": 3 }, { "bbox": [ 94, 186, 256, 201 ], "type": "text", "angle": 0, "index": 4, "lines": [ { "bbox": [ 94, 183, 258, 204 ], "spans": [ { "bbox": [ 94, 183, 146, 204 ], "type": "text", "content": "若[Y]补", "score": 0.957 }, { "bbox": [ 146, 185, 226, 202 ], "type": "inline_equation", "content": "\\mathbf { \\Psi } = \\mathsf { Y } _ { \\mathsf { S } } . \\mathsf { Y } _ { 1 } . . . . . \\mathsf { Y } _ { \\mathsf { n } }", "score": 0.86 }, { "bbox": [ 226, 183, 258, 204 ], "type": "text", "content": "，则：", "score": 0.916 } ] } ] }, { "bbox": [ 108, 206, 302, 223 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 108, 206, 302, 223 ], "spans": [ { "bbox": [ 108, 206, 302, 223 ], "type": "interline_equation", "content": "- [ - Y ] _ {\\text {补}} = \\overline {{Y _ {S}}} \\overline {{Y _ {1}}} \\dots \\dots \\overline {{Y _ {n}}} + 0. 0 \\dots \\dots 0 1", "image_path": "a00512c6c13063d6f0d24745175a8bb187e230002084848bd824d798a7574aa3.jpg" } ] } ], "index": 5 }, { "bbox": [ 86, 231, 258, 243 ], "type": "text", "angle": 0, "index": 6, "lines": [ { "bbox": [ 87, 232, 258, 244 ], "spans": [ { "bbox": [ 87, 232, 258, 244 ], "type": "text", "content": "：溢出：运算结果超出机器数的表示范围", "score": 0.972 } ] } ] }, { "bbox": [ 87, 248, 186, 259 ], "type": "text", "angle": 0, "index": 7, "lines": [ { "bbox": [ 88, 248, 186, 260 ], "spans": [ { "bbox": [ 88, 248, 186, 260 ], "type": "text", "content": "计算机硬件必须具备：", "score": 0.99 } ] } ] }, { "bbox": [ 98, 263, 245, 290 ], "type": "list", "angle": 0, "index": 10, "blocks": [ { "bbox": [ 98, 263, 245, 275 ], "type": "text", "angle": 0, "index": 8, "lines": [ { "bbox": [ 101, 264, 245, 275 ], "spans": [ { "bbox": [ 101, 264, 245, 275 ], "type": "text", "content": "·能够检测运算结果是否发生溢出；", "score": 0.953 } ] } ] }, { "bbox": [ 98, 279, 245, 290 ], "type": "text", "angle": 0, "index": 9, "lines": [ { "bbox": [ 100, 280, 245, 291 ], "spans": [ { "bbox": [ 100, 280, 245, 291 ], "type": "text", "content": "·能够指示运算结果是否发生溢出；", "score": 0.97 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 309, 234, 420, 246 ], "type": "text", "angle": 0, "index": 11, "lines": [ { "bbox": [ 309, 233, 420, 247 ], "spans": [ { "bbox": [ 309, 233, 420, 247 ], "type": "text", "content": "补码加减运算判溢方法：", "score": 0.994 } ] } ] }, { "bbox": [ 324, 250, 391, 294 ], "type": "list", "angle": 0, "index": 15, "blocks": [ { "bbox": [ 324, 250, 391, 262 ], "type": "text", "angle": 0, "index": 12, "lines": [ { "bbox": [ 324, 249, 391, 263 ], "spans": [ { "bbox": [ 324, 249, 391, 263 ], "type": "text", "content": "·单符号位判溢", "score": 0.922 } ] } ] }, { "bbox": [ 324, 266, 372, 278 ], "type": "text", "angle": 0, "index": 13, "lines": [ { "bbox": [ 323, 264, 374, 280 ], "spans": [ { "bbox": [ 323, 264, 374, 280 ], "type": "text", "content": "·进位判溢", "score": 0.982 } ] } ] }, { "bbox": [ 324, 282, 391, 294 ], "type": "text", "angle": 0, "index": 14, "lines": [ { "bbox": [ 324, 281, 392, 295 ], "spans": [ { "bbox": [ 324, 281, 392, 295 ], "type": "text", "content": "■双符号位判溢", "score": 0.925 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 86, 295, 251, 307 ], "type": "text", "angle": 0, "index": 16, "lines": [ { "bbox": [ 88, 295, 252, 307 ], "spans": [ { "bbox": [ 88, 295, 252, 307 ], "type": "text", "content": "对于加减运算，可能发生溢出的情况：", "score": 0.995 } ] } ] }, { "bbox": [ 98, 311, 185, 338 ], "type": "list", "angle": 0, "index": 19, "blocks": [ { "bbox": [ 98, 311, 185, 323 ], "type": "text", "angle": 0, "index": 17, "lines": [ { "bbox": [ 99, 311, 186, 323 ], "spans": [ { "bbox": [ 99, 311, 186, 323 ], "type": "text", "content": "■同号（两数）相加", "score": 0.925 } ] } ] }, { "bbox": [ 98, 326, 185, 338 ], "type": "text", "angle": 0, "index": 18, "lines": [ { "bbox": [ 99, 326, 186, 339 ], "spans": [ { "bbox": [ 99, 326, 186, 339 ], "type": "text", "content": "·异号（两数）相减", "score": 0.957 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 109, 350, 138, 362 ], "type": "text", "angle": 0, "index": 20, "lines": [ { "bbox": [ 107, 347, 140, 364 ], "spans": [ { "bbox": [ 107, 347, 140, 364 ], "type": "text", "content": "Why?", "score": 0.989 } ] } ] }, { "bbox": [ 201, 322, 310, 334 ], "type": "text", "angle": 0, "index": 21, "lines": [ { "bbox": [ 210, 322, 311, 334 ], "spans": [ { "bbox": [ 210, 322, 311, 334 ], "type": "text", "content": "一定会发生溢出的情况：", "score": 0.997 } ] } ] }, { "bbox": [ 214, 338, 372, 397 ], "type": "list", "angle": 0, "index": 26, "blocks": [ { "bbox": [ 214, 338, 361, 350 ], "type": "text", "angle": 0, "index": 22, "lines": [ { "bbox": [ 218, 339, 362, 350 ], "spans": [ { "bbox": [ 218, 339, 362, 350 ], "type": "text", "content": "正数相加，且运算结果符号位为1", "score": 0.998 } ] } ] }, { "bbox": [ 214, 354, 362, 366 ], "type": "text", "angle": 0, "index": 23, "lines": [ { "bbox": [ 215, 354, 363, 367 ], "spans": [ { "bbox": [ 215, 354, 363, 367 ], "type": "text", "content": "·负数相加，且运算结果符号位为0", "score": 0.981 } ] } ] }, { "bbox": [ 214, 370, 371, 382 ], "type": "text", "angle": 0, "index": 24, "lines": [ { "bbox": [ 215, 370, 372, 383 ], "spans": [ { "bbox": [ 215, 370, 372, 383 ], "type": "text", "content": "·正数－负数，且运算结果符号位为1", "score": 0.945 } ] } ] }, { "bbox": [ 214, 386, 372, 397 ], "type": "text", "angle": 0, "index": 25, "lines": [ { "bbox": [ 215, 385, 373, 399 ], "spans": [ { "bbox": [ 215, 385, 373, 399 ], "type": "text", "content": "■负数－正数，且运算结果符号位为0", "score": 0.971 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 413, 397, 426, 412 ], "type": "title", "angle": 0, "index": 27, "lines": [ { "bbox": [ 415, 401, 426, 411 ], "spans": [ { "bbox": [ 415, 401, 426, 411 ], "type": "text", "content": "18", "score": 0.99 } ] } ] }, { "bbox": [ 126, 425, 238, 439 ], "type": "title", "angle": 0, "index": 28, "lines": [ { "bbox": [ 126, 424, 238, 439 ], "spans": [ { "bbox": [ 126, 424, 238, 439 ], "type": "text", "content": "（1）单符号位判溢方法", "score": 0.969 } ] } ] }, { "bbox": [ 133, 445, 249, 460 ], "type": "text", "angle": 0, "index": 29, "lines": [ { "bbox": [ 133, 444, 251, 461 ], "spans": [ { "bbox": [ 133, 446, 205, 461 ], "type": "inline_equation", "content": "\\overline { { A D D } } / S U B = 0", "score": 0.69 }, { "bbox": [ 206, 444, 251, 461 ], "type": "text", "content": "：做加法", "score": 0.991 } ] } ] }, { "bbox": [ 134, 465, 249, 478 ], "type": "text", "angle": 0, "index": 30, "lines": [ { "bbox": [ 134, 464, 249, 480 ], "spans": [ { "bbox": [ 134, 465, 205, 480 ], "type": "inline_equation", "content": "\\overline { { A D D } } / S U B = 1", "score": 0.51 }, { "bbox": [ 205, 464, 249, 479 ], "type": "text", "content": "：做减法", "score": 0.996 } ] } ] }, { "bbox": [ 292, 425, 410, 439 ], "type": "text", "angle": 0, "index": 31, "lines": [ { "bbox": [ 293, 423, 411, 440 ], "spans": [ { "bbox": [ 293, 428, 305, 436 ], "type": "text", "content": "", "score": 0.0 }, { "bbox": [ 307, 423, 411, 440 ], "type": "text", "content": "【例4.3】的4种情况：", "score": 0.988 } ] } ] }, { "bbox": [ 279, 443, 397, 484 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 279, 443, 397, 484 ], "spans": [ { "bbox": [ 279, 443, 397, 484 ], "type": "interline_equation", "content": "\\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}", "image_path": "af33e894e0bc5bc9f1c8958716fb93b6806ae55dfec4cbe0afd5ccb203a48277.jpg" } ] } ], "index": 32 }, { "type": "table", "bbox": [ 107, 491, 519, 614 ], "blocks": [ { "bbox": [ 107, 491, 519, 614 ], "lines": [ { "bbox": [ 107, 491, 519, 614 ], "spans": [ { "bbox": [ 107, 491, 519, 614 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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
", "image_path": "ea812e338c51b36ff98fc816caadb34d0e22ff55762a1c584f92915146ff3477.jpg" } ] } ], "index": 33, "angle": 0, "type": "table_body" } ], "index": 33 }, { "bbox": [ 107, 623, 165, 637 ], "type": "text", "angle": 0, "index": 34, "lines": [ { "bbox": [ 107, 621, 167, 639 ], "spans": [ { "bbox": [ 107, 624, 132, 637 ], "type": "inline_equation", "content": "\\boldsymbol { \\mathsf { V } } = \\boldsymbol { \\mathsf { 1 } }", "score": 0.62 }, { "bbox": [ 132, 621, 167, 639 ], "type": "text", "content": "：溢出", "score": 0.979 } ] } ] } ], "discarded_blocks": [ { "bbox": [ 493, 624, 499, 631 ], "type": "page_number", "angle": 0, "index": 35, "lines": [ { "bbox": [ 493, 621, 500, 632 ], "spans": [ { "bbox": [ 493, 621, 500, 632 ], "type": "text", "content": "", "score": 0.0 } ] } ] } ], "page_size": [ 595, 841 ], "page_idx": 30 }, { "para_blocks": [ { "bbox": [ 99, 76, 210, 91 ], "type": "title", "angle": 0, "index": 0, "lines": [ { "bbox": [ 99, 77, 208, 90 ], "spans": [ { "bbox": [ 99, 77, 208, 90 ], "type": "text", "content": "（3）双符号位判溢方法", "score": 0.956 } ] } ] }, { "bbox": [ 108, 95, 468, 125 ], "type": "text", "angle": 0, "index": 1, "lines": [ { "bbox": [ 110, 94, 469, 109 ], "spans": [ { "bbox": [ 110, 94, 469, 109 ], "type": "text", "content": "·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", "score": 0.99 } ] }, { "bbox": [ 119, 109, 442, 125 ], "spans": [ { "bbox": [ 119, 109, 277, 124 ], "type": "text", "content": "为11；当运算结果的两位符号Fs1", "score": 0.995 }, { "bbox": [ 277, 111, 293, 125 ], "type": "inline_equation", "content": "\\bar { \\mathsf { F } } _ { 5 2 }", "score": 0.66 }, { "bbox": [ 294, 109, 442, 124 ], "type": "text", "content": "不同时（01或10），发生溢出。", "score": 0.993 } ] } ] }, { "bbox": [ 138, 133, 247, 179 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 138, 133, 247, 179 ], "spans": [ { "bbox": [ 138, 133, 247, 179 ], "type": "interline_equation", "content": "\\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}}}", "image_path": "8e4471389a14d592cef0763a38ba5b9149e96fb3d023ce5d82fe1d5ecec37bb1.jpg" } ] } ], "index": 2 }, { "bbox": [ 278, 134, 478, 179 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 278, 134, 478, 179 ], "spans": [ { "bbox": [ 278, 134, 478, 179 ], "type": "interline_equation", "content": "\\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}", "image_path": "33ca0463674fbdfdea12da1f4fc85e2b564531bea634d6ae07c5e5b2fd83b560.jpg" } ] } ], "index": 3 }, { "bbox": [ 151, 195, 422, 211 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 151, 195, 422, 211 ], "spans": [ { "bbox": [ 151, 195, 422, 211 ], "type": "interline_equation", "content": "\\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}", "image_path": "24d011e1161e6bf4c821bf0139a75899371b23eae04990612853b12e8d8ef95d.jpg" } ] } ], "index": 4 }, { "bbox": [ 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"blocks": [ { "bbox": [ 87, 290, 167, 301 ], "type": "text", "angle": 0, "index": 7, "lines": [ { "bbox": [ 88, 288, 168, 303 ], "spans": [ { "bbox": [ 88, 288, 168, 303 ], "type": "text", "content": "A:累加器，存放[X]补", "score": 0.957 } ] } ] }, { "bbox": [ 88, 303, 166, 314 ], "type": "text", "angle": 0, "index": 8, "lines": [ { "bbox": [ 87, 301, 166, 316 ], "spans": [ { "bbox": [ 87, 301, 148, 316 ], "type": "text", "content": "B:寄存器，存放", "score": 0.964 }, { "bbox": [ 149, 304, 166, 315 ], "type": "inline_equation", "content": "[ \\boldsymbol { \\mathsf { Y } } ] _ { \\sharp \\flat }", "score": 0.53 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 88, 317, 124, 327 ], "type": "text", "angle": 0, "index": 10, "lines": [ { "bbox": [ 88, 317, 125, 327 ], "spans": [ { "bbox": [ 88, 317, 125, 327 ], "type": "text", "content": "取反电路：", "score": 0.995 } ] } ] }, { "bbox": [ 89, 329, 210, 365 ], "type": "list", "angle": 0, "index": 13, "blocks": [ { "bbox": [ 89, 329, 210, 353 ], "type": "text", "angle": 0, "index": 11, "lines": [ { "bbox": [ 92, 329, 202, 340 ], "spans": [ { "bbox": [ 92, 329, 134, 340 ], "type": "text", "content": "·控制信号P", "score": 0.879 }, { "bbox": [ 135, 330, 145, 339 ], "type": "inline_equation", "content": "\\cdot = 1", "score": 0.51 }, { "bbox": [ 145, 329, 202, 340 ], "type": "text", "content": "，取反电路工作；", "score": 0.982 } ] }, { "bbox": [ 129, 342, 211, 354 ], "spans": [ { "bbox": [ 129, 343, 145, 353 ], "type": "inline_equation", "content": "\\mathsf { P } \\mathsf { = } \\mathsf { 0 }", "score": 0.62 }, { "bbox": [ 145, 342, 211, 354 ], "type": "text", "content": "：不工作 (不取反)", "score": 0.935 } ] } ] }, { "bbox": [ 90, 355, 148, 365 ], "type": "text", "angle": 0, "index": 12, "lines": [ { "bbox": [ 89, 353, 150, 367 ], "spans": [ { "bbox": [ 89, 353, 150, 367 ], "type": "text", "content": "· P= ADD/SUB", "score": 0.939 } ] } ] } ], "sub_type": "text" }, { "type": "image", "bbox": [ 213, 294, 388, 384 ], "blocks": [ { "bbox": [ 213, 294, 388, 384 ], 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"spans": [ { "bbox": [ 121, 283, 213, 297 ], "type": "text", "content": "（即输出端F）→IB", "score": 0.934 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 279, 194, 512, 299 ], "type": "list", "angle": 0, "index": 16, "blocks": [ { "bbox": [ 279, 194, 446, 208 ], "type": "text", "angle": 0, "index": 12, "lines": [ { "bbox": [ 284, 194, 446, 208 ], "spans": [ { "bbox": [ 284, 194, 446, 208 ], "type": "text", "content": "RA：执行读操作的寄存器地址", "score": 0.985 } ] } ] }, { "bbox": [ 280, 213, 451, 227 ], "type": "text", "angle": 0, "index": 13, "lines": [ { "bbox": [ 283, 213, 450, 227 ], "spans": [ { "bbox": [ 283, 213, 450, 227 ], "type": "text", "content": "WA：执行写操作的寄存器地址", "score": 0.977 } ] } ] }, { "bbox": [ 280, 232, 512, 263 ], "type": "text", "angle": 0, "index": 14, "lines": [ { "bbox": [ 293, 229, 515, 248 ], "spans": [ { "bbox": [ 293, 231, 339, 247 ], "type": "inline_equation", "content": "\\mathtt { G R } _ { \\mathtt { o u t } } = 1", "score": 0.91 }, { "bbox": [ 339, 229, 515, 248 ], 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"bbox": [ 95, 354, 217, 367 ], "type": "text", "content": "数据通路：指数据在硬件系", "score": 0.989 } ] }, { "bbox": [ 96, 370, 210, 381 ], "spans": [ { "bbox": [ 96, 370, 210, 381 ], "type": "text", "content": "上流动的过程与控制步骤", "score": 0.999 } ] } ] }, { "type": "image", "bbox": [ 216, 356, 464, 451 ], "blocks": [ { "bbox": [ 216, 356, 464, 451 ], "lines": [ { "bbox": [ 216, 356, 464, 451 ], "spans": [ { "bbox": [ 216, 356, 464, 451 ], "type": "image", "image_path": "125f1f976a45bde61707512608d443be1397a84c51bebbeef84d0565bd4ae8b7.jpg" } ] } ], "index": 18, "angle": 0, "type": "image_body" } ], "index": 18 }, { "bbox": [ 86, 458, 323, 470 ], "type": "text", "angle": 0, "index": 19, "lines": [ { "bbox": [ 87, 458, 323, 471 ], "spans": [ { "bbox": [ 87, 458, 323, 471 ], "type": "text", "content": "在总线上传送数据的数据通路：需要一个CPU周期", "score": 0.995 } ] } ] }, { "bbox": [ 96, 474, 434, 535 ], "type": "list", "angle": 0, "index": 23, "blocks": [ { "bbox": [ 96, 474, 307, 486 ], "type": "text", "angle": 0, "index": 20, "lines": [ { "bbox": [ 102, 475, 307, 486 ], "spans": [ { "bbox": [ 102, 475, 307, 486 ], "type": "text", "content": "源部件将数据送上总线；目的部件从总线上接收数据", "score": 0.992 } ] } ] }, { "bbox": [ 96, 488, 434, 512 ], "type": "text", "angle": 0, "index": 21, "lines": [ { "bbox": [ 109, 488, 434, 500 ], "spans": [ { "bbox": [ 109, 488, 434, 500 ], "type": "text", "content": "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", "score": 0.998 } ] }, { "bbox": [ 110, 501, 172, 513 ], "spans": [ { "bbox": [ 110, 501, 172, 513 ], "type": "text", "content": "由使能信号控制", "score": 0.997 } ] } ] }, { "bbox": [ 96, 514, 434, 535 ], "type": "text", "angle": 0, "index": 22, "lines": [ { "bbox": [ 99, 515, 434, 526 ], "spans": [ { "bbox": [ 99, 515, 434, 526 ], "type": "text", "content": "·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", "score": 0.989 } ] }, { "bbox": [ 110, 526, 324, 535 ], "spans": [ { "bbox": [ 110, 526, 324, 535 ], "type": "text", "content": "只能允许一个部件将数据送上总线以保证分时高用总线", "score": 0.985 } ] } ] } ], "sub_type": "text" } ], "discarded_blocks": [], "page_size": [ 595, 841 ], "page_idx": 36 }, { "para_blocks": [ { "type": "image", "bbox": [ 106, 109, 118, 127 ], "blocks": [ { "bbox": [ 106, 109, 118, 127 ], "lines": [ { "bbox": [ 106, 109, 118, 127 ], "spans": [ { "bbox": [ 106, 109, 118, 127 ], "type": "image", "image_path": "8c546a5f5a7aab5fcbb5bf8368f8ffbbd6e20baab9c2b514f1bcfa342a332678.jpg" } ] } ], "index": 1, "angle": 0, "type": "image_body" } ], "index": 1 }, { "bbox": [ 123, 111, 595, 157 ], "type": "text", "angle": 0, "index": 2, "lines": [ { "bbox": [ 132, 107, 595, 134 ], "spans": [ { "bbox": [ 132, 107, 595, 134 ], "type": "text", "content": "【例4.10】假设在单总线运算器中，完成一条指令ADDR，R", "score": 0.994 } ] }, { "bbox": [ 123, 134, 595, 158 ], "spans": [ { "bbox": [ 123, 134, 141, 157 ], "type": "text", "content": "作", "score": 1.0 }, { "bbox": [ 141, 134, 230, 158 ], "type": "inline_equation", "content": "\\mathbb { R } _ { 2 } + \\mathbb { R } _ { 7 } \\mathbb { R } _ { 3 }", "score": 0.57 }, { "bbox": [ 231, 134, 595, 157 ], "type": "text", "content": "，则分析该操作的数据通路，需要几个CPU周期？", "score": 0.995 } ] } ] }, { "type": "image", "bbox": [ 108, 163, 479, 304 ], "blocks": [ { "bbox": [ 108, 163, 479, 304 ], "lines": [ { "bbox": [ 108, 163, 479, 304 ], "spans": [ { "bbox": [ 108, 163, 479, 304 ], "type": "image", "image_path": "8195232877e38e022ce58354bf3e0f8e7017782e37ce393611d5c1f08bbd1c6a.jpg" } ] } ], "index": 3, "angle": 0, "type": "image_body" } ], "index": 3 }, { "bbox": [ 540, 241, 593, 260 ], "type": "text", "angle": 0, "index": 4, "lines": [ { "bbox": [ 555, 239, 595, 262 ], "spans": [ { "bbox": [ 555, 239, 595, 262 ], "type": "text", "content": "需要", "score": 1.0 } ] } ] }, { "type": "table", "bbox": [ 89, 306, 595, 423 ], "blocks": [ { "bbox": [ 89, 306, 595, 423 ], "lines": [ { "bbox": [ 89, 306, 595, 423 ], "spans": [ { "bbox": [ 89, 306, 595, 423 ], "type": "table", "html": "
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,
", "image_path": "676656b11afbd4bb4ed24c75e2c3bbdba810d2f3ee73f6b7d4aa3f20b3344706.jpg" } ] } ], "index": 5, "angle": 0, "type": "table_body" } ], "index": 5 }, { "type": "image", "bbox": [ 88, 433, 111, 459 ], "blocks": [ { "bbox": [ 88, 433, 111, 459 ], "lines": [ { "bbox": [ 88, 433, 111, 459 ], "spans": [ { "bbox": [ 88, 433, 111, 459 ], "type": "image", "image_path": "d814906f52ca58133470d1ec963e40201e7792ebe345adbefb39a1651947d1be.jpg" } ] } ], "index": 6, "angle": 0, "type": "image_body" } ], "index": 6 }, { "bbox": [ 101, 456, 524, 490 ], "type": "text", "angle": 0, "index": 7, "lines": [ { "bbox": [ 105, 455, 524, 473 ], "spans": [ { "bbox": [ 105, 461, 111, 468 ], "type": "text", "content": "X", "score": 0.897 }, { "bbox": [ 118, 455, 409, 472 ], "type": "text", "content": "【例4.10】假设在单总线运算器中，完成一条指令ADD", "score": 0.996 }, { "bbox": [ 409, 457, 426, 473 ], "type": "inline_equation", "content": "\\pmb { \\mathsf { R } } _ { 3 }", "score": 0.84 }, { "bbox": [ 434, 457, 451, 473 ], "type": "inline_equation", "content": "{ \\sf R } _ { 2 }", "score": 0.84 }, { "bbox": [ 451, 455, 524, 472 ], "type": "text", "content": "，R的运算操", "score": 0.982 } ] }, { "bbox": [ 113, 474, 449, 491 ], "spans": [ { "bbox": [ 113, 474, 120, 489 ], "type": "text", "content": "", "score": 0.0 }, { "bbox": [ 121, 474, 189, 491 ], "type": "inline_equation", "content": "\\mathsf { E R } _ { 2 } + \\mathsf { R } _ { 7 } \\to \\mathsf { R } _ { 3 }", "score": 0.89 }, { "bbox": [ 189, 474, 449, 489 ], "type": "text", "content": "，则分析该操作的数据通路，需要几个CPU周期？", "score": 0.992 } ] } ] }, { "type": "image", "bbox": [ 102, 494, 365, 593 ], "blocks": [ { "bbox": [ 102, 494, 365, 593 ], "lines": [ { "bbox": [ 102, 494, 365, 593 ], "spans": [ { "bbox": [ 102, 494, 365, 593 ], "type": "image", "image_path": "a7fb5924317ec14cc0f9c5e3f8fb93545692880d72c48a901eeeba9aab0db9c9.jpg" } ] } ], "index": 8, "angle": 0, "type": "image_body" } ], "index": 8 }, { "type": "table", "bbox": [ 89, 595, 537, 679 ], "blocks": [ { "bbox": [ 89, 595, 537, 679 ], "lines": [ { "bbox": [ 89, 595, 537, 679 ], "spans": [ { "bbox": [ 89, 595, 537, 679 ], "type": "table", "html": "
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
", "image_path": "9b13f97b15ecbf42a4b3fbc38d6a0264d9e3f9b7d55a93c3776bd8f1ba8fc74f.jpg" } ] } ], "index": 9, "angle": 0, "type": "table_body" } ], "index": 9 }, { "bbox": [ 408, 548, 517, 564 ], "type": "text", "angle": 0, "index": 10, "lines": [ { "bbox": [ 420, 548, 517, 565 ], "spans": [ { "bbox": [ 420, 548, 517, 565 ], "type": "text", "content": "需要3个CPU周期", "score": 0.999 } ] } ] }, { "type": "image", "bbox": [ 277, 674, 295, 686 ], "blocks": [ { "bbox": [ 277, 674, 295, 686 ], "lines": [ { "bbox": [ 277, 674, 295, 686 ], "spans": [ { "bbox": [ 277, 674, 295, 686 ], "type": "image", "image_path": "1ea251a75cc631e8da1edd057cec79441fb72193971d3eef097821a86412e2de.jpg" } ] } ], "index": 11, "angle": 0, "type": "image_body" } ], "index": 11 } ], "discarded_blocks": [ { "bbox": [ 167, 77, 329, 92 ], "type": "header", "angle": 0, "index": 0, "lines": [ { "bbox": [ 166, 79, 330, 93 ], "spans": [ { "bbox": [ 166, 79, 330, 93 ], "type": "text", "content": "（）车芯线给构", "score": 0.785 } ] } ] } ], "page_size": [ 595, 841 ], "page_idx": 37 }, { "para_blocks": [ { "bbox": [ 100, 84, 135, 97 ], "type": "title", "angle": 0, "index": 0, "lines": [ { "bbox": [ 98, 82, 138, 99 ], "spans": [ { "bbox": [ 98, 82, 138, 99 ], "type": "text", "content": "构成：", "score": 0.913 } ] } ] }, { "bbox": [ 105, 100, 238, 165 ], "type": "list", "angle": 0, "index": 5, "blocks": [ { "bbox": [ 105, 100, 226, 114 ], "type": "text", "angle": 0, "index": 1, "lines": [ { "bbox": [ 107, 100, 226, 114 ], "spans": [ { "bbox": [ 107, 100, 226, 114 ], "type": "text", "content": "·2条内部总线：IB1、IB2", "score": 0.951 } ] } ] }, { "bbox": [ 105, 119, 135, 129 ], "type": "text", "angle": 0, "index": 2, "lines": [ { "bbox": [ 105, 117, 138, 131 ], "spans": [ { "bbox": [ 105, 117, 138, 131 ], "type": "text", "content": "· ALU", "score": 0.847 } ] } ] }, { "bbox": [ 106, 136, 168, 148 ], "type": "text", "angle": 0, "index": 3, "lines": [ { "bbox": [ 105, 135, 170, 148 ], "spans": [ { "bbox": [ 105, 135, 170, 148 ], "type": "text", "content": "·暂存器：LC", "score": 0.924 } ] } ] }, { "bbox": [ 106, 153, 238, 165 ], "type": "text", "angle": 0, "index": 4, "lines": [ { "bbox": [ 107, 153, 238, 165 ], "spans": [ { "bbox": [ 107, 153, 238, 165 ], "type": "text", "content": "·通用寄存器堆GPR：n+1个", "score": 0.959 } ] } ] } ], "sub_type": "text" }, { "type": "image", "bbox": [ 273, 78, 471, 179 ], "blocks": [ { "bbox": [ 273, 78, 471, 179 ], "lines": [ { "bbox": [ 273, 78, 471, 179 ], "spans": [ { "bbox": [ 273, 78, 471, 179 ], "type": "image", "image_path": "a87051a1213d96b6ac50fd128c53e03bcfdec6caf2a3592e7cd20df2d14f35b1.jpg" } ] } ], "index": 6, "angle": 0, "type": "image_body" } ], "index": 6 }, { "bbox": [ 95, 186, 284, 269 ], "type": "list", "angle": 0, "index": 13, "blocks": [ { "bbox": [ 95, 186, 267, 198 ], "type": "text", "angle": 0, "index": 7, "lines": [ { "bbox": [ 95, 185, 267, 198 ], "spans": [ { "bbox": [ 95, 185, 106, 198 ], "type": "text", "content": "：", "score": 0.837 }, { "bbox": [ 107, 186, 136, 198 ], "type": "inline_equation", "content": "\\iota C _ { \\mathrm { i n } } = 1", "score": 0.79 }, { "bbox": [ 136, 185, 267, 198 ], "type": "text", "content": "：ALU运算结果写入LC，即F→LC", "score": 0.972 } ] } ] }, { "bbox": [ 95, 200, 284, 212 ], "type": "text", "angle": 0, "index": 8, "lines": [ { "bbox": [ 100, 199, 286, 214 ], "spans": [ { "bbox": [ 100, 200, 143, 213 ], "type": "inline_equation", "content": "\\dot { } \\cdot \\mathsf { L C } _ { \\mathsf { o u t } } = 1", "score": 0.8 }, { "bbox": [ 143, 199, 286, 214 ], "type": "text", "content": "：LC中数据送上总线IB1，即LC→IB1", "score": 0.994 } ] } ] }, { "bbox": [ 95, 215, 224, 226 ], "type": "text", "angle": 0, "index": 9, "lines": [ { "bbox": [ 95, 213, 225, 227 ], "spans": [ { "bbox": [ 95, 216, 105, 226 ], "type": "inline_equation", "content": "\\ast", "score": 0.61 }, { "bbox": [ 105, 213, 225, 227 ], "type": "text", "content": "ALU_OP:ALU功能码/运算码", "score": 0.99 } ] } ] }, { "bbox": [ 95, 229, 260, 240 ], "type": "text", "angle": 0, "index": 10, "lines": [ { "bbox": [ 95, 228, 260, 240 ], "spans": [ { "bbox": [ 95, 230, 105, 240 ], "type": "inline_equation", "content": "\\ast", "score": 0.61 }, { "bbox": [ 105, 228, 260, 240 ], "type": "text", "content": "RA1：执行读出数据到IB1的寄存器地址", "score": 0.987 } ] } ] }, { "bbox": [ 95, 243, 260, 255 ], "type": "text", "angle": 0, "index": 11, "lines": [ { "bbox": [ 95, 243, 261, 255 ], "spans": [ { "bbox": [ 95, 244, 105, 254 ], "type": "inline_equation", "content": "\\ast", "score": 0.57 }, { "bbox": [ 105, 243, 261, 255 ], "type": "text", "content": "RA2：执行读出数据到IB2的寄存器地址", "score": 0.991 } ] } ] }, { "bbox": [ 95, 258, 227, 269 ], "type": "text", "angle": 0, "index": 12, "lines": [ { "bbox": [ 95, 258, 227, 269 ], "spans": [ { "bbox": [ 95, 259, 105, 269 ], "type": "inline_equation", "content": "^ \\ast", "score": 0.53 }, { "bbox": [ 105, 258, 227, 269 ], "type": "text", "content": "WA：执行写操作的寄存器地址", "score": 0.99 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 291, 187, 470, 264 ], "type": "list", "angle": 0, "index": 17, "blocks": [ { "bbox": [ 291, 187, 470, 211 ], "type": "text", "angle": 0, "index": 14, "lines": [ { "bbox": [ 303, 187, 470, 200 ], "spans": [ { "bbox": [ 303, 188, 342, 200 ], "type": "inline_equation", "content": "\\mathsf { G R } _ { \\mathsf { o u t 1 } } = 1", "score": 0.85 }, { "bbox": [ 342, 187, 470, 200 ], "type": "text", "content": "：读出RA1指定的寄存器数据送到", "score": 0.991 } ] }, { "bbox": [ 302, 198, 408, 211 ], "spans": [ { "bbox": [ 302, 198, 408, 211 ], "type": "text", "content": "IB1上，即Reg[RA1]→IB1", "score": 0.976 } ] } ] }, { "bbox": [ 291, 214, 470, 238 ], "type": "text", "angle": 0, "index": 15, "lines": [ { "bbox": [ 303, 214, 470, 227 ], "spans": [ { "bbox": [ 303, 214, 342, 227 ], "type": "inline_equation", "content": "\\mathsf { G R } _ { \\mathsf { o u t } 2 } = 1", "score": 0.83 }, { "bbox": [ 342, 214, 470, 226 ], "type": "text", "content": "：读出RA2指定的寄存器数据送到", "score": 0.994 } ] }, { "bbox": [ 303, 226, 408, 238 ], "spans": [ { "bbox": [ 303, 226, 408, 238 ], "type": "text", "content": "IB2上，即Reg[RA2]→IB2", "score": 0.984 } ] } ] }, { "bbox": [ 291, 240, 470, 264 ], "type": "text", "angle": 0, "index": 16, "lines": [ { "bbox": [ 303, 240, 470, 253 ], "spans": [ { "bbox": [ 303, 240, 334, 253 ], "type": "inline_equation", "content": "\\mathsf { G R } _ { \\mathrm { i n } } = 1", "score": 0.89 }, { "bbox": [ 334, 240, 470, 252 ], "type": "text", "content": "：将IB1上的数据写入由写地址WA", "score": 0.992 } ] }, { "bbox": [ 303, 253, 426, 265 ], "spans": [ { "bbox": [ 303, 253, 426, 265 ], "type": "text", "content": "中的寄存器，即IB1→Reg[WA]", "score": 0.982 } ] } ] } ], "sub_type": "text" }, { "type": "image", "bbox": [ 88, 283, 119, 322 ], "blocks": [ { "bbox": [ 88, 283, 119, 322 ], "lines": [ { "bbox": [ 88, 283, 119, 322 ], "spans": [ { "bbox": [ 88, 283, 119, 322 ], "type": "image", "image_path": "75625929eabda9a925a66bd9baf77befd3d36f41294bd86703c1f96680c42d1e.jpg" } ] } ], "index": 18, "angle": 0, "type": "image_body" } ], "index": 18 }, { "bbox": [ 152, 285, 271, 306 ], "type": "title", "angle": 0, "index": 19, "lines": [ { "bbox": [ 150, 283, 273, 309 ], "spans": [ { "bbox": [ 150, 283, 273, 309 ], "type": "text", "content": "（2）双总线结构", "score": 0.967 } ] } ] }, { "bbox": [ 107, 319, 309, 425 ], "type": "list", "angle": 0, "index": 22, "blocks": [ { "bbox": [ 107, 319, 309, 388 ], "type": "text", "angle": 0, "index": 20, "lines": [ { "bbox": [ 126, 319, 309, 335 ], "spans": [ { "bbox": [ 126, 319, 309, 335 ], "type": "text", "content": "【例4.11】假设在双总线运算器中", "score": 0.994 } ] }, { "bbox": [ 124, 336, 308, 354 ], "spans": [ { "bbox": [ 124, 336, 239, 354 ], "type": "text", "content": "，同样完成指令ADD", "score": 0.998 }, { "bbox": [ 239, 338, 255, 354 ], "type": "inline_equation", "content": "{ \\sf R } _ { 3 }", "score": 0.82 }, { "bbox": [ 265, 338, 281, 354 ], "type": "inline_equation", "content": "\\mathsf { R } _ { 2 }", "score": 0.8 }, { "bbox": [ 291, 338, 308, 354 ], "type": "inline_equation", "content": "\\mathsf { R } _ { 7 }", "score": 0.77 } ] }, { "bbox": [ 121, 354, 309, 372 ], "spans": [ { "bbox": [ 121, 354, 185, 372 ], "type": "text", "content": "的运算操作", "score": 1.0 }, { "bbox": [ 185, 355, 248, 371 ], "type": "inline_equation", "content": "R _ { 2 } + R _ { 7 } R _ { 3 }", "score": 0.88 }, { "bbox": [ 248, 354, 309, 372 ], "type": "text", "content": "，分析数据", "score": 0.992 } ] }, { "bbox": [ 121, 373, 266, 388 ], "spans": [ { "bbox": [ 121, 373, 266, 388 ], "type": "text", "content": "通路，需要几个CPU周期？", "score": 0.989 } ] } ] }, { "bbox": [ 110, 410, 220, 425 ], "type": "text", "angle": 0, "index": 21, "lines": [ { "bbox": [ 122, 410, 221, 425 ], "spans": [ { "bbox": [ 122, 410, 221, 425 ], "type": "text", "content": "需要2个CPU周期", "score": 0.999 } ] } ] } ], "sub_type": "text" }, { "type": "image", "bbox": [ 316, 312, 568, 433 ], "blocks": [ { "bbox": [ 316, 312, 568, 433 ], "lines": [ { "bbox": [ 316, 312, 568, 433 ], "spans": [ { "bbox": [ 316, 312, 568, 433 ], "type": "image", "image_path": "2f5b4666b8610e3c937ac6d9db58dffad8bf5997aa2c849c2a86b02e3a84305b.jpg" } ] } ], "index": 23, "angle": 0, "type": "image_body" } ], "index": 23 }, { "type": "table", "bbox": [ 99, 437, 559, 512 ], "blocks": [ { "bbox": [ 99, 437, 559, 512 ], "lines": [ { "bbox": [ 99, 437, 559, 512 ], "spans": [ { "bbox": [ 99, 437, 559, 512 ], "type": "table", "html": "
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
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"score": 0.996 }, { "bbox": [ 283, 182, 352, 206 ], "type": "text", "content": "SF =Fn", "score": 0.873 } ] } ] }, { "bbox": [ 146, 206, 512, 222 ], "type": "text", "angle": 0, "index": 8, "lines": [ { "bbox": [ 147, 204, 514, 222 ], "spans": [ { "bbox": [ 147, 204, 264, 222 ], "type": "text", "content": "·运算结果为正数时：", "score": 0.997 }, { "bbox": [ 264, 206, 298, 222 ], "type": "inline_equation", "content": "\\pmb { S F = 0 }", "score": 0.63 }, { "bbox": [ 298, 204, 367, 222 ], "type": "text", "content": "；为负数时：", "score": 0.988 }, { "bbox": [ 367, 206, 399, 221 ], "type": "inline_equation", "content": "s F { = } 1", "score": 0.72 }, { "bbox": [ 399, 204, 514, 222 ], "type": "text", "content": "。 (无溢出时才正确)", "score": 0.988 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 127, 226, 431, 242 ], "type": "text", "angle": 0, "index": 10, "lines": [ { "bbox": [ 129, 224, 431, 243 ], "spans": [ { "bbox": [ 129, 227, 143, 242 ], "type": "inline_equation", "content": "\\textcircled{5}", "score": 0.78 }, { "bbox": [ 143, 224, 431, 243 ], "type": "text", "content": "PF：奇偶标志，反映运算结果中“1”的个数的奇偶性", "score": 0.981 } ] } ] }, { "bbox": [ 146, 245, 341, 279 ], "type": "list", "angle": 0, "index": 13, "blocks": [ { "bbox": [ 146, 245, 340, 260 ], "type": "text", "angle": 0, "index": 11, "lines": [ { "bbox": [ 147, 243, 342, 260 ], "spans": [ { "bbox": [ 147, 243, 342, 260 ], "type": "text", "content": "·结果中“1”的个数为偶数：PF=1", "score": 0.986 } ] } ] }, { "bbox": [ 146, 264, 341, 279 ], "type": "text", "angle": 0, "index": 12, "lines": [ { "bbox": [ 147, 263, 342, 280 ], "spans": [ { "bbox": [ 147, 263, 342, 280 ], "type": "text", "content": "·结果中“1”的个数为奇数：PF=0", "score": 0.983 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 353, 250, 549, 275 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 353, 250, 549, 275 ], "spans": [ { "bbox": [ 353, 250, 549, 275 ], "type": "interline_equation", "content": "P F = \\overline {{F _ {n} \\oplus F _ {n - 1} \\oplus \\dots . \\oplus F _ {0}}}", "image_path": "7c93d59d5353deea7dc93ce4178f1d5db92fe203d58ff6893f32dd9086d3f0f0.jpg" } ] } ], "index": 14 }, { "bbox": [ 102, 366, 281, 386 ], "type": "title", "angle": 0, "index": 16, "lines": [ { "bbox": [ 119, 365, 282, 387 ], "spans": [ { "bbox": [ 119, 365, 282, 387 ], "type": "text", "content": "假设两个浮点数X和Y", "score": 0.963 } ] } ] }, { "bbox": [ 224, 399, 350, 426 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 224, 399, 350, 426 ], "spans": [ { "bbox": [ 224, 399, 350, 426 ], "type": "interline_equation", "content": "X = M _ {X} \\times 2 ^ {E _ {X}}", "image_path": "fc2ec54c2995e1381192330e4733e8db4f3b32307ef1e25ce2f16a081d1839cd.jpg" } ] } ], "index": 17 }, { "bbox": [ 414, 398, 537, 426 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 414, 398, 537, 426 ], "spans": [ { "bbox": [ 414, 398, 537, 426 ], "type": "interline_equation", "content": "Y = M _ {Y} \\times 2 ^ {E _ {Y}}", "image_path": "86cb4df029cc660adee008112e1ea0073e028a6315d8dd849ab6c401adf302a0.jpg" } ] } ], "index": 18 }, { "bbox": [ 102, 454, 593, 510 ], "type": "list", "angle": 0, "index": 21, "blocks": [ { "bbox": [ 102, 454, 593, 476 ], "type": "text", "angle": 0, "index": 19, "lines": [ { "bbox": [ 103, 454, 595, 476 ], "spans": [ { "bbox": [ 103, 454, 595, 476 ], "type": "text", "content": "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", "score": 0.997 } ] } ] }, { "bbox": [ 102, 489, 411, 510 ], "type": "text", "angle": 0, "index": 20, "lines": [ { "bbox": [ 102, 488, 412, 511 ], "spans": [ { "bbox": [ 102, 488, 412, 511 ], "type": "text", "content": "然后：对尾数（有效数位）做加减运算", "score": 0.994 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 156, 528, 594, 556 ], "type": "interline_equation", "angle": 0, "lines": [ { "bbox": [ 156, 528, 594, 556 ], "spans": [ { "bbox": [ 156, 528, 594, 556 ], "type": "interline_equation", "content": "Z = 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", "image_path": "31a12e7058a4d903852aab62b787f3f8e53dd7bd69f6616fc35cae13cf3d45c5.jpg" } ] } ], "index": 22 } ], "discarded_blocks": [ { "bbox": [ 528, 285, 552, 301 ], "type": "page_number", "angle": 0, "index": 15, "lines": [ { "bbox": [ 534, 290, 545, 300 ], "spans": [ { "bbox": [ 534, 290, 545, 300 ], "type": "text", "content": "74", "score": 0.998 } ] } ] } ], "page_size": [ 595, 841 ], "page_idx": 41 }, { "para_blocks": [ { "bbox": [ 92, 79, 142, 93 ], "type": "text", "angle": 0, "index": 0, "lines": [ { "bbox": [ 91, 78, 144, 95 ], "spans": [ { "bbox": [ 91, 78, 144, 95 ], "type": "text", "content": "(2）对阶：", "score": 0.926 } ] } ] }, { "bbox": [ 88, 99, 216, 138 ], "type": "list", "angle": 0, "index": 3, "blocks": [ { "bbox": [ 88, 99, 216, 116 ], "type": "text", "angle": 0, "index": 1, "lines": [ { "bbox": [ 85, 97, 218, 116 ], "spans": [ { "bbox": [ 85, 97, 218, 116 ], "type": "text", "content": "目标是：对齐小数点", "score": 0.996 } ] } ] }, { "bbox": [ 88, 121, 216, 138 ], "type": "text", "angle": 0, "index": 2, "lines": [ { "bbox": [ 85, 119, 218, 140 ], "spans": [ { "bbox": [ 85, 119, 218, 140 ], "type": "text", "content": "原则是：小阶对大阶", "score": 0.998 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 101, 141, 389, 189 ], "type": "list", "angle": 0, "index": 7, "blocks": [ { "bbox": [ 101, 141, 357, 155 ], "type": "text", "angle": 0, "index": 4, "lines": [ { "bbox": [ 105, 141, 357, 156 ], "spans": [ { "bbox": [ 105, 141, 357, 156 ], "type": "text", "content": "求阶差△E=Ex-Eγ，若△E≠0，即Ex≠E时需要对阶。", "score": 0.923 } ] } ] }, { "bbox": [ 101, 158, 389, 172 ], "type": "text", "angle": 0, "index": 5, "lines": [ { "bbox": [ 103, 155, 389, 174 ], "spans": [ { "bbox": [ 103, 155, 295, 174 ], "type": "text", "content": "若△E>0，则Ex>Eγ，M每右移一位，", "score": 0.919 }, { "bbox": [ 295, 158, 315, 173 ], "type": "inline_equation", "content": "\\mathbb { E } _ { \\mathsf { Y } ^ { + } }", "score": 0.58 }, { "bbox": [ 315, 155, 357, 174 ], "type": "text", "content": "1，直至", "score": 0.943 }, { "bbox": [ 357, 158, 389, 173 ], "type": "inline_equation", "content": "\\mathsf { E } _ { \\mathsf { v } } = \\mathsf { E } _ { \\mathsf { X } }", "score": 0.89 } ] } ] }, { "bbox": [ 101, 174, 387, 189 ], "type": "text", "angle": 0, "index": 6, "lines": [ { "bbox": [ 104, 173, 387, 190 ], "spans": [ { "bbox": [ 104, 173, 176, 190 ], "type": "text", "content": "若△E<0，则", "score": 0.936 }, { "bbox": [ 177, 175, 207, 190 ], "type": "inline_equation", "content": "\\mathsf { E } _ { \\mathsf { X } } { < } \\mathsf { E } _ { \\mathsf { Y } }", "score": 0.53 }, { "bbox": [ 215, 175, 233, 190 ], "type": "inline_equation", "content": "\\pmb { M } _ { \\mathbf { X } }", "score": 0.69 }, { "bbox": [ 233, 173, 295, 190 ], "type": "text", "content": "每右移一位，", "score": 0.996 }, { "bbox": [ 296, 175, 324, 190 ], "type": "inline_equation", "content": "\\mathtt { E _ { X } } + 1", "score": 0.83 }, { "bbox": [ 324, 173, 359, 190 ], "type": "text", "content": "，直至", "score": 0.988 }, { "bbox": [ 359, 175, 387, 190 ], "type": "inline_equation", "content": "\\therefore x = E _ { y }", "score": 0.68 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 92, 191, 171, 205 ], "type": "text", "angle": 0, "index": 8, "lines": [ { "bbox": [ 92, 192, 171, 206 ], "spans": [ { "bbox": [ 92, 192, 171, 206 ], "type": "text", "content": "(3）尾数相加减", "score": 0.974 } ] } ] }, { "bbox": [ 101, 208, 464, 253 ], "type": "list", "angle": 0, "index": 11, "blocks": [ { "bbox": [ 101, 208, 398, 222 ], "type": "text", "angle": 0, "index": 9, "lines": [ { "bbox": [ 105, 208, 398, 222 ], "spans": [ { "bbox": [ 105, 208, 398, 222 ], "type": "text", "content": "·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", "score": 0.973 } ] } ] }, { "bbox": [ 101, 225, 464, 253 ], "type": "text", "angle": 0, "index": 10, "lines": [ { "bbox": [ 103, 225, 465, 239 ], "spans": [ { "bbox": [ 103, 225, 465, 239 ], "type": "text", "content": "■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，", "score": 0.988 } ] }, { "bbox": [ 112, 239, 324, 254 ], "spans": [ { "bbox": [ 112, 239, 324, 254 ], "type": "text", "content": "同时设置更宽的寄存器来存放中间运算结果)", "score": 0.995 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 461, 255, 481, 267 ], "type": "text", "angle": 0, "index": 12, "lines": [ { "bbox": [ 467, 259, 475, 267 ], "spans": [ { "bbox": [ 467, 259, 475, 267 ], "type": "text", "content": "82", "score": 0.997 } ] } ] }, { "bbox": [ 117, 292, 265, 308 ], "type": "title", "angle": 0, "index": 13, "lines": [ { "bbox": [ 115, 294, 266, 309 ], "spans": [ { "bbox": [ 115, 294, 266, 309 ], "type": "text", "content": "浮点加减运算步骤", "score": 0.925 } ] } ] }, { "bbox": [ 86, 322, 460, 338 ], "type": "text", "angle": 0, "index": 14, "lines": [ { "bbox": [ 87, 322, 462, 339 ], "spans": [ { "bbox": [ 87, 322, 462, 339 ], "type": "text", "content": "【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：", "score": 0.98 } ] } ] }, { "bbox": [ 88, 343, 552, 441 ], "type": "list", "angle": 0, "index": 18, "blocks": [ { "bbox": [ 96, 343, 449, 360 ], "type": "text", "angle": 0, "index": 15, "lines": [ { "bbox": [ 98, 342, 450, 360 ], "spans": [ { "bbox": [ 98, 342, 450, 360 ], "type": "text", "content": "·尾数溢出：需要右规（1次），即尾数右移1位，阶码+1", "score": 0.974 } ] } ] }, { "bbox": [ 88, 364, 552, 400 ], "type": "text", "angle": 0, "index": 16, "lines": [ { "bbox": [ 108, 363, 553, 382 ], "spans": [ { "bbox": [ 108, 363, 151, 382 ], "type": "text", "content": "尾数|", "score": 0.844 }, { "bbox": [ 151, 364, 182, 381 ], "type": "inline_equation", "content": "< 2 ^ { - 1 }", "score": 0.61 }, { "bbox": [ 182, 363, 553, 382 ], "type": "text", "content": "：需要左规，即尾数左移1位，阶码-1，左规可能多次，直到", "score": 0.985 } ] }, { "bbox": [ 111, 383, 239, 399 ], "spans": [ { "bbox": [ 111, 383, 239, 399 ], "type": "text", "content": "尾数变为规格化形式。", "score": 0.994 } ] } ] }, { "bbox": [ 96, 424, 412, 441 ], "type": "text", "angle": 0, "index": 17, "lines": [ { "bbox": [ 99, 425, 412, 442 ], "spans": [ { "bbox": [ 99, 425, 412, 442 ], "type": "text", "content": "·先判断是否溢出，如果没有，再判断是否有前导零", "score": 0.992 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 86, 467, 442, 505 ], "type": "list", "angle": 0, "index": 21, "blocks": [ { "bbox": [ 86, 467, 442, 484 ], "type": "text", "angle": 0, "index": 19, "lines": [ { "bbox": [ 86, 467, 443, 485 ], "spans": [ { "bbox": [ 86, 467, 443, 485 ], "type": "text", "content": "[5）舍入：将尾数多余的位数舍去，变成规定的浮点数格式", "score": 0.983 } ] } ] }, { "bbox": [ 96, 488, 417, 505 ], "type": "text", "angle": 0, "index": 20, "lines": [ { "bbox": [ 98, 488, 417, 506 ], "spans": [ { "bbox": [ 98, 488, 417, 506 ], "type": "text", "content": "舍入策略：舍去多余位数的方法，简单的舍入策略：", "score": 0.992 } ] } ] } ], "sub_type": "text" }, { "bbox": [ 117, 508, 496, 557 ], "type": "list", "angle": 0, "index": 25, "blocks": [ { "bbox": [ 117, 508, 245, 523 ], "type": "text", "angle": 0, "index": 22, "lines": [ { "bbox": [ 119, 507, 245, 523 ], "spans": [ { "bbox": [ 119, 507, 245, 523 ], "type": "text", "content": "·截断法：多余的全舍去", "score": 0.976 } ] } ] }, { 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"index": 1, "lines": [ { "bbox": [ 114, 105, 437, 117 ], "spans": [ { "bbox": [ 114, 105, 125, 117 ], "type": "inline_equation", "content": "\\textcircled{1}", "score": 0.74 }, { "bbox": [ 126, 105, 437, 117 ], "type": "text", "content": "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", "score": 0.996 } ] }, { "bbox": [ 123, 117, 295, 130 ], "spans": [ { "bbox": [ 123, 117, 295, 130 ], "type": "text", "content": "位进1；为负数时，则采用简单的截断法", "score": 0.986 } ] } ] }, { "bbox": [ 112, 132, 438, 156 ], "type": "text", "angle": 0, "index": 2, "lines": [ { "bbox": [ 114, 132, 439, 145 ], "spans": [ { "bbox": [ 114, 133, 125, 145 ], "type": "inline_equation", "content": "\\textcircled{2}", "score": 0.65 }, { "bbox": [ 126, 132, 439, 145 ], "type": "text", "content": "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", "score": 0.981 } ] }, { "bbox": [ 123, 145, 255, 156 ], "spans": [ { "bbox": [ 123, 145, 255, 156 ], "type": "text", "content": "为负数时，则向最低有效位进1", "score": 0.997 } ] } ] }, { "bbox": [ 112, 160, 439, 185 ], "type": 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