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进制基数R权Wi数码符号
十进制R=1010i0~9
二进制R=22i0、1
八进制R=88i0~7
十六进制R=1616i0~9、A~F
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"content": null, "poly": [ 243, 1606, 1187, 1606, 1187, 1641, 243, 1641 ] }, { "type": "text", "bbox": [ 0.148, 0.706, 0.39, 0.72 ], "angle": 0, "content": null, "poly": [ 244, 1651, 645, 1651, 645, 1684, 244, 1684 ] }, { "type": "text", "bbox": [ 0.148, 0.725, 0.399, 0.739 ], "angle": 0, "content": null, "poly": [ 244, 1695, 659, 1695, 659, 1728, 244, 1728 ] }, { "type": "list", "bbox": [ 0.147, 0.669, 0.718, 0.739 ], "angle": 0, "content": null }, { "type": "title", "bbox": [ 0.157, 0.743, 0.268, 0.757 ], "angle": 0, "content": null, "poly": [ 259, 1737, 443, 1737, 443, 1770, 259, 1770 ] }, { "type": "text", "bbox": [ 0.147, 0.761, 0.447, 0.776 ], "angle": 0, "content": null, "poly": [ 243, 1779, 739, 1779, 739, 1815, 243, 1815 ] }, { "type": "text", "bbox": [ 0.148, 0.78, 0.341, 0.794 ], "angle": 0, "content": null, "poly": [ 244, 1824, 564, 1824, 564, 1857, 244, 1857 ] }, { "type": "text", "bbox": [ 0.148, 0.798, 0.324, 0.813 ], "angle": 0, "content": null, "poly": [ 244, 1866, 535, 1866, 535, 1901, 244, 1901 ] }, { "type": "list", "bbox": [ 0.147, 0.761, 0.447, 0.813 ], "angle": 0, "content": null }, { "type": "text", "bbox": [ 0.147, 0.817, 0.514, 0.851 ], "angle": 0, "content": null, "poly": [ 243, 1910, 850, 1910, 850, 1990, 243, 1990 ] } ], [ { "type": "title", "bbox": [ 0.157, 0.108, 0.21, 0.149 ], "angle": 0, "content": null, "poly": [ 259, 252, 347, 252, 347, 348, 259, 348 ] }, { "type": "equation", "bbox": [ 0.222, 0.1, 0.536, 0.164 ], "angle": 0, "content": "\\[\n[ \\mathbf {X} ] _ {\\text {反}} = \\left\\{ \\begin{array}{l l} \\mathbf {X} & \\mathbf {X} \\geq 0 \\\\ 2 ^ {n + 1} - 1 + \\mathbf {X} & \\mathbf {X} \\leq 0 \\end{array} \\right.\n\\]" }, { "type": "equation", "bbox": [ 0.29, 0.17, 0.493, 0.193 ], "angle": 0, "content": "\\[\n(\\mod (2 ^ {n + 1} - 1))\n\\]" }, { "type": "title", "bbox": [ 0.604, 0.113, 0.656, 0.153 ], "angle": 0, "content": null, "poly": [ 999, 264, 1085, 264, 1085, 357, 999, 357 ] }, { "type": "equation", "bbox": [ 0.671, 0.102, 0.975, 0.164 ], "angle": 0, "content": "\\[\n[ \\mathrm {X} ] _ {\\text {反}} = \\left\\{ \\begin{array}{l l} \\mathrm {X} & \\mathrm {X} \\geq 0 \\\\ 2 - 2 ^ {- n} + \\mathrm {X} & \\mathrm {X} \\leq 0 \\end{array} \\right.\n\\]" }, { "type": "text", "bbox": [ 0.739, 0.168, 0.921, 0.191 ], "angle": 0, "content": null, "poly": [ 1222, 392, 1523, 392, 1523, 446, 1222, 446 ] }, { "type": "text", "bbox": [ 0.146, 0.205, 0.529, 0.221 ], "angle": 0, "content": null, "poly": [ 241, 479, 874, 479, 874, 516, 241, 516 ] }, { "type": "text", "bbox": [ 0.147, 0.224, 0.386, 0.239 ], "angle": 0, "content": null, "poly": [ 243, 523, 638, 523, 638, 559, 243, 559 ] }, { "type": "text", "bbox": [ 0.147, 0.242, 0.605, 0.259 ], "angle": 0, "content": null, "poly": [ 243, 566, 1000, 566, 1000, 605, 243, 605 ] }, { "type": "list", "bbox": [ 0.146, 0.205, 0.605, 0.259 ], "angle": 0, "content": null }, { "type": "text", "bbox": [ 0.153, 0.275, 0.443, 0.284 ], "angle": 0, "content": null, "poly": [ 253, 643, 732, 643, 732, 664, 253, 664 ] }, { "type": "text", "bbox": [ 0.163, 0.288, 0.247, 0.301 ], "angle": 0, "content": null, "poly": [ 269, 673, 408, 673, 408, 704, 269, 704 ] }, { "type": "text", "bbox": [ 0.266, 0.286, 0.5, 0.299 ], "angle": 0, "content": null, "poly": [ 439, 668, 827, 668, 827, 699, 439, 699 ] }, { "type": "text", "bbox": [ 0.266, 0.3, 0.515, 0.311 ], "angle": 0, "content": null, "poly": [ 439, 701, 851, 701, 851, 727, 439, 727 ] }, { "type": "text", "bbox": [ 0.163, 0.323, 0.247, 0.334 ], "angle": 0, "content": null, "poly": [ 269, 755, 408, 755, 408, 781, 269, 781 ] }, { "type": "text", "bbox": [ 0.266, 0.321, 0.51, 0.333 ], "angle": 0, "content": null, "poly": [ 439, 750, 843, 750, 843, 778, 439, 778 ] }, { "type": "text", "bbox": [ 0.266, 0.334, 0.532, 0.351 ], "angle": 0, "content": null, "poly": [ 439, 781, 879, 781, 879, 820, 439, 820 ] }, { "type": "list", "bbox": [ 0.266, 0.321, 0.532, 0.351 ], "angle": 0, "content": null }, { "type": "text", "bbox": [ 0.146, 0.361, 0.393, 0.373 ], "angle": 0, "content": null, "poly": [ 241, 844, 650, 844, 650, 872, 241, 872 ] }, { "type": "equation", "bbox": [ 0.164, 0.377, 0.267, 0.388 ], "angle": 0, "content": "\\[\n\\begin{array}{r l} {[ + 0 ] _ {\\text {反}} = 0 0 \\dots 0} \\end{array}\n\\]" }, { "type": "equation", "bbox": [ 0.339, 0.377, 0.424, 0.389 ], "angle": 0, "content": "\\[\n[ - 0 ] _ {\\text {反}} = 1 1 \\dots 1\n\\]" }, { "type": "text", "bbox": [ 0.146, 0.391, 0.554, 0.403 ], "angle": 0, "content": null, "poly": [ 241, 914, 916, 914, 916, 942, 241, 942 ] }, { "type": "text", "bbox": [ 0.163, 0.406, 0.382, 0.418 ], "angle": 0, "content": null, "poly": [ 269, 949, 631, 949, 631, 977, 269, 977 ] }, { "type": "text", "bbox": [ 0.163, 0.421, 0.4, 0.433 ], "angle": 0, "content": null, "poly": [ 269, 984, 661, 984, 661, 1012, 269, 1012 ] }, { "type": "list", "bbox": [ 0.163, 0.406, 0.4, 0.433 ], "angle": 0, "content": null }, { "type": "text", "bbox": [ 0.146, 0.446, 0.187, 0.46 ], "angle": 0, "content": null, "poly": [ 241, 1043, 309, 1043, 309, 1075, 241, 1075 ] }, { "type": "title", "bbox": [ 0.189, 0.469, 0.241, 0.51 ], "angle": 0, "content": null, "poly": [ 312, 1096, 398, 1096, 398, 1192, 312, 1192 ] }, { "type": "equation", "bbox": [ 0.272, 0.474, 0.534, 0.51 ], "angle": 0, "content": "\\[\n[ \\mathrm {X} ] _ {\\text {移}} = 2 ^ {\\mathrm {n}} + \\mathrm {X}\n\\]" }, { "type": "equation", "bbox": [ 0.336, 0.524, 0.484, 0.547 ], "angle": 0, "content": "\\[\n(\\mod 2 ^ {n + 1})\n\\]" }, { "type": "text", "bbox": [ 0.146, 0.557, 0.54, 0.573 ], "angle": 0, "content": null, "poly": [ 241, 1302, 893, 1302, 893, 1340, 241, 1340 ] }, { "type": "text", "bbox": [ 0.147, 0.576, 0.387, 0.591 ], "angle": 0, "content": null, "poly": [ 243, 1347, 640, 1347, 640, 1382, 243, 1382 ] }, { "type": "text", "bbox": [ 0.147, 0.594, 0.714, 0.61 ], "angle": 0, "content": null, "poly": [ 243, 1389, 1180, 1389, 1180, 1426, 243, 1426 ] }, { "type": "list", "bbox": [ 0.147, 0.576, 0.714, 0.61 ], "angle": 0, "content": null }, { "type": "text", "bbox": [ 0.146, 0.628, 0.978, 0.641 ], "angle": 0, "content": null, "poly": [ 241, 1468, 1617, 1468, 1617, 1499, 241, 1499 ] }, { "type": "title", "bbox": [ 0.158, 0.709, 0.373, 0.731 ], "angle": 0, "content": null, "poly": [ 261, 1658, 616, 1658, 616, 1709, 261, 1709 ] }, { "type": "text", "bbox": [ 0.745, 0.666, 0.913, 0.714 ], "angle": 0, "content": null, "poly": [ 1232, 1557, 1510, 1557, 1510, 1670, 1232, 1670 ] }, { "type": "text", "bbox": [ 0.198, 0.749, 0.813, 0.777 ], "angle": 0, "content": null, "poly": [ 327, 1751, 1344, 1751, 1344, 1817, 327, 1817 ] }, { "type": "text", "bbox": [ 0.199, 0.791, 0.901, 0.821 ], "angle": 0, "content": null, "poly": [ 329, 1850, 1490, 1850, 1490, 1920, 329, 1920 ] }, { "type": "list", "bbox": [ 0.198, 0.749, 0.901, 0.821 ], "angle": 0, "content": null }, { "type": "text", "bbox": [ 0.157, 0.835, 0.495, 0.851 ], "angle": 0, "content": null, "poly": [ 259, 1953, 818, 1953, 818, 1990, 259, 1990 ] }, { "type": "text", "bbox": [ 0.148, 0.854, 0.397, 0.869 ], "angle": 0, "content": null, "poly": [ 244, 1997, 656, 1997, 656, 2032, 244, 2032 ] }, { "type": "text", "bbox": [ 0.147, 0.872, 0.72, 0.888 ], "angle": 0, "content": null, "poly": [ 243, 2039, 1190, 2039, 1190, 2077, 243, 2077 ] }, { "type": "text", "bbox": [ 0.148, 0.891, 0.39, 0.905 ], "angle": 0, "content": null, "poly": [ 244, 2084, 645, 2084, 645, 2116, 244, 2116 ] }, { "type": "list", "bbox": [ 0.147, 0.854, 0.72, 0.905 ], "angle": 0, "content": null } ], [ { "type": "image", "bbox": [ 0.175, 0.098, 0.233, 0.133 ], "angle": 0, "content": null }, { "type": "title", "bbox": [ 0.266, 0.097, 0.496, 0.117 ], "angle": 0, "content": null, "poly": [ 439, 226, 820, 226, 820, 273, 439, 273 ] }, { "type": "title", "bbox": [ 0.554, 0.1, 0.683, 0.118 ], "angle": 0, "content": null, "poly": [ 916, 233, 1129, 233, 1129, 276, 916, 276 ] }, { "type": "title", "bbox": [ 0.218, 0.168, 0.303, 0.186 ], "angle": 0, "content": null, "poly": [ 360, 392, 501, 392, 501, 435, 360, 435 ] }, { "type": "table", "bbox": [ 0.306, 0.123, 0.829, 0.234 ], "angle": 0, "content": "
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
" }, { "type": "title", "bbox": [ 0.202, 0.281, 0.246, 0.315 ], "angle": 0, "content": null, "poly": [ 334, 657, 406, 657, 406, 736, 334, 736 ] }, { "type": "table", "bbox": [ 0.256, 0.239, 0.832, 0.358 ], "angle": 0, "content": "
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
" }, { "type": "table", "bbox": [ 0.148, 0.396, 0.971, 0.621 ], "angle": 0, "content": "
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
" }, { "type": "table_caption", "bbox": [ 0.285, 0.652, 0.398, 0.669 ], "angle": 0, "content": null, "poly": [ 471, 1525, 658, 1525, 658, 1564, 471, 1564 ] }, { "type": "table", "bbox": [ 0.155, 0.677, 0.516, 0.791 ], "angle": 0, "content": "
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
" } ], [ { "type": "text", "bbox": [ 0.156, 0.104, 0.269, 0.121 ], "angle": 0, "content": null, "poly": [ 258, 243, 444, 243, 444, 283, 258, 283 ] }, { "type": "equation", "bbox": [ 0.156, 0.104, 0.333, 0.172 ], "angle": 0, "content": "\\[\n\\begin{array}{l} \\because [ X ] _ {\\text {原}} = X _ {S}, X _ {1} X _ {2} \\dots X _ {n} \\\\ \\cdot X _ {S} = 0: X = + X _ {1} X _ {2} \\dots X _ {n} \\\\ X _ {S} = 1: X = - X _ {1} X _ {2} \\dots X _ {n} \\\\ \\end{array}\n\\]" }, { "type": "text", "bbox": [ 0.423, 0.104, 0.535, 0.12 ], "angle": 0, "content": null, "poly": [ 699, 243, 884, 243, 884, 280, 699, 280 ] }, { "type": "equation", "bbox": [ 0.423, 0.104, 0.619, 0.173 ], "angle": 0, "content": "\\[\n\\begin{array}{l} \\because [ X ] _ {\\text {反}} = X _ {S}, X _ {1} X _ {2} \\dots X _ {n} \\\\ = X _ {S} = 0: X = + X _ {1} X _ {2} \\dots X _ {n} \\\\ \\cdot \\mathbf {x} _ {s} = 1: X = - \\overline {{X _ {1}}} \\overline {{X _ {2}}} \\dots \\overline {{X _ {n}}} \\\\ \\end{array}\n\\]" }, { "type": "text", "bbox": [ 0.156, 0.196, 0.266, 0.212 ], "angle": 0, "content": null, "poly": [ 258, 458, 439, 458, 439, 495, 258, 495 ] }, { "type": "equation", "bbox": [ 0.156, 0.215, 0.387, 0.264 ], "angle": 0, "content": "\\[\n\\begin{array}{l} \\because [ X ] _ {\\text {补}} = X _ {S}, X _ {1} X _ {2} \\dots X _ {n} \\\\ \\cdot X _ {S} = 0: X = + X _ {1} X _ {2} \\dots X _ {n} \\\\ \\cdot X _ {S} = 1: X = - \\left(\\overline {{X _ {1}}} \\overline {{X _ {2}}} \\dots \\overline {{X _ {n}}} + 1\\right) \\\\ \\end{array}\n\\]" }, { "type": "text", "bbox": [ 0.423, 0.197, 0.535, 0.214 ], "angle": 0, "content": null, "poly": [ 699, 460, 884, 460, 884, 500, 699, 500 ] }, { "type": "equation", "bbox": [ 0.423, 0.217, 0.655, 0.266 ], "angle": 0, "content": "\\[\n\\begin{array}{l} \\because [ X ] _ {\\text {移}} = X _ {S}, X _ {1} X _ {2} \\dots X _ {n} \\\\ = X _ {S} = 1: X = + X _ {1} X _ {2} \\dots X _ {n} \\\\ \\cdot \\mathbf {X} _ {s} = \\mathbf {0}: X = - (\\overline {{X _ {1}}} \\overline {{X _ {2}}} \\dots \\overline {{X _ {n}}} + 1) \\\\ \\end{array}\n\\]" }, { "type": "title", "bbox": [ 0.148, 0.279, 0.241, 0.294 ], "angle": 0, "content": null, "poly": [ 244, 652, 398, 652, 398, 687, 244, 687 ] }, { "type": "text", "bbox": [ 0.15, 0.303, 0.267, 0.317 ], "angle": 0, "content": null, "poly": [ 248, 708, 441, 708, 441, 741, 248, 741 ] }, { "type": "equation", "bbox": [ 0.343, 0.301, 0.454, 0.315 ], "angle": 0, "content": "\\[\nN = M \\times R ^ {E}\n\\]" }, { "type": "text", "bbox": [ 0.15, 0.32, 0.576, 0.333 ], "angle": 0, "content": null, "poly": [ 248, 748, 952, 748, 952, 778, 248, 778 ] }, { "type": "text", "bbox": [ 0.15, 0.336, 0.499, 0.349 ], "angle": 0, "content": null, "poly": [ 248, 785, 825, 785, 825, 816, 248, 816 ] }, { "type": "list", "bbox": [ 0.15, 0.32, 0.576, 0.349 ], "angle": 0, "content": null }, { "type": "text", "bbox": [ 0.159, 0.358, 0.205, 0.386 ], "angle": 0, "content": null, "poly": [ 262, 837, 339, 837, 339, 902, 262, 902 ] }, { "type": "text", "bbox": [ 0.157, 0.402, 0.212, 0.429 ], "angle": 0, "content": null, "poly": [ 259, 940, 350, 940, 350, 1003, 259, 1003 ] }, { "type": "image", "bbox": [ 0.28, 0.358, 0.58, 0.401 ], "angle": 0, "content": null }, { "type": "text", "bbox": [ 0.266, 0.406, 0.384, 0.418 ], "angle": 0, "content": null, "poly": [ 439, 949, 635, 949, 635, 977, 439, 977 ] }, { "type": "text", "bbox": [ 0.286, 0.42, 0.531, 0.432 ], "angle": 0, "content": null, "poly": [ 473, 982, 878, 982, 878, 1010, 473, 1010 ] }, { "type": "text", "bbox": [ 0.286, 0.434, 0.533, 0.446 ], "angle": 0, "content": null, "poly": [ 473, 1015, 881, 1015, 881, 1043, 473, 1043 ] }, { "type": "text", "bbox": [ 0.286, 0.448, 0.493, 0.459 ], "angle": 0, "content": null, "poly": [ 473, 1047, 815, 1047, 815, 1073, 473, 1073 ] }, { "type": "text", "bbox": [ 0.286, 0.462, 0.52, 0.474 ], "angle": 0, "content": null, "poly": [ 473, 1080, 860, 1080, 860, 1108, 473, 1108 ] }, { "type": "list", "bbox": [ 0.286, 0.42, 0.533, 0.474 ], "angle": 0, "content": null }, { "type": "title", "bbox": [ 0.165, 0.501, 0.319, 0.516 ], "angle": 0, "content": null, "poly": [ 272, 1171, 527, 1171, 527, 1206, 272, 1206 ] }, { "type": "equation", "bbox": [ 0.528, 0.5, 0.718, 0.514 ], "angle": 0, "content": "\\[\n0. 1 0 1 1 1 0 \\times 2 ^ {- 2} = 0. 0 0 1 0 1 1 1\n\\]" }, { "type": "equation", "bbox": [ 0.564, 0.52, 0.697, 0.539 ], "angle": 0, "content": "\\[\nN = M \\times R ^ {E}\n\\]" }, { "type": "text", "bbox": [ 0.187, 0.522, 0.493, 0.535 ], "angle": 0, "content": null, "poly": [ 309, 1220, 815, 1220, 815, 1251, 309, 1251 ] }, { "type": "text", "bbox": [ 0.188, 0.541, 0.478, 0.554 ], "angle": 0, "content": null, "poly": [ 310, 1265, 790, 1265, 790, 1295, 310, 1295 ] }, { "type": "text", "bbox": [ 0.188, 0.56, 0.463, 0.573 ], "angle": 0, "content": null, "poly": [ 310, 1309, 765, 1309, 765, 1340, 310, 1340 ] }, { "type": "list", "bbox": [ 0.187, 0.522, 0.493, 0.573 ], "angle": 0, "content": null }, { "type": "title", "bbox": 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0, "content": null, "poly": [ 243, 1854, 428, 1854, 428, 1889, 243, 1889 ] }, { "type": "text", "bbox": [ 0.146, 0.812, 0.523, 0.827 ], "angle": 0, "content": null, "poly": [ 241, 1899, 865, 1899, 865, 1934, 241, 1934 ] }, { "type": "text", "bbox": [ 0.147, 0.831, 0.171, 0.845 ], "angle": 0, "content": null, "poly": [ 243, 1943, 282, 1943, 282, 1976, 243, 1976 ] }, { "type": "equation", "bbox": [ 0.302, 0.853, 0.6, 0.879 ], "angle": 0, "content": "\\[\nT ^ {2} U _ {w} (x) = \\left\\{ \\begin{array}{c} x + 2 ^ {w}, x < 0 \\\\ x, x > 0 \\end{array} \\right., \\text {即} T 2 U _ {w} (x) = (x + 2 ^ {w}) \\mod 2 ^ {w}\n\\]" }, { "type": "equation", "bbox": [ 0.148, 0.883, 0.755, 0.897 ], "angle": 0, "content": "\\[\nB 2 T _ {k} \\left(\\left[ x _ {k - 1}, \\dots , x _ {0} \\right]\\right) = U 2 T _ {w} \\left(\\left[ B 2 T _ {w} \\left(\\left[ x _ {w - 1}, x _ {w - 2}, \\dots , x _ {0} \\right]\\right) + 2 ^ {w} \\right] \\mod 2 ^ {w} \\right] \\mod 2 ^ {k}) = U 2 T _ {w} \\left(B 2 U _ {w} 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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
" }, { "type": "image", "bbox": [ 0.149, 0.602, 0.777, 0.828 ], "angle": 0, "content": null }, { "type": "text", "bbox": [ 0.146, 0.846, 0.525, 0.862 ], "angle": 0, "content": null, "poly": [ 241, 1978, 868, 1978, 868, 2016, 241, 2016 ] }, { "type": "text", "bbox": [ 0.147, 0.871, 0.411, 0.891 ], "angle": 0, "content": null, "poly": [ 243, 2037, 679, 2037, 679, 2084, 243, 2084 ] } ], [ { "type": "equation", "bbox": [ 0.149, 0.092, 0.449, 0.109 ], "angle": 0, "content": "\\[\nB 2 U _ {w} (\\vec {x}) \\doteq x _ {w - 1} \\cdot 2 ^ {w - 1} + x _ {w - 2} \\cdot 2 ^ {w - 2} \\dots\n\\]" }, { "type": "text", "bbox": [ 0.146, 0.131, 0.421, 0.147 ], "angle": 0, "content": null, "poly": [ 241, 306, 696, 306, 696, 343, 241, 343 ] }, { "type": "text", "bbox": [ 0.147, 0.15, 0.435, 0.165 ], "angle": 0, "content": null, "poly": [ 243, 350, 719, 350, 719, 385, 243, 385 ] }, { "type": "equation", "bbox": [ 0.149, 0.167, 0.466, 0.183 ], "angle": 0, "content": "\\[\nB 2 T _ {w} (\\vec {x}) \\dot {=} x _ {w - 1} \\cdot - 2 ^ {w - 1} + x _ {w - 2} \\cdot 2 ^ {w - 2} \\dots\n\\]" }, { "type": "text", "bbox": [ 0.146, 0.205, 0.576, 0.221 ], "angle": 0, "content": null, "poly": [ 241, 479, 952, 479, 952, 516, 241, 516 ] }, { "type": "text", "bbox": [ 0.147, 0.224, 0.312, 0.239 ], "angle": 0, "content": null, "poly": [ 243, 523, 516, 523, 516, 559, 243, 559 ] }, { "type": "text", "bbox": [ 0.146, 0.242, 0.663, 0.258 ], "angle": 0, "content": null, "poly": [ 241, 566, 1096, 566, 1096, 603, 241, 603 ] }, { "type": "text", "bbox": [ 0.147, 0.261, 0.522, 0.276 ], "angle": 0, "content": null, "poly": [ 243, 610, 863, 610, 863, 645, 243, 645 ] }, { "type": "text", "bbox": [ 0.147, 0.28, 0.307, 0.295 ], "angle": 0, "content": null, "poly": [ 243, 654, 507, 654, 507, 690, 243, 690 ] }, { "type": "text", "bbox": [ 0.147, 0.298, 0.503, 0.313 ], "angle": 0, "content": null, "poly": [ 243, 697, 831, 697, 831, 732, 243, 732 ] }, { "type": "text", "bbox": [ 0.146, 0.317, 0.564, 0.333 ], "angle": 0, "content": null, "poly": [ 241, 741, 932, 741, 932, 778, 241, 778 ] }, { "type": "text", "bbox": [ 0.146, 0.335, 0.484, 0.35 ], "angle": 0, "content": null, "poly": [ 241, 783, 800, 783, 800, 818, 241, 818 ] }, { "type": "title", "bbox": [ 0.146, 0.412, 0.517, 0.435 ], "angle": 0, "content": null, "poly": [ 241, 963, 855, 963, 855, 1017, 241, 1017 ] }, { "type": "text", "bbox": [ 0.146, 0.478, 0.557, 0.494 ], "angle": 0, "content": null, "poly": [ 241, 1118, 921, 1118, 921, 1155, 241, 1155 ] }, { "type": "equation", "bbox": [ 0.147, 0.498, 0.222, 0.511 ], "angle": 0, "content": "\\[\nS = a + b\n\\]" }, { "type": "text", "bbox": [ 0.146, 0.515, 0.848, 0.549 ], "angle": 0, "content": null, "poly": [ 241, 1204, 1402, 1204, 1402, 1284, 241, 1284 ] }, { "type": "equation", "bbox": [ 0.147, 0.553, 0.266, 0.567 ], "angle": 0, "content": "\\[\nR = S \\bmod 2 ^ {\\wedge} w\n\\]" }, { "type": "text", "bbox": [ 0.146, 0.571, 0.848, 0.604 ], "angle": 0, "content": null, "poly": [ 241, 1335, 1402, 1335, 1402, 1412, 241, 1412 ] }, { "type": "text", "bbox": [ 0.146, 0.608, 0.848, 0.641 ], "angle": 0, "content": null, "poly": [ 241, 1422, 1402, 1422, 1402, 1499, 241, 1499 ] }, { "type": "text", "bbox": [ 0.175, 0.645, 0.847, 0.696 ], "angle": 0, "content": null, "poly": [ 289, 1508, 1400, 1508, 1400, 1627, 289, 1627 ] }, { "type": "text", "bbox": [ 0.176, 0.701, 0.848, 0.751 ], "angle": 0, "content": null, "poly": [ 291, 1639, 1402, 1639, 1402, 1756, 291, 1756 ] }, { "type": "text", "bbox": [ 0.176, 0.757, 0.848, 0.825 ], "angle": 0, "content": null, "poly": [ 291, 1770, 1402, 1770, 1402, 1929, 291, 1929 ] }, { "type": "list", "bbox": [ 0.175, 0.645, 0.848, 0.825 ], "angle": 0, "content": null }, { "type": "title", "bbox": [ 0.146, 0.831, 0.408, 0.845 ], "angle": 0, "content": null, "poly": [ 241, 1943, 674, 1943, 674, 1976, 241, 1976 ] }, { "type": "text", "bbox": [ 0.146, 0.849, 0.838, 0.883 ], "angle": 0, "content": null, "poly": [ 241, 1985, 1386, 1985, 1386, 2065, 241, 2065 ] } ], [ { "type": "title", "bbox": [ 0.146, 0.094, 0.33, 0.109 ], "angle": 0, "content": null, "poly": [ 241, 219, 545, 219, 545, 254, 241, 254 ] }, { "type": "text", "bbox": [ 0.146, 0.113, 0.838, 0.145 ], "angle": 0, "content": null, "poly": [ 241, 264, 1386, 264, 1386, 339, 241, 339 ] }, { "type": "text", "bbox": [ 0.146, 0.149, 0.438, 0.165 ], "angle": 0, "content": null, "poly": [ 241, 348, 724, 348, 724, 385, 241, 385 ] }, { "type": "text", "bbox": [ 0.146, 0.169, 0.421, 0.184 ], "angle": 0, "content": null, "poly": [ 241, 395, 696, 395, 696, 430, 241, 430 ] }, { "type": "text", "bbox": [ 0.146, 0.187, 0.507, 0.202 ], "angle": 0, "content": null, "poly": [ 241, 437, 838, 437, 838, 472, 241, 472 ] }, { "type": "title", "bbox": [ 0.146, 0.205, 0.325, 0.22 ], "angle": 0, "content": null, "poly": [ 241, 479, 537, 479, 537, 514, 241, 514 ] }, { "type": "text", "bbox": [ 0.177, 0.224, 0.612, 0.239 ], "angle": 0, "content": null, "poly": [ 292, 523, 1012, 523, 1012, 559, 292, 559 ] }, { 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"angle": 0, "content": null, "poly": [ 241, 914, 1075, 914, 1075, 949, 241, 949 ] }, { "type": "list", "bbox": [ 0.146, 0.298, 0.855, 0.406 ], "angle": 0, "content": null }, { "type": "text", "bbox": [ 0.176, 0.409, 0.729, 0.424 ], "angle": 0, "content": null, "poly": [ 291, 956, 1205, 956, 1205, 991, 291, 991 ] }, { "type": "text", "bbox": [ 0.176, 0.428, 0.605, 0.443 ], "angle": 0, "content": null, "poly": [ 291, 1001, 1000, 1001, 1000, 1036, 291, 1036 ] }, { "type": "title", "bbox": [ 0.147, 0.464, 0.24, 0.479 ], "angle": 0, "content": null, "poly": [ 243, 1085, 396, 1085, 396, 1120, 243, 1120 ] }, { "type": "text", "bbox": [ 0.147, 0.483, 0.251, 0.499 ], "angle": 0, "content": null, "poly": [ 243, 1129, 415, 1129, 415, 1167, 243, 1167 ] }, { "type": "text", "bbox": [ 0.146, 0.502, 0.434, 0.517 ], "angle": 0, "content": null, "poly": [ 241, 1174, 717, 1174, 717, 1209, 241, 1209 ] }, { "type": "text", "bbox": [ 0.146, 0.539, 0.819, 0.579 ], "angle": 0, "content": null, "poly": [ 241, 1260, 1354, 1260, 1354, 1354, 241, 1354 ] }, { "type": "text", "bbox": [ 0.146, 0.594, 0.566, 0.61 ], "angle": 0, "content": null, "poly": [ 241, 1389, 936, 1389, 936, 1426, 241, 1426 ] }, { "type": "text", "bbox": [ 0.147, 0.613, 0.416, 0.628 ], "angle": 0, "content": null, "poly": [ 243, 1433, 688, 1433, 688, 1468, 243, 1468 ] }, { "type": "code", "bbox": [ 0.146, 0.634, 0.443, 0.78 ], "angle": 0, "content": "Int uadd.ok(unsigned x,unsigned y) \n{ unsigned sum \\(\\equiv\\) x+y; If (sum \\(\\rightharpoondown\\) x) \nReturn 1; else return 0; \n}" }, { "type": "title", "bbox": [ 0.147, 0.786, 0.24, 0.801 ], "angle": 0, "content": null, "poly": [ 243, 1838, 396, 1838, 396, 1873, 243, 1873 ] }, { "type": "text", "bbox": [ 0.146, 0.805, 0.755, 0.839 ], "angle": 0, "content": null, "poly": [ 241, 1882, 1248, 1882, 1248, 1962, 241, 1962 ] }, { "type": "text", "bbox": [ 0.147, 0.842, 0.346, 0.857 ], "angle": 0, "content": null, "poly": [ 243, 1969, 572, 1969, 572, 2004, 243, 2004 ] } ], [ { "type": "image", "bbox": [ 0.149, 0.09, 0.684, 0.313 ], "angle": 0, "content": null }, { "type": "text", "bbox": [ 0.148, 0.316, 0.249, 0.332 ], "angle": 0, "content": null, "poly": [ 244, 739, 411, 739, 411, 776, 244, 776 ] }, { "type": "text", "bbox": [ 0.149, 0.334, 0.248, 0.35 ], "angle": 0, "content": null, "poly": [ 246, 781, 410, 781, 410, 818, 246, 818 ] }, { "type": "text", "bbox": [ 0.149, 0.353, 0.312, 0.369 ], "angle": 0, "content": null, "poly": [ 246, 825, 516, 825, 516, 863, 246, 863 ] }, { "type": "code", "bbox": [ 0.148, 0.39, 0.336, 0.407 ], "angle": 0, "content": "\\(x - y = x + (-y) = x + (-y + 1)\\)" }, { "type": "image", "bbox": [ 0.149, 0.407, 0.678, 0.604 ], "angle": 0, "content": null }, { "type": "equation", "bbox": [ 0.148, 0.687, 0.765, 0.745 ], "angle": 0, "content": "\\[\nF o r x a n d y, x + \\mathbf {\\Lambda} _ {w} ^ {t} y = \\left\\{ \\begin{array}{l l} x + y - 2 ^ {w - 1} - 2 ^ {w - 1} = x + y - 2 ^ {w}, 2 ^ {w - 1} \\leq x + y, \\text {正 溢 出} \\\\ x + y, - 2 ^ {w - 1} \\leq x + y < 2 ^ {w - 1} \\\\ x + y + 2 ^ {w}, x + y < - 2 ^ {w - 1}, \\text {负 溢 出} \\end{array} \\right.\n\\]" }, { "type": "text", "bbox": [ 0.145, 0.761, 0.85, 0.814 ], "angle": 0, "content": null, "poly": [ 239, 1779, 1405, 1779, 1405, 1903, 239, 1903 ] }, { "type": "text", "bbox": [ 0.145, 0.817, 0.85, 0.851 ], "angle": 0, "content": null, "poly": [ 239, 1910, 1405, 1910, 1405, 1990, 239, 1990 ] }, { "type": "text", "bbox": [ 0.147, 0.853, 0.267, 0.869 ], "angle": 0, "content": null, "poly": [ 243, 1995, 441, 1995, 441, 2032, 243, 2032 ] }, { "type": "text", "bbox": [ 0.146, 0.872, 0.452, 0.888 ], "angle": 0, "content": null, "poly": [ 241, 2039, 747, 2039, 747, 2077, 241, 2077 ] }, { "type": "text", "bbox": [ 0.147, 0.891, 0.444, 0.906 ], "angle": 0, "content": null, "poly": [ 243, 2084, 734, 2084, 734, 2119, 243, 2119 ] } ], [ { "type": "text", "bbox": [ 0.146, 0.094, 0.223, 0.109 ], "angle": 0, "content": null, "poly": [ 241, 219, 368, 219, 368, 254, 241, 254 ] }, { "type": "equation", "bbox": [ 0.148, 0.111, 0.438, 0.127 ], "angle": 0, "content": "\\[\nF o r x, 0 \\leq x < 2 ^ {w}, x + x ^ {\\prime} = x ^ {\\prime} + x = 0\n\\]" }, { "type": "equation", "bbox": [ 0.146, 0.15, 0.228, 0.166 ], "angle": 0, "content": "\\[\ny - x - > y + x ^ {\\prime}.\n\\]" }, { "type": "text", "bbox": [ 0.146, 0.168, 0.425, 0.184 ], "angle": 0, "content": null, "poly": [ 241, 392, 702, 392, 702, 430, 241, 430 ] }, { "type": "equation", "bbox": [ 0.148, 0.187, 0.306, 0.227 ], "angle": 0, "content": "\\[\nx ^ {\\prime} = \\left\\{ \\begin{array}{l} x, x = 0 \\\\ 2 ^ {w} - x, x > 0 \\end{array} \\right.\n\\]" }, { "type": "text", "bbox": [ 0.146, 0.242, 0.47, 0.258 ], "angle": 0, "content": null, "poly": [ 241, 566, 777, 566, 777, 603, 241, 603 ] }, { "type": "equation", "bbox": [ 0.148, 0.261, 0.35, 0.302 ], "angle": 0, "content": "\\[\nx ^ {\\prime} = \\left\\{ \\begin{array}{l} - x, x > T M i n _ {w} \\\\ T M i n _ {w}, x = T M i n _ {w} \\end{array} \\right.\n\\]" }, { "type": "text", "bbox": [ 0.146, 0.316, 0.453, 0.332 ], "angle": 0, "content": null, "poly": [ 241, 739, 749, 739, 749, 776, 241, 776 ] }, { "type": "text", "bbox": [ 0.147, 0.335, 0.264, 0.349 ], "angle": 0, "content": null, "poly": [ 243, 783, 436, 783, 436, 816, 243, 816 ] }, { "type": "text", "bbox": [ 0.146, 0.353, 0.517, 0.369 ], "angle": 0, "content": null, "poly": [ 241, 825, 855, 825, 855, 863, 241, 863 ] }, { "type": "text", "bbox": [ 0.148, 0.372, 0.17, 0.386 ], "angle": 0, "content": null, "poly": [ 244, 870, 281, 870, 281, 902, 244, 902 ] }, { "type": "equation", "bbox": [ 0.148, 0.389, 0.372, 0.405 ], "angle": 0, "content": "\\[\nT \\min _ {w} + T \\min _ {w} = - 2 ^ {w} = 0\n\\]" }, { "type": "text", "bbox": [ 0.146, 0.427, 0.825, 0.462 ], "angle": 0, "content": null, "poly": [ 241, 998, 1364, 998, 1364, 1080, 241, 1080 ] }, { "type": "text", "bbox": [ 0.147, 0.465, 0.485, 0.481 ], "angle": 0, "content": null, "poly": [ 243, 1087, 802, 1087, 802, 1125, 243, 1125 ] }, { "type": "text", "bbox": [ 0.146, 0.483, 0.843, 0.517 ], "angle": 0, "content": null, "poly": [ 241, 1129, 1394, 1129, 1394, 1209, 241, 1209 ] }, { "type": "text", "bbox": [ 0.147, 0.52, 0.506, 0.536 ], "angle": 0, "content": null, "poly": [ 243, 1216, 836, 1216, 836, 1253, 243, 1253 ] }, { "type": "text", "bbox": [ 0.147, 0.539, 0.706, 0.554 ], "angle": 0, "content": null, "poly": [ 243, 1260, 1167, 1260, 1167, 1295, 243, 1295 ] }, { "type": "text", "bbox": [ 0.146, 0.557, 0.78, 0.573 ], "angle": 0, "content": null, "poly": [ 241, 1302, 1290, 1302, 1290, 1340, 241, 1340 ] }, { "type": "text", "bbox": [ 0.147, 0.576, 0.347, 0.591 ], "angle": 0, "content": null, "poly": [ 243, 1347, 573, 1347, 573, 1382, 243, 1382 ] }, { "type": "text", "bbox": [ 0.147, 0.594, 0.23, 0.609 ], "angle": 0, "content": null, "poly": [ 243, 1389, 380, 1389, 380, 1424, 243, 1424 ] }, { "type": "equation", "bbox": [ 0.148, 0.613, 0.184, 0.627 ], "angle": 0, "content": "\\[\nK = 0\n\\]" }, { "type": "equation", "bbox": [ 0.148, 0.631, 0.375, 0.645 ], "angle": 0, "content": "\\[\n1 1 0 0 1 1 1 1 1 1 0 0 1 1 0 0 - 1 2 3 4 0\n\\]" }, { "type": "equation", "bbox": [ 0.147, 0.65, 0.578, 0.666 ], "angle": 0, "content": "\\[\nK = 4 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 - 7 7 2 \\text {而} 1 2 3 4 0 / 2 ^ {\\wedge} k = - 7 7 1. 2 5;\n\\]" }, { "type": "text", "bbox": [ 0.146, 0.668, 0.738, 0.684 ], "angle": 0, "content": null, "poly": [ 241, 1562, 1220, 1562, 1220, 1599, 241, 1599 ] }, { "type": "text", "bbox": [ 0.185, 0.686, 0.382, 0.701 ], "angle": 0, "content": null, "poly": [ 305, 1604, 631, 1604, 631, 1639, 305, 1639 ] }, { "type": "equation", "bbox": [ 0.148, 0.706, 0.418, 0.723 ], "angle": 0, "content": "\\[\n(x < 0? x + (1 < < k) - 1: x) > > K\n\\]" }, { "type": "text", "bbox": [ 0.146, 0.742, 0.452, 0.777 ], "angle": 0, "content": null, "poly": [ 241, 1735, 747, 1735, 747, 1817, 241, 1817 ] } ], [ { "type": "table", "bbox": [ 0.139, 0.155, 0.86, 0.306 ], "angle": 0, "content": "
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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0.313, 0.627, 0.329 ], "angle": 0, "content": null, "poly": [ 281, 732, 1037, 732, 1037, 769, 281, 769 ] }, { "type": "text", "bbox": [ 0.171, 0.33, 0.43, 0.346 ], "angle": 0, "content": null, "poly": [ 282, 771, 711, 771, 711, 809, 282, 809 ] }, { "type": "text", "bbox": [ 0.171, 0.347, 0.435, 0.363 ], "angle": 0, "content": null, "poly": [ 282, 811, 719, 811, 719, 849, 282, 849 ] }, { "type": "text", "bbox": [ 0.171, 0.364, 0.637, 0.38 ], "angle": 0, "content": null, "poly": [ 282, 851, 1053, 851, 1053, 888, 282, 888 ] }, { "type": "text", "bbox": [ 0.148, 0.39, 0.258, 0.406 ], "angle": 0, "content": null, "poly": [ 244, 912, 426, 912, 426, 949, 244, 949 ] }, { "type": "text", "bbox": [ 0.149, 0.409, 0.258, 0.424 ], "angle": 0, "content": null, "poly": [ 246, 956, 426, 956, 426, 991, 246, 991 ] }, { "type": "image", "bbox": [ 0.148, 0.441, 0.705, 0.544 ], "angle": 0, "content": null }, { "type": "equation", "bbox": [ 0.148, 0.611, 0.309, 0.628 ], "angle": 0, "content": "\\[\nV = (- 1) ^ {S} \\times M \\times 2 ^ {E}\n\\]" }, { "type": "text", "bbox": [ 0.146, 0.65, 0.348, 0.666 ], "angle": 0, "content": null, "poly": [ 241, 1520, 575, 1520, 575, 1557, 241, 1557 ] }, { "type": "text", "bbox": [ 0.146, 0.668, 0.398, 0.684 ], "angle": 0, "content": null, "poly": [ 241, 1562, 658, 1562, 658, 1599, 241, 1599 ] }, { "type": "text", "bbox": [ 0.146, 0.687, 0.795, 0.703 ], "angle": 0, "content": null, "poly": [ 241, 1606, 1314, 1606, 1314, 1644, 241, 1644 ] }, { "type": "text", "bbox": [ 0.147, 0.706, 0.581, 0.721 ], "angle": 0, "content": null, "poly": [ 243, 1651, 960, 1651, 960, 1686, 243, 1686 ] }, { "type": "text", "bbox": [ 0.148, 0.724, 0.601, 0.739 ], "angle": 0, "content": null, "poly": [ 244, 1693, 994, 1693, 994, 1728, 244, 1728 ] }, { "type": "image", "bbox": [ 0.15, 0.741, 0.49, 0.858 ], "angle": 0, "content": null } ], [ { "type": "header", "bbox": [ 0.148, 0.094, 0.36, 0.109 ], "angle": 0, "content": null, "poly": [ 244, 219, 595, 219, 595, 254, 244, 254 ] 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"text", "bbox": [ 0.146, 0.761, 0.847, 0.795 ], "angle": 0, "content": null, "poly": [ 241, 1779, 1400, 1779, 1400, 1859, 241, 1859 ] }, { "type": "list", "bbox": [ 0.146, 0.742, 0.847, 0.795 ], "angle": 0, "content": null }, { "type": "text", "bbox": [ 0.147, 0.798, 0.657, 0.814 ], "angle": 0, "content": null, "poly": [ 243, 1866, 1086, 1866, 1086, 1903, 243, 1903 ] } ], [ { "type": "image", "bbox": [ 0.149, 0.09, 0.782, 0.306 ], "angle": 0, "content": null }, { "type": "text", "bbox": [ 0.147, 0.316, 0.85, 0.349 ], "angle": 0, "content": null, "poly": [ 243, 739, 1405, 739, 1405, 816, 243, 816 ] }, { "type": "image", "bbox": [ 0.148, 0.35, 0.777, 0.55 ], "angle": 0, "content": null }, { "type": "table_caption", "bbox": [ 0.177, 0.562, 0.257, 0.575 ], "angle": 0, "content": null, "poly": [ 292, 1314, 425, 1314, 425, 1344, 292, 1344 ] }, { "type": "table", "bbox": [ 0.17, 0.576, 0.478, 0.713 ], "angle": 0, "content": "
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
" }, { "type": "table_footnote", "bbox": [ 0.494, 0.694, 0.68, 0.707 ], "angle": 0, "content": null, "poly": [ 817, 1623, 1124, 1623, 1124, 1653, 817, 1653 ] }, { "type": "table", "bbox": [ 0.167, 0.745, 0.416, 0.893 ], "angle": 0, "content": "
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
" }, { "type": "table", "bbox": [ 0.432, 0.743, 0.68, 0.893 ], "angle": 0, "content": "
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
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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}} \\)
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"angle": 0, "content": null }, { "type": "text", "bbox": [ 0.178, 0.387, 0.674, 0.401 ], "angle": 0, "content": null, "poly": [ 294, 905, 1114, 905, 1114, 937, 294, 937 ] }, { "type": "text", "bbox": [ 0.159, 0.404, 0.591, 0.42 ], "angle": 0, "content": null, "poly": [ 262, 944, 977, 944, 977, 982, 262, 982 ] }, { "type": "text", "bbox": [ 0.178, 0.422, 0.634, 0.436 ], "angle": 0, "content": null, "poly": [ 294, 987, 1048, 987, 1048, 1019, 294, 1019 ] }, { "type": "text", "bbox": [ 0.159, 0.438, 0.67, 0.454 ], "angle": 0, "content": null, "poly": [ 262, 1024, 1108, 1024, 1108, 1061, 262, 1061 ] }, { "type": "text", "bbox": [ 0.159, 0.456, 0.427, 0.47 ], "angle": 0, "content": null, "poly": [ 262, 1066, 706, 1066, 706, 1099, 262, 1099 ] }, { "type": "list", "bbox": [ 0.159, 0.438, 0.67, 0.47 ], "angle": 0, "content": null }, { "type": "text", "bbox": [ 0.178, 0.472, 0.625, 0.485 ], "angle": 0, "content": null, "poly": [ 294, 1104, 1033, 1104, 1033, 1134, 294, 1134 ] }, { "type": "title", "bbox": [ 0.169, 0.531, 0.406, 0.548 ], "angle": 0, "content": null, "poly": [ 279, 1242, 671, 1242, 671, 1281, 279, 1281 ] }, { "type": "title", "bbox": [ 0.432, 0.52, 0.529, 0.547 ], "angle": 0, "content": null, "poly": [ 714, 1216, 874, 1216, 874, 1279, 714, 1279 ] }, { "type": "text", "bbox": [ 0.191, 0.551, 0.689, 0.567 ], "angle": 0, "content": null, "poly": [ 315, 1288, 1139, 1288, 1139, 1326, 315, 1326 ] }, { "type": "equation", "bbox": [ 0.214, 0.57, 0.73, 0.603 ], "angle": 0, "content": "\\[\n\\begin{array}{l} \\cdot [ \\mathrm {Y} ] _ {\\text {浮}} = 4 1 3 6 0 0 0 0 \\mathrm {H} = 0 1 0 0 / 0 0 0 1 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 B \\\\ \\cdot \\mathrm {M} _ {\\mathrm {s}} = 0 \\quad \\mathrm {E} = 1 0 0 0 0 0 1 0 \\mathrm {B} = 1 3 0 \\quad \\mathrm {M} = 0 1 1 0 1 1 0 0 0 0 0 0 0 \\\\ \\end{array}\n\\]" }, { "type": "text", "bbox": [ 0.149, 0.607, 0.609, 0.621 ], "angle": 0, "content": null, "poly": [ 246, 1419, 1007, 1419, 1007, 1452, 246, 1452 ] }, { "type": "text", "bbox": [ 0.149, 0.624, 0.627, 0.64 ], "angle": 0, "content": null, "poly": [ 246, 1459, 1037, 1459, 1037, 1496, 246, 1496 ] }, { "type": "text", "bbox": [ 0.159, 0.652, 0.545, 0.665 ], "angle": 0, "content": null, "poly": [ 262, 1525, 901, 1525, 901, 1555, 262, 1555 ] }, { "type": "text", "bbox": [ 0.211, 0.662, 0.677, 0.676 ], "angle": 0, "content": null, "poly": [ 348, 1548, 1119, 1548, 1119, 1581, 348, 1581 ] }, { "type": "text", "bbox": [ 0.19, 0.68, 0.446, 0.695 ], "angle": 0, "content": null, "poly": [ 314, 1590, 737, 1590, 737, 1625, 314, 1625 ] }, { "type": "equation", "bbox": [ 0.19, 0.68, 0.598, 0.73 ], "angle": 0, "content": "\\[\n\\begin{array}{l} Y = M ^ {\\prime} \\times 2 ^ {E ^ {\\prime}} = + 1. 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 \\times 2 ^ {3} \\\\ = + 1 0 1 1. 0 1 1 B = + 1 1. 3 7 5 \\\\ \\end{array}\n\\]" }, { "type": "text", "bbox": [ 0.147, 0.742, 0.434, 0.758 ], "angle": 0, "content": null, "poly": [ 243, 1735, 717, 1735, 717, 1772, 243, 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"angle": 0, "content": null, "poly": [ 243, 1302, 1175, 1302, 1175, 1340, 243, 1340 ] }, { "type": "text", "bbox": [ 0.147, 0.576, 0.518, 0.591 ], "angle": 0, "content": null, "poly": [ 243, 1347, 856, 1347, 856, 1382, 243, 1382 ] }, { "type": "list", "bbox": [ 0.147, 0.094, 0.795, 0.591 ], "angle": 0, "content": null }, { "type": "title", "bbox": [ 0.147, 0.613, 0.223, 0.628 ], "angle": 0, "content": null, "poly": [ 243, 1433, 368, 1433, 368, 1468, 243, 1468 ] }, { "type": "text", "bbox": [ 0.178, 0.635, 0.361, 0.651 ], "angle": 0, "content": null, "poly": [ 294, 1485, 597, 1485, 597, 1522, 294, 1522 ] }, { "type": "equation", "bbox": [ 0.197, 0.655, 0.361, 0.671 ], "angle": 0, "content": "\\[\n= [ X + Y ] _ {\\text {补}} = [ X ] _ {\\text {补}} + [ Y ] _ {\\text {补}}\n\\]" }, { "type": "text", "bbox": [ 0.437, 0.634, 0.62, 0.649 ], "angle": 0, "content": null, "poly": [ 722, 1482, 1025, 1482, 1025, 1518, 722, 1518 ] }, { "type": "equation", "bbox": [ 0.458, 0.653, 0.636, 0.685 ], "angle": 0, "content": "\\[\n\\begin{array}{l} - [ X - Y ] _ {\\text {补}} = [ X + (- Y) ] _ {\\text {补}} \\\\ = [ \\mathrm {X} ] _ {\\text {补}} + [ - \\mathrm {Y} ] _ {\\text {补}} \\\\ \\end{array}\n\\]" }, { "type": "text", "bbox": [ 0.189, 0.677, 0.229, 0.69 ], "angle": 0, "content": null, "poly": [ 312, 1583, 378, 1583, 378, 1613, 312, 1613 ] }, { "type": "equation", "bbox": [ 0.196, 0.692, 0.422, 0.707 ], "angle": 0, "content": "\\[\n[ X ] _ {\\text {补}} = 2 ^ {n + 1} + X \\quad (\\mathrm {m o d} 2 ^ {n + 1})\n\\]" }, { "type": "equation", "bbox": [ 0.196, 0.712, 0.422, 0.727 ], "angle": 0, "content": "\\[\n[ Y ] _ {\\text {补}} = 2 ^ {n + 1} + Y \\quad (\\mathrm {m o d} 2 ^ {n + 1})\n\\]" }, { "type": "equation", "bbox": [ 0.196, 0.731, 0.566, 0.788 ], "angle": 0, "content": "\\[\n\\begin{array}{l} [ X ] _ {\\text {补}} + [ Y ] _ {\\text {补}} = 2 ^ {n + 1} + X + 2 ^ {n + 1} + Y \\quad (\\mathrm {m o d} 2 ^ {n + 1}) \\\\ = 2 ^ {n + 1} + (X + Y) \\quad (\\text {m o d} 2 ^ {n + 1}) \\\\ = [ X + Y ] _ {\\text {补}} \\quad (\\mathrm {m o d} 2 ^ {n + 1}) \\\\ \\end{array}\n\\]" }, { "type": "text", "bbox": [ 0.167, 0.8, 0.457, 0.814 ], "angle": 0, "content": null, "poly": [ 276, 1871, 755, 1871, 755, 1903, 276, 1903 ] }, { "type": "text", "bbox": [ 0.167, 0.817, 0.609, 0.831 ], "angle": 0, "content": null, "poly": [ 276, 1910, 1007, 1910, 1007, 1943, 276, 1943 ] }, { "type": "list", "bbox": [ 0.167, 0.8, 0.609, 0.831 ], "angle": 0, "content": null } ], [ { "type": "title", "bbox": [ 0.207, 0.115, 0.455, 0.138 ], "angle": 0, "content": null, "poly": [ 342, 268, 752, 268, 752, 322, 342, 322 ] }, { "type": "text", "bbox": [ 0.159, 0.149, 0.667, 0.168 ], "angle": 0, "content": null, "poly": [ 262, 348, 1103, 348, 1103, 392, 262, 392 ] }, { "type": "text", "bbox": [ 0.159, 0.173, 0.439, 0.192 ], "angle": 0, "content": null, "poly": [ 262, 404, 726, 404, 726, 449, 262, 449 ] }, { "type": "equation", "bbox": [ 0.182, 0.197, 0.429, 0.217 ], "angle": 0, "content": "\\[\n- [ - Y ] _ {\\text {补}} = \\overline {{Y _ {S}}} \\overline {{Y _ {1}}} \\dots \\dots \\overline {{Y _ {n}}} + 1\n\\]" }, { "type": "text", "bbox": [ 0.159, 0.222, 0.431, 0.24 ], "angle": 0, "content": null, "poly": [ 262, 519, 712, 519, 712, 561, 262, 561 ] }, { "type": "equation", "bbox": [ 0.182, 0.245, 0.509, 0.266 ], "angle": 0, "content": "\\[\n- [ - Y ] _ {\\text {补}} = \\overline {{Y _ {S}}} \\overline {{Y _ {1}}} \\dots \\dots \\overline {{Y _ {n}}} + 0. 0 \\dots \\dots 0 1\n\\]" }, { "type": "text", "bbox": [ 0.146, 0.275, 0.434, 0.29 ], "angle": 0, "content": null, "poly": [ 241, 643, 717, 643, 717, 678, 241, 678 ] }, { "type": "text", "bbox": [ 0.147, 0.295, 0.313, 0.309 ], "angle": 0, "content": null, "poly": [ 243, 690, 517, 690, 517, 722, 243, 722 ] }, { "type": "text", "bbox": [ 0.165, 0.313, 0.412, 0.327 ], "angle": 0, "content": null, "poly": [ 272, 732, 681, 732, 681, 764, 272, 764 ] }, { "type": "text", "bbox": [ 0.165, 0.332, 0.412, 0.346 ], "angle": 0, "content": null, 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1031, 1033, 1064, 597, 1064 ] }, { "type": "text", "bbox": [ 0.361, 0.459, 0.626, 0.473 ], "angle": 0, "content": null, "poly": [ 597, 1073, 1035, 1073, 1035, 1106, 597, 1106 ] }, { "type": "list", "bbox": [ 0.361, 0.403, 0.626, 0.473 ], "angle": 0, "content": null }, { "type": "title", "bbox": [ 0.695, 0.473, 0.716, 0.491 ], "angle": 0, "content": null, "poly": [ 1149, 1106, 1184, 1106, 1184, 1148, 1149, 1148 ] }, { "type": "title", "bbox": [ 0.212, 0.506, 0.4, 0.522 ], "angle": 0, "content": null, "poly": [ 350, 1183, 661, 1183, 661, 1220, 350, 1220 ] }, { "type": "text", "bbox": [ 0.225, 0.53, 0.42, 0.547 ], "angle": 0, "content": null, "poly": [ 372, 1239, 694, 1239, 694, 1279, 372, 1279 ] }, { "type": "text", "bbox": [ 0.226, 0.553, 0.42, 0.569 ], "angle": 0, "content": null, "poly": [ 373, 1293, 694, 1293, 694, 1330, 373, 1330 ] }, { "type": "text", "bbox": [ 0.491, 0.506, 0.69, 0.522 ], "angle": 0, "content": null, "poly": [ 812, 1183, 1141, 1183, 1141, 1220, 812, 1220 ] }, { "type": "equation", "bbox": [ 0.469, 0.527, 0.668, 0.576 ], "angle": 0, "content": "\\[\n\\begin{array}{l} [ \\mathrm {X} ] _ {\\text {补}} = \\mathrm {X} _ {S} \\mathrm {X} _ {1} \\dots \\dots \\mathrm {X} _ {n} \\\\ [ \\mathrm {Y} ] _ {\\text {补}} = \\mathrm {Y} _ {S} \\mathrm {Y} _ {1} \\dots \\dots \\mathrm {Y} _ {n} \\\\ [ X \\pm Y ] _ {\\text {补}} = F _ {s} F _ {1} \\dots \\dots F _ {n} \\\\ \\end{array}\n\\]" }, { "type": "table", "bbox": [ 0.18, 0.584, 0.873, 0.731 ], "angle": 0, "content": "
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
" }, { "type": "text", "bbox": [ 0.18, 0.741, 0.278, 0.758 ], "angle": 0, "content": null, "poly": [ 297, 1733, 459, 1733, 459, 1772, 297, 1772 ] }, { "type": "page_number", "bbox": [ 0.83, 0.742, 0.839, 0.751 ], "angle": 0, "content": null, "poly": [ 1372, 1735, 1387, 1735, 1387, 1756, 1372, 1756 ] } ], [ { "type": "title", "bbox": [ 0.167, 0.091, 0.353, 0.109 ], "angle": 0, "content": null, "poly": [ 276, 212, 583, 212, 583, 254, 276, 254 ] }, { "type": "text", "bbox": [ 0.182, 0.113, 0.787, 0.149 ], "angle": 0, "content": null, "poly": [ 301, 264, 1301, 264, 1301, 348, 301, 348 ] }, { "type": "equation", "bbox": [ 0.233, 0.159, 0.416, 0.214 ], "angle": 0, "content": "\\[\n\\frac {\\mathrm {X} _ {\\mathrm {S}} \\mathrm {X} _ {\\mathrm {S}} \\mathrm {X} _ {1} \\mathrm {X} _ {2} \\dots \\dots \\mathrm {X} _ {\\mathrm {n}}}{\\mathrm {Y} _ {\\mathrm {S}} \\mathrm {Y} _ {\\mathrm {S}} \\mathrm {Y} _ {1} \\mathrm {Y} _ {2} \\dots \\dots \\mathrm {Y} _ {\\mathrm {n}}}\n\\]" }, { "type": "equation", "bbox": [ 0.468, 0.16, 0.804, 0.213 ], "angle": 0, "content": "\\[\n\\begin{array}{r l} & \\mathrm {X} _ {\\mathrm {S}} \\mathrm {X} _ {1} \\mathrm {X} _ {2} \\dots \\dots \\mathrm {X} _ {\\mathrm {n}} \\\\ + & \\mathrm {Y} _ {\\mathrm {S}} \\mathrm {Y} _ {1} \\mathrm {Y} _ {2} \\dots \\dots \\mathrm {Y} _ {\\mathrm {n}} \\\\ \\hline & \\mathrm {F} _ {\\mathrm {S}} \\mathrm {F} _ {1} \\mathrm {F} _ {2} \\dots \\dots \\mathrm {F} _ {\\mathrm {n}} \\end{array} \\quad \\begin{array}{r l} & \\mathrm {F} _ {\\mathrm {S} 1} = \\mathrm {X} _ {\\mathrm {S}} \\oplus \\mathrm {Y} _ {\\mathrm {S}} \\oplus \\mathrm {C} _ {\\mathrm {S}} \\\\ & \\mathrm {F} _ {\\mathrm {S} 2} = \\mathrm {F} _ {\\mathrm {S}} \\end{array}\n\\]" }, { "type": "equation", "bbox": [ 0.255, 0.233, 0.71, 0.251 ], "angle": 0, "content": "\\[\n\\begin{array}{l} \\mathbf {V} = \\mathbf {F} _ {\\mathbf {S} 1} \\oplus \\mathbf {F} _ {\\mathbf {S} 2} \\\\ \\cdot \\mathbf {V} = \\mathbf {F} _ {\\mathbf {S} 1} \\oplus \\mathbf {F} _ {\\mathbf {S} 2} = \\mathbf {X} _ {\\mathbf {S}} \\oplus \\mathbf {Y} _ {\\mathbf {S}} \\oplus \\mathbf {C} _ {\\mathbf {S}} \\oplus \\mathbf {F} _ {\\mathbf {S}} \\\\ \\end{array}\n\\]" }, { "type": "text", "bbox": [ 0.256, 0.258, 0.651, 0.277 ], "angle": 0, "content": null, "poly": [ 423, 603, 1076, 603, 1076, 647, 423, 647 ] }, { "type": "text", "bbox": [ 0.146, 0.33, 0.391, 0.343 ], "angle": 0, "content": null, "poly": [ 241, 771, 646, 771, 646, 802, 241, 802 ] }, { "type": "text", "bbox": [ 0.147, 0.346, 0.281, 0.359 ], "angle": 0, "content": null, "poly": [ 243, 809, 464, 809, 464, 839, 243, 839 ] }, { "type": "text", "bbox": [ 0.149, 0.361, 0.279, 0.374 ], "angle": 0, "content": null, "poly": [ 246, 844, 461, 844, 461, 874, 246, 874 ] }, { "type": "list", "bbox": [ 0.147, 0.346, 0.281, 0.374 ], "angle": 0, "content": null }, { "type": "text", "bbox": [ 0.148, 0.377, 0.209, 0.389 ], "angle": 0, "content": null, "poly": [ 244, 881, 345, 881, 345, 909, 244, 909 ] }, 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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,
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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
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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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"type": "text", "bbox": [ 0.211, 0.602, 0.439, 0.62 ], "angle": 0, "content": null, "poly": [ 348, 1408, 726, 1408, 726, 1450, 348, 1450 ] }, { "type": "equation", "bbox": [ 0.504, 0.6, 0.789, 0.623 ], "angle": 0, "content": "\\[\nZ F = \\overline {{F _ {n} + F _ {n - 1} + . . . . . . + F _ {0}}}\n\\]" }, { "type": "text", "bbox": [ 0.211, 0.624, 0.467, 0.641 ], "angle": 0, "content": null, "poly": [ 348, 1459, 772, 1459, 772, 1499, 348, 1499 ] }, { "type": "text", "bbox": [ 0.18, 0.646, 0.706, 0.663 ], "angle": 0, "content": null, "poly": [ 297, 1510, 1167, 1510, 1167, 1550, 297, 1550 ] }, { "type": "text", "bbox": [ 0.211, 0.668, 0.704, 0.686 ], "angle": 0, "content": null, "poly": [ 348, 1562, 1164, 1562, 1164, 1604, 348, 1604 ] }, { "type": "text", "bbox": [ 0.211, 0.69, 0.783, 0.708 ], "angle": 0, "content": null, "poly": [ 348, 1613, 1295, 1613, 1295, 1656, 348, 1656 ] }, { "type": "list", "bbox": [ 0.211, 0.668, 0.783, 0.708 ], "angle": 0, "content": null }, { "type": "text", "bbox": [ 0.241, 0.716, 0.296, 0.745 ], "angle": 0, "content": null, "poly": [ 398, 1674, 489, 1674, 489, 1742, 398, 1742 ] }, { "type": "equation", "bbox": [ 0.405, 0.718, 0.79, 0.747 ], "angle": 0, "content": "\\[\nC F = \\overline {{\\overline {{A D D}} / S U B}} \\cdot C + \\overline {{A D D}} / S U B \\cdot \\overline {{C}}\n\\]" }, { "type": "image", "bbox": [ 0.849, 0.745, 0.889, 0.76 ], "angle": 0, "content": null } ], [ { "type": "text", "bbox": [ 0.214, 0.088, 0.904, 0.105 ], "angle": 0, "content": null, "poly": [ 353, 205, 1495, 205, 1495, 245, 353, 245 ] }, { "type": "text", "bbox": [ 0.235, 0.106, 0.411, 0.124 ], "angle": 0, "content": null, "poly": [ 388, 247, 679, 247, 679, 290, 388, 290 ] }, { "type": "text", "bbox": [ 0.247, 0.128, 0.425, 0.145 ], "angle": 0, "content": null, "poly": [ 408, 299, 702, 299, 702, 339, 408, 339 ] }, { "type": "text", "bbox": [ 0.247, 0.15, 0.465, 0.167 ], "angle": 0, "content": null, "poly": [ 408, 350, 769, 350, 769, 390, 408, 390 ] }, { "type": "list", "bbox": [ 0.247, 0.128, 0.465, 0.167 ], "angle": 0, "content": null }, { "type": "equation", "bbox": [ 0.529, 0.113, 0.884, 0.189 ], "angle": 0, "content": "\\[\n\\begin{array}{c c} O F = \\overline {{A D D / S U B}} \\left(\\overline {{X _ {S}}} \\overline {{Y _ {S}}} F _ {S} + X _ {S} Y _ {S} \\overline {{F _ {S}}}\\right) \\\\ + \\overline {{A D D}} / S U B \\left(\\overline {{X _ {S}}} Y _ {S} F _ {S} + X _ {S} \\overline {{Y _ {S}}} \\overline {{F _ {S}}}\\right) \\\\ \\hline O F = C _ {1} \\oplus C _ {S} & O F = F _ {S 1} \\oplus F _ {S 2} \\end{array}\n\\]" }, { "type": "text", "bbox": [ 0.214, 0.197, 0.578, 0.216 ], "angle": 0, "content": null, "poly": [ 353, 460, 956, 460, 956, 505, 353, 505 ] }, { "type": "text", "bbox": [ 0.247, 0.22, 0.59, 0.242 ], "angle": 0, "content": null, "poly": [ 408, 514, 975, 514, 975, 566, 408, 566 ] }, { "type": "text", "bbox": [ 0.247, 0.245, 0.862, 0.264 ], "angle": 0, "content": null, "poly": [ 408, 573, 1425, 573, 1425, 617, 408, 617 ] }, { "type": "list", "bbox": [ 0.247, 0.22, 0.862, 0.264 ], "angle": 0, "content": null }, { "type": "text", "bbox": [ 0.214, 0.269, 0.725, 0.288 ], "angle": 0, "content": null, "poly": [ 353, 629, 1199, 629, 1199, 673, 353, 673 ] }, { "type": "text", "bbox": [ 0.247, 0.292, 0.573, 0.31 ], "angle": 0, "content": null, "poly": [ 408, 682, 947, 682, 947, 725, 408, 725 ] }, { "type": "text", "bbox": [ 0.247, 0.314, 0.574, 0.332 ], "angle": 0, "content": null, "poly": [ 408, 734, 949, 734, 949, 776, 408, 776 ] }, { "type": "list", "bbox": [ 0.247, 0.292, 0.574, 0.332 ], "angle": 0, "content": null }, { "type": "equation", "bbox": [ 0.594, 0.298, 0.924, 0.328 ], "angle": 0, "content": "\\[\nP F = \\overline {{F _ {n} \\oplus F _ {n - 1} \\oplus \\dots . \\oplus F _ {0}}}\n\\]" }, { "type": "page_number", "bbox": [ 0.889, 0.34, 0.928, 0.358 ], "angle": 0, "content": null, "poly": [ 1470, 795, 1534, 795, 1534, 837, 1470, 837 ] }, { "type": "title", "bbox": [ 0.172, 0.436, 0.473, 0.46 ], "angle": 0, "content": null, "poly": [ 284, 1019, 782, 1019, 782, 1075, 284, 1075 ] }, { "type": "equation", "bbox": [ 0.377, 0.475, 0.589, 0.507 ], "angle": 0, "content": "\\[\nX = M _ {X} \\times 2 ^ {E _ {X}}\n\\]" }, { "type": "equation", "bbox": [ 0.696, 0.474, 0.904, 0.507 ], "angle": 0, "content": "\\[\nY = M _ {Y} \\times 2 ^ {E _ {Y}}\n\\]" }, { "type": "text", "bbox": [ 0.172, 0.541, 0.998, 0.566 ], "angle": 0, "content": null, "poly": [ 284, 1265, 1650, 1265, 1650, 1323, 284, 1323 ] }, { "type": "text", "bbox": [ 0.172, 0.582, 0.691, 0.607 ], "angle": 0, "content": null, "poly": [ 284, 1361, 1142, 1361, 1142, 1419, 284, 1419 ] }, { "type": "list", "bbox": [ 0.172, 0.541, 0.998, 0.607 ], "angle": 0, "content": null }, { "type": "equation", "bbox": [ 0.263, 0.629, 0.999, 0.662 ], "angle": 0, "content": "\\[\nZ = X \\pm Y = \\left(M _ {X} \\cdot 2 ^ {\\left(E _ {X} - E _ {Y}\\right)} \\pm M _ {Y}\\right) \\times 2 ^ {E _ {Y}} \\quad E _ {X} \\leq\n\\]" } ], [ { "type": 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