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Subtractor

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1581: 1129: 25: 2285: 1118: 711:. The subtractor is best understood by considering that the subtrahend and both borrow bits have negative weights, whereas the X and D bits are positive. The operation performed by the subtractor is to rewrite 2622: 1819: 1543: 2279: 880: 521: 959: 2668: 2220:. When a borrow out is generated, 2 is added in the current digit. (This is similar to the subtraction algorithm in decimal. Instead of adding 2, we add 10 when we borrow.) Therefore, 2523: 3735: 2218: 2112: 762: 1363: 1264: 1021: 814: 1959: 1737: 1494: 1231: 2159: 2033: 1986: 1912: 1772: 2707: 709: 1290: 676: 649: 622: 591: 514: 3846: 3029: 1467: 1441: 1415: 1389: 1030: 3548: 2179: 2132: 2073: 2053: 2006: 1932: 1885: 1865: 1710: 1571: 1330: 1310: 1204: 1184: 1161: 3705: 3271: 3088: 507: 3051: 3700: 3772: 1828:
X ── XOR ─┬─────── |X-Y|, is 0 if X equals Y, 1 otherwise ┌──┘ └──┐ Y ─┴─────── AND ── borrow, is 1 if Y > X, 0 otherwise
3525: 2114:. Like the half subtractor, the full subtractor generates a borrow out when it needs to borrow from the next digit. Since we are subtracting 4469: 3593: 2856: 2700: 1136:
The half subtractors can be designed through the combinational Boolean logic circuits as shown in Figure 1 and 2.The half subtractor is a
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Consequently, a simplified half-subtract circuit, advantageously avoiding crossed traces in particular as well as a negate gate is:
108: 2938: 2529: 4602: 4165: 3058: 3024: 3019: 2903: 4577: 4474: 3875: 3782: 3583: 2826: 2804: 2693: 1233:. The borrow out signal is set when the subtractor needs to borrow from the next digit in a multi-digit subtraction. That is, 3322: 2757: 46: 1778: 1502: 554:
subtraction process is summarized below. As with an adder, in the general case of calculations on multi-bit numbers, three
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notation, by providing an addition/subtraction selector to the carry-in and to invert the second operand.
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Subtractors are usually implemented within a binary adder for only a small cost when using the standard
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Beltran, A.A., Nones, K., Salanguit, R.L., Santos, J.B., Santos, J.M., & Dizon, K.J. (2021).
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that performs subtraction of numbers – can be designed using the same approach as that of an
4587: 4520: 4361: 4268: 4222: 4029: 4024: 4019: 4014: 4009: 3999: 3869: 3836: 3747: 3742: 3651: 3503: 3498: 3481: 3469: 3408: 2972: 2950: 2836: 2814: 2732: 2680: 2652: 2642: 1580: 1269: 1113:{\displaystyle {\begin{alignedat}{2}A-B&=A+(-B)\\&=A+{\bar {B}}+1\\\end{alignedat}}} 407: 336: 252: 242: 1831:
where lines to the right are outputs and others (from the top, bottom or left) are inputs.
1417:. An important point worth mentioning is that the half subtractor diagram aside implements 654: 627: 600: 569: 4501: 4486: 4434: 4338: 4313: 4150: 4143: 3994: 3989: 3984: 3923: 3831: 3821: 3543: 3378: 3330: 3093: 2977: 2945: 2846: 2841: 2762: 543: 298: 293: 152: 1446: 1420: 1394: 1368: 82: 4612: 4446: 4429: 4422: 4318: 4175: 3912: 3826: 3757: 3340: 3302: 3251: 3246: 3241: 2955: 2779: 2647: 2164: 2117: 2058: 2038: 1991: 1917: 1870: 1850: 1695: 1556: 1315: 1295: 1189: 1169: 1146: 1128: 4632: 4407: 4323: 3363: 3345: 3138: 2831: 1840: 1137: 147: 4617: 4555: 4371: 4348: 4160: 3881: 2819: 1689: 966: 331: 4402: 4366: 4077: 4049: 3907: 3762: 2669:
Low Power NAND Gate–based Half and Full Adder / Subtractor Using CMOS Technique.
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This is an important distinction to make since subtraction itself is not
1140:
which is used to perform subtraction of two bits. It has two inputs, the
3203: 3161: 1141: 563: 4506: 3218: 3183: 3148: 3676: 3208: 3178: 1127: 4540: 3688: 3608: 3198: 1914:. The full subtractor generates two output bits: the difference 2689: 558:
are involved in performing the subtraction for each bit of the
3128: 3118: 1844: 555: 18: 2617:{\displaystyle B_{out}={\bar {X}}B_{in}+{\bar {X}}Y+YB_{in}} 2681:
N bit Binary addition or subtraction using single circuit.
764:(which can take the values -2, -1, 0, or 1) as the sum 2532: 2483: 2226: 2187: 2167: 2140: 2120: 2081: 2061: 2041: 2014: 1994: 1967: 1940: 1920: 1893: 1873: 1853: 1843:
which is used to perform subtraction of three input
1814:{\displaystyle B_{\text{out}}={\overline {X}}\cdot Y} 1781: 1748: 1718: 1698: 1559: 1538:{\displaystyle B_{\text{out}}={\overline {X}}\cdot Y} 1505: 1475: 1449: 1423: 1397: 1371: 1338: 1318: 1298: 1272: 1239: 1212: 1192: 1172: 1149: 1033: 985: 889: 825: 770: 717: 684: 657: 630: 603: 572: 4570: 4519: 4455: 4393: 4347: 4299: 4254: 4174: 4101: 4070: 3975: 3896: 3860: 3814: 3714: 3640: 3574: 3524: 3435: 3426: 3399: 3354: 3321: 3293: 3284: 3104: 3007: 2996: 2867: 2723: 2664:
Foundations Of Digital Electronics by Elijah Mwangi
2274:{\displaystyle D=X-Y-B_{\text{in}}+2B_{\text{out}}} 49:. Unsourced material may be challenged and removed. 2616: 2517: 2273: 2212: 2173: 2153: 2126: 2106: 2067: 2047: 2027: 2000: 1980: 1953: 1926: 1906: 1879: 1859: 1813: 1766: 1731: 1704: 1565: 1537: 1488: 1461: 1435: 1409: 1383: 1357: 1324: 1304: 1284: 1258: 1225: 1198: 1178: 1155: 1112: 1015: 953: 875:{\displaystyle D_{i}=X_{}\oplus Y_{i}\oplus B_{i}} 874: 808: 756: 703: 670: 643: 616: 585: 1988:is set when the previous digit is borrowed from 1584:Figure 2: Half-subtractor using NAND gate only. 954:{\displaystyle B_{i+1}=X_{i}<(Y_{i}+B_{i})} 2701: 1132:Figure 1: Logic diagram for a half subtractor 515: 8: 2291:The truth table for the full subtractor is: 1692:, we find the following logic equations for 3706:Computer performance by orders of magnitude 4171: 3811: 3432: 3290: 3004: 2708: 2694: 2686: 2181:, a borrow out needs to be generated when 522: 508: 190: 120: 2605: 2581: 2580: 2568: 2553: 2552: 2537: 2531: 2506: 2482: 2265: 2249: 2225: 2204: 2186: 2166: 2145: 2139: 2119: 2098: 2080: 2060: 2040: 2019: 2013: 1993: 1972: 1966: 1945: 1939: 1919: 1898: 1892: 1872: 1852: 1795: 1786: 1780: 1747: 1723: 1717: 1697: 1558: 1519: 1510: 1504: 1480: 1474: 1448: 1422: 1396: 1370: 1343: 1337: 1317: 1297: 1271: 1244: 1238: 1217: 1211: 1191: 1171: 1148: 1089: 1088: 1034: 1032: 1023:(definition of two's complement notation) 996: 995: 984: 942: 929: 913: 894: 888: 866: 853: 843: 830: 824: 800: 781: 769: 748: 735: 722: 716: 689: 683: 662: 656: 635: 629: 608: 602: 577: 571: 109:Learn how and when to remove this message 2518:{\displaystyle D=X\oplus Y\oplus B_{in}} 2293: 2283: 1594: 1579: 651:). The outputs are the difference bit ( 477: 454: 423: 375: 352: 314: 286: 268: 200: 188: 145: 128: 7: 3677:Floating-point operations per second 2213:{\displaystyle X<Y+B_{\text{in}}} 47:adding citations to reliable sources 14: 2107:{\displaystyle X-Y-B_{\text{in}}} 757:{\displaystyle X_{i}-Y_{i}-B_{i}} 16:Circuit that performs subtraction 4603:Semiconductor device fabrication 1358:{\displaystyle B_{\text{out}}=1} 1259:{\displaystyle B_{\text{out}}=1} 327:Booth's multiplication algorithm 23: 4578:History of general-purpose CPUs 2805:Nondeterministic Turing machine 1186:and two outputs the difference 1016:{\displaystyle -B={\bar {B}}+1} 809:{\displaystyle -2B_{i+1}+D_{i}} 34:needs additional citations for 2758:Deterministic finite automaton 2586: 2558: 1954:{\displaystyle B_{\text{out}}} 1732:{\displaystyle B_{\text{out}}} 1489:{\displaystyle B_{\text{out}}} 1226:{\displaystyle B_{\text{out}}} 1094: 1069: 1060: 1001: 948: 922: 1: 3549:Simultaneous and heterogenous 2154:{\displaystyle B_{\text{in}}} 2028:{\displaystyle B_{\text{in}}} 1981:{\displaystyle B_{\text{in}}} 1907:{\displaystyle B_{\text{in}}} 432:Multiply–accumulate operation 173:Signed number representations 4233:Integrated memory controller 4215:Translation lookaside buffer 3414:Memory dependence prediction 2857:Random-access stored program 2810:Probabilistic Turing machine 1800: 1688:Using the table above and a 1592:for the half subtractor is: 1524: 462:Category:Computer arithmetic 3689:Synaptic updates per second 2475:Therefore the equation is: 1767:{\displaystyle D=X\oplus Y} 1496:on the diagram is given by 4675: 4093:Heterogeneous architecture 3015:Orthogonal instruction set 2785:Alternating Turing machine 2773:Quantum cellular automaton 2055:as well as the subtrahend 457:Category:Binary arithmetic 4644:Arithmetic logic circuits 4583:Microprocessor chronology 4546:Dynamic frequency scaling 3701:Cache performance metrics 2299: 2296: 1839:The full subtractor is a 1600: 1597: 1553:, but the difference bit 129:Arithmetic logic circuits 4598:Hardware security module 3941:Digital signal processor 3918:Graphics processing unit 3730:Graphics processing unit 2035:is also subtracted from 426:Kochanski multiplication 322:Multiplication algorithm 4551:Dynamic voltage scaling 4334:Memory address register 4228:Branch target predictor 4192:Address generation unit 3935:Physics processing unit 3724:Central processing unit 3683:Transactions per second 3671:Instructions per second 3594:Array processing (SIMT) 2738:Stored-program computer 1573:is calculated using an 704:{\displaystyle B_{i+1}} 168:Two's complement number 163:Ones' complement number 4357:Hardwired control unit 4239:Memory management unit 4204:Memory management unit 3953:Secure cryptoprocessor 3947:Tensor Processing Unit 3929:Vision processing unit 3663:Cycles per instruction 3657:Instructions per cycle 3604:Associative processing 3295:Instruction pipelining 2717:Processor technologies 2618: 2519: 2288: 2275: 2214: 2175: 2155: 2128: 2108: 2069: 2049: 2029: 2002: 1982: 1955: 1928: 1908: 1881: 1861: 1815: 1768: 1733: 1706: 1585: 1577:which is commutative. 1567: 1539: 1490: 1463: 1437: 1411: 1385: 1359: 1326: 1306: 1286: 1285:{\displaystyle X<Y} 1260: 1227: 1200: 1180: 1157: 1133: 1114: 1017: 955: 876: 810: 758: 705: 672: 645: 618: 587: 4440:Sum-addressed decoder 4186:Arithmetic logic unit 3313:Classic RISC pipeline 3267:Epiphany architecture 3114:Motorola 68000 series 2638:Carry-lookahead adder 2619: 2520: 2287: 2276: 2215: 2176: 2156: 2129: 2109: 2070: 2050: 2030: 2003: 1983: 1956: 1929: 1909: 1882: 1862: 1841:combinational circuit 1816: 1769: 1734: 1707: 1583: 1568: 1540: 1491: 1464: 1438: 1412: 1386: 1360: 1327: 1307: 1287: 1261: 1228: 1201: 1181: 1158: 1138:combinational circuit 1131: 1115: 1018: 956: 877: 811: 759: 706: 673: 671:{\displaystyle D_{i}} 646: 644:{\displaystyle B_{i}} 619: 617:{\displaystyle Y_{i}} 588: 586:{\displaystyle X_{i}} 495:Mechanical calculator 223:Carry-lookahead adder 4649:Adders (electronics) 4561:Performance per watt 4139:replacement policies 3805:Package on a package 3695:Performance per watt 3599:Pipelined processing 3369:Tomasulo's algorithm 3174:Clipper architecture 3030:Application-specific 2743:Finite-state machine 2530: 2481: 2224: 2185: 2165: 2138: 2118: 2079: 2059: 2039: 2012: 1992: 1965: 1938: 1918: 1891: 1871: 1851: 1779: 1746: 1716: 1696: 1557: 1503: 1473: 1447: 1421: 1395: 1369: 1336: 1316: 1296: 1270: 1237: 1210: 1190: 1170: 1147: 1031: 983: 887: 823: 768: 715: 682: 655: 628: 601: 570: 265:Adder–subtractor (Âą) 43:improve this article 4593:Digital electronics 4246:Instruction decoder 4198:Floating-point unit 3852:Soft microprocessor 3799:System in a package 3374:Reservation station 2904:Transport-triggered 2633:Adder (electronics) 1462:{\displaystyle Y-X} 1436:{\displaystyle X-Y} 1410:{\displaystyle Y=1} 1384:{\displaystyle X=0} 965:where ⊕ represents 124:Part of a series on 4465:Integrated circuit 4309:Processor register 3963:Baseband processor 3308:Operand forwarding 2768:Cellular automaton 2614: 2515: 2289: 2271: 2210: 2171: 2151: 2124: 2104: 2065: 2045: 2025: 1998: 1978: 1951: 1924: 1904: 1877: 1857: 1811: 1764: 1729: 1702: 1586: 1563: 1535: 1486: 1459: 1433: 1407: 1381: 1355: 1322: 1302: 1282: 1256: 1223: 1196: 1176: 1153: 1134: 1110: 1108: 1013: 951: 872: 806: 754: 701: 668: 641: 614: 583: 428:(exponentiation) 360:Division algorithm 248:Carry-select adder 218:Ripple-carry adder 4659:Binary arithmetic 4626: 4625: 4515: 4514: 4134:Instruction cache 4124:Scratchpad memory 3971: 3970: 3958:Network processor 3887:Network on a chip 3842:Ultra-low-voltage 3793:Multi-chip module 3636: 3635: 3422: 3421: 3409:Branch prediction 3386:Register renaming 3280: 3279: 3262:VISC architecture 3084:Quantum computing 3079:VISC architecture 2961:Secondary storage 2877:Microarchitecture 2837:Register machines 2589: 2561: 2473: 2472: 2268: 2252: 2207: 2174:{\displaystyle X} 2148: 2127:{\displaystyle Y} 2101: 2075:. Or in symbols: 2068:{\displaystyle Y} 2048:{\displaystyle X} 2022: 2001:{\displaystyle X} 1975: 1948: 1927:{\displaystyle D} 1901: 1880:{\displaystyle Y} 1860:{\displaystyle X} 1803: 1789: 1726: 1705:{\displaystyle D} 1686: 1685: 1566:{\displaystyle D} 1527: 1513: 1483: 1346: 1325:{\displaystyle Y} 1305:{\displaystyle X} 1247: 1220: 1199:{\displaystyle D} 1179:{\displaystyle Y} 1156:{\displaystyle X} 1097: 1004: 678:) and borrow bit 532: 531: 440: 439: 378:Bitwise operation 317:Binary multiplier 233:Kogge–Stone adder 119: 118: 111: 93: 4666: 4639:Digital circuits 4588:Processor design 4480:Power management 4362:Instruction unit 4223:Branch predictor 4172: 3870:System on a chip 3812: 3652:Transistor count 3576:Flynn's taxonomy 3433: 3291: 3094:Addressing modes 3005: 2951:Memory hierarchy 2815:Hypercomputation 2733:Abstract machine 2710: 2703: 2696: 2687: 2653:Adder-subtractor 2643:Carry-save adder 2623: 2621: 2620: 2615: 2613: 2612: 2591: 2590: 2582: 2576: 2575: 2563: 2562: 2554: 2548: 2547: 2524: 2522: 2521: 2516: 2514: 2513: 2294: 2280: 2278: 2277: 2272: 2270: 2269: 2266: 2254: 2253: 2250: 2219: 2217: 2216: 2211: 2209: 2208: 2205: 2180: 2178: 2177: 2172: 2160: 2158: 2157: 2152: 2150: 2149: 2146: 2133: 2131: 2130: 2125: 2113: 2111: 2110: 2105: 2103: 2102: 2099: 2074: 2072: 2071: 2066: 2054: 2052: 2051: 2046: 2034: 2032: 2031: 2026: 2024: 2023: 2020: 2007: 2005: 2004: 1999: 1987: 1985: 1984: 1979: 1977: 1976: 1973: 1960: 1958: 1957: 1952: 1950: 1949: 1946: 1933: 1931: 1930: 1925: 1913: 1911: 1910: 1905: 1903: 1902: 1899: 1887:, and borrow in 1886: 1884: 1883: 1878: 1866: 1864: 1863: 1858: 1820: 1818: 1817: 1812: 1804: 1796: 1791: 1790: 1787: 1773: 1771: 1770: 1765: 1738: 1736: 1735: 1730: 1728: 1727: 1724: 1711: 1709: 1708: 1703: 1595: 1572: 1570: 1569: 1564: 1544: 1542: 1541: 1536: 1528: 1520: 1515: 1514: 1511: 1495: 1493: 1492: 1487: 1485: 1484: 1481: 1468: 1466: 1465: 1460: 1442: 1440: 1439: 1434: 1416: 1414: 1413: 1408: 1390: 1388: 1387: 1382: 1364: 1362: 1361: 1356: 1348: 1347: 1344: 1331: 1329: 1328: 1323: 1311: 1309: 1308: 1303: 1291: 1289: 1288: 1283: 1265: 1263: 1262: 1257: 1249: 1248: 1245: 1232: 1230: 1229: 1224: 1222: 1221: 1218: 1205: 1203: 1202: 1197: 1185: 1183: 1182: 1177: 1162: 1160: 1159: 1154: 1119: 1117: 1116: 1111: 1109: 1099: 1098: 1090: 1075: 1022: 1020: 1019: 1014: 1006: 1005: 997: 974:two's complement 960: 958: 957: 952: 947: 946: 934: 933: 918: 917: 905: 904: 881: 879: 878: 873: 871: 870: 858: 857: 845: 844: 835: 834: 815: 813: 812: 807: 805: 804: 792: 791: 763: 761: 760: 755: 753: 752: 740: 739: 727: 726: 710: 708: 707: 702: 700: 699: 677: 675: 674: 669: 667: 666: 650: 648: 647: 642: 640: 639: 623: 621: 620: 615: 613: 612: 592: 590: 589: 584: 582: 581: 524: 517: 510: 408:Bit manipulation 337:Dadda multiplier 271:Adder–subtractor 253:Carry-skip adder 243:Carry-save adder 228:Brent–Kung adder 191: 134:Quick navigation 121: 114: 107: 103: 100: 94: 92: 51: 27: 19: 4674: 4673: 4669: 4668: 4667: 4665: 4664: 4663: 4629: 4628: 4627: 4622: 4608:Tick–tock model 4566: 4522: 4511: 4451: 4435:Address decoder 4389: 4343: 4339:Program counter 4314:Status register 4295: 4250: 4210:Load–store unit 4177: 4170: 4097: 4066: 3967: 3924:Image processor 3899: 3892: 3862: 3856: 3832:Microcontroller 3822:Embedded system 3810: 3710: 3643: 3632: 3570: 3520: 3418: 3395: 3379:Re-order buffer 3350: 3331:Data dependency 3317: 3276: 3106: 3100: 2999: 2998:Instruction set 2992: 2978:Multiprocessing 2946:Cache hierarchy 2939:Register/memory 2863: 2763:Queue automaton 2719: 2714: 2677: 2661: 2629: 2601: 2564: 2533: 2528: 2527: 2502: 2479: 2478: 2333: 2320: 2261: 2245: 2222: 2221: 2200: 2183: 2182: 2163: 2162: 2141: 2136: 2135: 2116: 2115: 2094: 2077: 2076: 2057: 2056: 2037: 2036: 2015: 2010: 2009: 1990: 1989: 1968: 1963: 1962: 1941: 1936: 1935: 1934:and borrow out 1916: 1915: 1894: 1889: 1888: 1869: 1868: 1849: 1848: 1837: 1835:Full subtractor 1829: 1782: 1777: 1776: 1744: 1743: 1719: 1714: 1713: 1694: 1693: 1626: 1555: 1554: 1506: 1501: 1500: 1476: 1471: 1470: 1445: 1444: 1419: 1418: 1393: 1392: 1367: 1366: 1365:if and only if 1339: 1334: 1333: 1314: 1313: 1294: 1293: 1268: 1267: 1240: 1235: 1234: 1213: 1208: 1207: 1206:and borrow out 1188: 1187: 1168: 1167: 1145: 1144: 1126: 1124:Half subtractor 1107: 1106: 1073: 1072: 1047: 1029: 1028: 981: 980: 938: 925: 909: 890: 885: 884: 862: 849: 839: 826: 821: 820: 796: 777: 766: 765: 744: 731: 718: 713: 712: 685: 680: 679: 658: 653: 652: 631: 626: 625: 604: 599: 598: 573: 568: 567: 544:digital circuit 528: 499: 476: 475: 466: 453: 452: 443: 436: 422: 421: 412: 374: 373: 364: 351: 350: 341: 313: 312: 303: 299:Half subtractor 294:Full subtractor 285: 284: 275: 267: 266: 257: 199: 198: 187: 186: 177: 153:Boolean algebra 144: 143: 115: 104: 98: 95: 52: 50: 40: 28: 17: 12: 11: 5: 4672: 4670: 4662: 4661: 4656: 4651: 4646: 4641: 4631: 4630: 4624: 4623: 4621: 4620: 4615: 4613:Pin grid array 4610: 4605: 4600: 4595: 4590: 4585: 4580: 4574: 4572: 4568: 4567: 4565: 4564: 4558: 4553: 4548: 4543: 4538: 4533: 4527: 4525: 4517: 4516: 4513: 4512: 4510: 4509: 4504: 4499: 4494: 4489: 4484: 4483: 4482: 4477: 4472: 4461: 4459: 4453: 4452: 4450: 4449: 4447:Barrel shifter 4444: 4443: 4442: 4437: 4430:Binary decoder 4427: 4426: 4425: 4415: 4410: 4405: 4399: 4397: 4391: 4390: 4388: 4387: 4382: 4374: 4369: 4364: 4359: 4353: 4351: 4345: 4344: 4342: 4341: 4336: 4331: 4326: 4321: 4319:Stack register 4316: 4311: 4305: 4303: 4297: 4296: 4294: 4293: 4292: 4291: 4286: 4276: 4271: 4266: 4260: 4258: 4252: 4251: 4249: 4248: 4243: 4242: 4241: 4230: 4225: 4220: 4219: 4218: 4212: 4201: 4195: 4189: 4182: 4180: 4169: 4168: 4163: 4158: 4153: 4148: 4147: 4146: 4141: 4136: 4131: 4126: 4121: 4111: 4105: 4103: 4099: 4098: 4096: 4095: 4090: 4085: 4080: 4074: 4072: 4068: 4067: 4065: 4064: 4063: 4062: 4052: 4047: 4042: 4037: 4032: 4027: 4022: 4017: 4012: 4007: 4002: 3997: 3992: 3987: 3981: 3979: 3973: 3972: 3969: 3968: 3966: 3965: 3960: 3955: 3950: 3944: 3938: 3932: 3926: 3921: 3915: 3913:AI accelerator 3910: 3904: 3902: 3894: 3893: 3891: 3890: 3884: 3879: 3876:Multiprocessor 3873: 3866: 3864: 3858: 3857: 3855: 3854: 3849: 3844: 3839: 3834: 3829: 3827:Microprocessor 3824: 3818: 3816: 3815:By application 3809: 3808: 3802: 3796: 3790: 3785: 3780: 3775: 3770: 3765: 3760: 3758:Tile processor 3755: 3750: 3745: 3740: 3739: 3738: 3727: 3720: 3718: 3712: 3711: 3709: 3708: 3703: 3698: 3692: 3686: 3680: 3674: 3668: 3667: 3666: 3654: 3648: 3646: 3638: 3637: 3634: 3633: 3631: 3630: 3629: 3628: 3618: 3613: 3612: 3611: 3606: 3601: 3596: 3586: 3580: 3578: 3572: 3571: 3569: 3568: 3563: 3558: 3553: 3552: 3551: 3546: 3544:Hyperthreading 3536: 3530: 3528: 3526:Multithreading 3522: 3521: 3519: 3518: 3513: 3508: 3507: 3506: 3496: 3495: 3494: 3489: 3479: 3478: 3477: 3472: 3462: 3457: 3456: 3455: 3450: 3439: 3437: 3430: 3424: 3423: 3420: 3419: 3417: 3416: 3411: 3405: 3403: 3397: 3396: 3394: 3393: 3388: 3383: 3382: 3381: 3376: 3366: 3360: 3358: 3352: 3351: 3349: 3348: 3343: 3338: 3333: 3327: 3325: 3319: 3318: 3316: 3315: 3310: 3305: 3303:Pipeline stall 3299: 3297: 3288: 3282: 3281: 3278: 3277: 3275: 3274: 3269: 3264: 3259: 3256: 3255: 3254: 3252:z/Architecture 3249: 3244: 3239: 3231: 3226: 3221: 3216: 3211: 3206: 3201: 3196: 3191: 3186: 3181: 3176: 3171: 3170: 3169: 3164: 3159: 3151: 3146: 3141: 3136: 3131: 3126: 3121: 3116: 3110: 3108: 3102: 3101: 3099: 3098: 3097: 3096: 3086: 3081: 3076: 3071: 3066: 3061: 3056: 3055: 3054: 3044: 3043: 3042: 3032: 3027: 3022: 3017: 3011: 3009: 3002: 2994: 2993: 2991: 2990: 2985: 2980: 2975: 2970: 2965: 2964: 2963: 2958: 2956:Virtual memory 2948: 2943: 2942: 2941: 2936: 2931: 2926: 2916: 2911: 2906: 2901: 2896: 2895: 2894: 2884: 2879: 2873: 2871: 2865: 2864: 2862: 2861: 2860: 2859: 2854: 2849: 2844: 2834: 2829: 2824: 2823: 2822: 2817: 2812: 2807: 2802: 2797: 2792: 2787: 2780:Turing machine 2777: 2776: 2775: 2770: 2765: 2760: 2755: 2750: 2740: 2735: 2729: 2727: 2721: 2720: 2715: 2713: 2712: 2705: 2698: 2690: 2684: 2683: 2676: 2675:External links 2673: 2672: 2671: 2665: 2660: 2657: 2656: 2655: 2650: 2648:Adding machine 2645: 2640: 2635: 2628: 2625: 2611: 2608: 2604: 2600: 2597: 2594: 2588: 2585: 2579: 2574: 2571: 2567: 2560: 2557: 2551: 2546: 2543: 2540: 2536: 2512: 2509: 2505: 2501: 2498: 2495: 2492: 2489: 2486: 2471: 2470: 2467: 2464: 2461: 2458: 2454: 2453: 2450: 2447: 2444: 2441: 2437: 2436: 2433: 2430: 2427: 2424: 2420: 2419: 2416: 2413: 2410: 2407: 2403: 2402: 2399: 2396: 2393: 2390: 2386: 2385: 2382: 2379: 2376: 2373: 2369: 2368: 2365: 2362: 2359: 2356: 2352: 2351: 2348: 2345: 2342: 2339: 2335: 2334: 2331: 2326: 2321: 2318: 2313: 2308: 2302: 2301: 2298: 2264: 2260: 2257: 2248: 2244: 2241: 2238: 2235: 2232: 2229: 2203: 2199: 2196: 2193: 2190: 2170: 2144: 2123: 2097: 2093: 2090: 2087: 2084: 2064: 2044: 2018: 1997: 1971: 1944: 1923: 1897: 1876: 1856: 1847:: the minuend 1836: 1833: 1827: 1823: 1822: 1810: 1807: 1802: 1799: 1794: 1785: 1774: 1763: 1760: 1757: 1754: 1751: 1722: 1701: 1684: 1683: 1680: 1677: 1674: 1670: 1669: 1666: 1663: 1660: 1656: 1655: 1652: 1649: 1646: 1642: 1641: 1638: 1635: 1632: 1628: 1627: 1624: 1619: 1614: 1609: 1603: 1602: 1599: 1562: 1547: 1546: 1534: 1531: 1526: 1523: 1518: 1509: 1479: 1458: 1455: 1452: 1432: 1429: 1426: 1406: 1403: 1400: 1380: 1377: 1374: 1354: 1351: 1342: 1321: 1301: 1281: 1278: 1275: 1255: 1252: 1243: 1216: 1195: 1175: 1152: 1125: 1122: 1121: 1120: 1105: 1102: 1096: 1093: 1087: 1084: 1081: 1078: 1076: 1074: 1071: 1068: 1065: 1062: 1059: 1056: 1053: 1050: 1048: 1046: 1043: 1040: 1037: 1036: 1025: 1024: 1012: 1009: 1003: 1000: 994: 991: 988: 963: 962: 950: 945: 941: 937: 932: 928: 924: 921: 916: 912: 908: 903: 900: 897: 893: 882: 869: 865: 861: 856: 852: 848: 842: 838: 833: 829: 803: 799: 795: 790: 787: 784: 780: 776: 773: 751: 747: 743: 738: 734: 730: 725: 721: 698: 695: 692: 688: 665: 661: 638: 634: 611: 607: 580: 576: 530: 529: 527: 526: 519: 512: 504: 501: 500: 498: 497: 492: 487: 482: 473: 472: 471: 468: 467: 465: 464: 459: 450: 449: 448: 445: 444: 442: 441: 438: 437: 435: 434: 429: 419: 418: 417: 414: 413: 411: 410: 405: 400: 395: 390: 385: 380: 371: 370: 369: 366: 365: 363: 362: 357: 355:Binary Divider 348: 347: 346: 343: 342: 340: 339: 334: 329: 324: 319: 311:Multiplier (×) 310: 309: 308: 305: 304: 302: 301: 296: 291: 283:Subtractor (−) 282: 281: 280: 277: 276: 274: 273: 264: 263: 262: 259: 258: 256: 255: 250: 245: 240: 235: 230: 225: 220: 215: 210: 205: 196: 195: 194: 184: 183: 182: 179: 178: 176: 175: 170: 165: 160: 155: 150: 141: 140: 139: 136: 135: 131: 130: 126: 125: 117: 116: 31: 29: 22: 15: 13: 10: 9: 6: 4: 3: 2: 4671: 4660: 4657: 4655: 4652: 4650: 4647: 4645: 4642: 4640: 4637: 4636: 4634: 4619: 4616: 4614: 4611: 4609: 4606: 4604: 4601: 4599: 4596: 4594: 4591: 4589: 4586: 4584: 4581: 4579: 4576: 4575: 4573: 4569: 4562: 4559: 4557: 4554: 4552: 4549: 4547: 4544: 4542: 4539: 4537: 4534: 4532: 4529: 4528: 4526: 4524: 4518: 4508: 4505: 4503: 4500: 4498: 4495: 4493: 4490: 4488: 4485: 4481: 4478: 4476: 4473: 4471: 4468: 4467: 4466: 4463: 4462: 4460: 4458: 4454: 4448: 4445: 4441: 4438: 4436: 4433: 4432: 4431: 4428: 4424: 4421: 4420: 4419: 4416: 4414: 4411: 4409: 4408:Demultiplexer 4406: 4404: 4401: 4400: 4398: 4396: 4392: 4386: 4383: 4381: 4378: 4375: 4373: 4370: 4368: 4365: 4363: 4360: 4358: 4355: 4354: 4352: 4350: 4346: 4340: 4337: 4335: 4332: 4330: 4329:Memory buffer 4327: 4325: 4324:Register file 4322: 4320: 4317: 4315: 4312: 4310: 4307: 4306: 4304: 4302: 4298: 4290: 4287: 4285: 4282: 4281: 4280: 4277: 4275: 4272: 4270: 4267: 4265: 4264:Combinational 4262: 4261: 4259: 4257: 4253: 4247: 4244: 4240: 4237: 4236: 4234: 4231: 4229: 4226: 4224: 4221: 4216: 4213: 4211: 4208: 4207: 4205: 4202: 4199: 4196: 4193: 4190: 4187: 4184: 4183: 4181: 4179: 4173: 4167: 4164: 4162: 4159: 4157: 4154: 4152: 4149: 4145: 4142: 4140: 4137: 4135: 4132: 4130: 4127: 4125: 4122: 4120: 4117: 4116: 4115: 4112: 4110: 4107: 4106: 4104: 4100: 4094: 4091: 4089: 4086: 4084: 4081: 4079: 4076: 4075: 4073: 4069: 4061: 4058: 4057: 4056: 4053: 4051: 4048: 4046: 4043: 4041: 4038: 4036: 4033: 4031: 4028: 4026: 4023: 4021: 4018: 4016: 4013: 4011: 4008: 4006: 4003: 4001: 3998: 3996: 3993: 3991: 3988: 3986: 3983: 3982: 3980: 3978: 3974: 3964: 3961: 3959: 3956: 3954: 3951: 3948: 3945: 3942: 3939: 3936: 3933: 3930: 3927: 3925: 3922: 3919: 3916: 3914: 3911: 3909: 3906: 3905: 3903: 3901: 3895: 3888: 3885: 3883: 3880: 3877: 3874: 3871: 3868: 3867: 3865: 3859: 3853: 3850: 3848: 3845: 3843: 3840: 3838: 3835: 3833: 3830: 3828: 3825: 3823: 3820: 3819: 3817: 3813: 3806: 3803: 3800: 3797: 3794: 3791: 3789: 3786: 3784: 3781: 3779: 3776: 3774: 3771: 3769: 3766: 3764: 3761: 3759: 3756: 3754: 3751: 3749: 3746: 3744: 3741: 3737: 3734: 3733: 3731: 3728: 3725: 3722: 3721: 3719: 3717: 3713: 3707: 3704: 3702: 3699: 3696: 3693: 3690: 3687: 3684: 3681: 3678: 3675: 3672: 3669: 3664: 3661: 3660: 3658: 3655: 3653: 3650: 3649: 3647: 3645: 3639: 3627: 3624: 3623: 3622: 3619: 3617: 3614: 3610: 3607: 3605: 3602: 3600: 3597: 3595: 3592: 3591: 3590: 3587: 3585: 3582: 3581: 3579: 3577: 3573: 3567: 3564: 3562: 3559: 3557: 3554: 3550: 3547: 3545: 3542: 3541: 3540: 3537: 3535: 3532: 3531: 3529: 3527: 3523: 3517: 3514: 3512: 3509: 3505: 3502: 3501: 3500: 3497: 3493: 3490: 3488: 3485: 3484: 3483: 3480: 3476: 3473: 3471: 3468: 3467: 3466: 3463: 3461: 3458: 3454: 3451: 3449: 3446: 3445: 3444: 3441: 3440: 3438: 3434: 3431: 3429: 3425: 3415: 3412: 3410: 3407: 3406: 3404: 3402: 3398: 3392: 3389: 3387: 3384: 3380: 3377: 3375: 3372: 3371: 3370: 3367: 3365: 3364:Scoreboarding 3362: 3361: 3359: 3357: 3353: 3347: 3346:False sharing 3344: 3342: 3339: 3337: 3334: 3332: 3329: 3328: 3326: 3324: 3320: 3314: 3311: 3309: 3306: 3304: 3301: 3300: 3298: 3296: 3292: 3289: 3287: 3283: 3273: 3270: 3268: 3265: 3263: 3260: 3257: 3253: 3250: 3248: 3245: 3243: 3240: 3238: 3235: 3234: 3232: 3230: 3227: 3225: 3222: 3220: 3217: 3215: 3212: 3210: 3207: 3205: 3202: 3200: 3197: 3195: 3192: 3190: 3187: 3185: 3182: 3180: 3177: 3175: 3172: 3168: 3165: 3163: 3160: 3158: 3155: 3154: 3152: 3150: 3147: 3145: 3142: 3140: 3139:Stanford MIPS 3137: 3135: 3132: 3130: 3127: 3125: 3122: 3120: 3117: 3115: 3112: 3111: 3109: 3103: 3095: 3092: 3091: 3090: 3087: 3085: 3082: 3080: 3077: 3075: 3072: 3070: 3067: 3065: 3062: 3060: 3057: 3053: 3050: 3049: 3048: 3045: 3041: 3038: 3037: 3036: 3033: 3031: 3028: 3026: 3023: 3021: 3018: 3016: 3013: 3012: 3010: 3006: 3003: 3001: 3000:architectures 2995: 2989: 2986: 2984: 2981: 2979: 2976: 2974: 2971: 2969: 2968:Heterogeneous 2966: 2962: 2959: 2957: 2954: 2953: 2952: 2949: 2947: 2944: 2940: 2937: 2935: 2932: 2930: 2927: 2925: 2922: 2921: 2920: 2919:Memory access 2917: 2915: 2912: 2910: 2907: 2905: 2902: 2900: 2897: 2893: 2890: 2889: 2888: 2885: 2883: 2880: 2878: 2875: 2874: 2872: 2870: 2866: 2858: 2855: 2853: 2852:Random-access 2850: 2848: 2845: 2843: 2840: 2839: 2838: 2835: 2833: 2832:Stack machine 2830: 2828: 2825: 2821: 2818: 2816: 2813: 2811: 2808: 2806: 2803: 2801: 2798: 2796: 2793: 2791: 2788: 2786: 2783: 2782: 2781: 2778: 2774: 2771: 2769: 2766: 2764: 2761: 2759: 2756: 2754: 2751: 2749: 2748:with datapath 2746: 2745: 2744: 2741: 2739: 2736: 2734: 2731: 2730: 2728: 2726: 2722: 2718: 2711: 2706: 2704: 2699: 2697: 2692: 2691: 2688: 2682: 2679: 2678: 2674: 2670: 2666: 2663: 2662: 2658: 2654: 2651: 2649: 2646: 2644: 2641: 2639: 2636: 2634: 2631: 2630: 2626: 2624: 2609: 2606: 2602: 2598: 2595: 2592: 2583: 2577: 2572: 2569: 2565: 2555: 2549: 2544: 2541: 2538: 2534: 2525: 2510: 2507: 2503: 2499: 2496: 2493: 2490: 2487: 2484: 2476: 2468: 2465: 2462: 2459: 2456: 2455: 2451: 2448: 2445: 2442: 2439: 2438: 2434: 2431: 2428: 2425: 2422: 2421: 2417: 2414: 2411: 2408: 2405: 2404: 2400: 2397: 2394: 2391: 2388: 2387: 2383: 2380: 2377: 2374: 2371: 2370: 2366: 2363: 2360: 2357: 2354: 2353: 2349: 2346: 2343: 2340: 2337: 2336: 2330: 2327: 2325: 2322: 2317: 2314: 2312: 2309: 2307: 2304: 2303: 2295: 2292: 2286: 2282: 2262: 2258: 2255: 2246: 2242: 2239: 2236: 2233: 2230: 2227: 2201: 2197: 2194: 2191: 2188: 2168: 2142: 2121: 2095: 2091: 2088: 2085: 2082: 2062: 2042: 2016: 1995: 1969: 1942: 1921: 1895: 1874: 1867:, subtrahend 1854: 1846: 1842: 1834: 1832: 1826: 1808: 1805: 1797: 1792: 1783: 1775: 1761: 1758: 1755: 1752: 1749: 1742: 1741: 1740: 1720: 1699: 1691: 1681: 1678: 1675: 1672: 1671: 1667: 1664: 1661: 1658: 1657: 1653: 1650: 1647: 1644: 1643: 1639: 1636: 1633: 1630: 1629: 1623: 1620: 1618: 1615: 1613: 1610: 1608: 1605: 1604: 1596: 1593: 1591: 1582: 1578: 1576: 1560: 1552: 1532: 1529: 1521: 1516: 1507: 1499: 1498: 1497: 1477: 1456: 1453: 1450: 1430: 1427: 1424: 1404: 1401: 1398: 1378: 1375: 1372: 1352: 1349: 1340: 1319: 1299: 1279: 1276: 1273: 1253: 1250: 1241: 1214: 1193: 1173: 1166: 1150: 1143: 1139: 1130: 1123: 1103: 1100: 1091: 1085: 1082: 1079: 1077: 1066: 1063: 1057: 1054: 1051: 1049: 1044: 1041: 1038: 1027: 1026: 1010: 1007: 998: 992: 989: 986: 979: 978: 977: 975: 970: 968: 943: 939: 935: 930: 926: 919: 914: 910: 906: 901: 898: 895: 891: 883: 867: 863: 859: 854: 850: 846: 840: 836: 831: 827: 819: 818: 817: 801: 797: 793: 788: 785: 782: 778: 774: 771: 749: 745: 741: 736: 732: 728: 723: 719: 696: 693: 690: 686: 663: 659: 636: 632: 609: 605: 596: 578: 574: 565: 561: 557: 553: 549: 545: 541: 537: 525: 520: 518: 513: 511: 506: 505: 503: 502: 496: 493: 491: 488: 486: 483: 481: 478: 470: 469: 463: 460: 458: 455: 447: 446: 433: 430: 427: 424: 416: 415: 409: 406: 404: 401: 399: 396: 394: 391: 389: 386: 384: 381: 379: 376: 368: 367: 361: 358: 356: 353: 345: 344: 338: 335: 333: 330: 328: 325: 323: 320: 318: 315: 307: 306: 300: 297: 295: 292: 290: 287: 279: 278: 272: 269: 261: 260: 254: 251: 249: 246: 244: 241: 239: 236: 234: 231: 229: 226: 224: 221: 219: 216: 214: 211: 209: 206: 204: 201: 193: 192: 189: 181: 180: 174: 171: 169: 166: 164: 161: 159: 156: 154: 151: 149: 148:Binary number 146: 138: 137: 133: 132: 127: 123: 122: 113: 110: 102: 99:December 2009 91: 88: 84: 81: 77: 74: 70: 67: 63: 60: â€“  59: 55: 54:Find sources: 48: 44: 38: 37: 32:This article 30: 26: 21: 20: 4618:Chip carrier 4556:Clock gating 4475:Mixed-signal 4372:Write buffer 4349:Control unit 4161:Clock signal 3900:accelerators 3882:Cypress PSoC 3539:Simultaneous 3356:Out-of-order 2988:Neuromorphic 2869:Architecture 2827:Belt machine 2820:Zeno machine 2753:Hierarchical 2526: 2477: 2474: 2328: 2323: 2315: 2310: 2305: 2290: 1838: 1830: 1824: 1690:Karnaugh map 1687: 1621: 1616: 1611: 1606: 1587: 1548: 1135: 971: 967:exclusive or 964: 539: 533: 332:Wallace tree 288: 105: 96: 86: 79: 72: 65: 58:"Subtractor" 53: 41:Please help 36:verification 33: 4654:Subtraction 4403:Multiplexer 4367:Data buffer 4078:Single-core 4050:bit slicing 3908:Coprocessor 3763:Coprocessor 3644:performance 3566:Cooperative 3556:Speculative 3516:Distributed 3475:Superscalar 3460:Instruction 3428:Parallelism 3401:Speculative 3233:System/3x0 3105:Instruction 2882:Von Neumann 2795:Post–Turing 1590:truth table 1551:commutative 536:electronics 372:Bitwise ops 349:Divider (á) 4633:Categories 4523:management 4418:Multiplier 4279:Logic gate 4269:Sequential 4176:Functional 4156:Clock rate 4129:Data cache 4102:Components 4083:Multi-core 4071:Core count 3561:Preemptive 3465:Pipelining 3448:Bit-serial 3391:Wide-issue 3336:Structural 3258:Tilera ISA 3224:MicroBlaze 3194:ETRAX CRIS 3089:Comparison 2934:Load–store 2914:Endianness 2659:References 1332:are bits, 1165:subtrahend 595:subtrahend 560:difference 540:subtractor 451:Categories 403:Bit shifts 289:Subtractor 238:Ling adder 213:Full adder 208:Half adder 185:Components 158:Logic gate 69:newspapers 4457:Circuitry 4377:Microcode 4301:Registers 4144:coherence 4119:CPU cache 3977:Word size 3642:Processor 3286:Execution 3189:DEC Alpha 3167:Power ISA 2983:Cognitive 2790:Universal 2587:¯ 2559:¯ 2500:⊕ 2494:⊕ 2243:− 2237:− 2092:− 2086:− 1806:⋅ 1801:¯ 1759:⊕ 1530:⋅ 1525:¯ 1454:− 1428:− 1095:¯ 1064:− 1042:− 1002:¯ 987:− 860:⊕ 847:⊕ 772:− 742:− 729:− 197:Adder (+) 4395:Datapath 4088:Manycore 4060:variable 3898:Hardware 3534:Temporal 3214:OpenRISC 2909:Cellular 2899:Dataflow 2892:modified 2627:See also 2300:Outputs 2008:. Thus, 1601:Outputs 1575:XOR gate 1443:and not 1292:. Since 474:See also 420:See also 4571:Related 4502:Quantum 4492:Digital 4487:Boolean 4385:Counter 4284:Quantum 4045:512-bit 4040:256-bit 4035:128-bit 3878:(MPSoC) 3863:on chip 3861:Systems 3679:(FLOPS) 3492:Process 3341:Control 3323:Hazards 3209:Itanium 3204:Unicore 3162:PowerPC 2887:Harvard 2847:Pointer 2842:Counter 2800:Quantum 2297:Inputs 1598:Inputs 1142:minuend 564:minuend 83:scholar 4507:Switch 4497:Analog 4235:(IMC) 4206:(MMU) 4055:others 4030:64-bit 4025:48-bit 4020:32-bit 4015:24-bit 4010:16-bit 4005:15-bit 4000:12-bit 3837:Mobile 3753:Stream 3748:Barrel 3743:Vector 3732:(GPU) 3691:(SUPS) 3659:(IPC) 3511:Memory 3504:Vector 3487:Thread 3470:Scalar 3272:Others 3219:RISC-V 3184:SuperH 3153:Power 3149:MIPS-X 3124:PDP-11 2973:Fabric 2725:Models 1469:since 562:: the 552:binary 550:. The 142:Theory 85:  78:  71:  64:  56:  4563:(PPW) 4521:Power 4413:Adder 4289:Array 4256:Logic 4217:(TLB) 4200:(FPU) 4194:(AGU) 4188:(ALU) 4178:units 4114:Cache 3995:8-bit 3990:4-bit 3985:1-bit 3949:(TPU) 3943:(DSP) 3937:(PPU) 3931:(VPU) 3920:(GPU) 3889:(NoC) 3872:(SoC) 3807:(PoP) 3801:(SiP) 3795:(MCM) 3736:GPGPU 3726:(CPU) 3716:Types 3697:(PPW) 3685:(TPS) 3673:(IPS) 3665:(CPI) 3436:Level 3247:S/390 3242:S/370 3237:S/360 3179:SPARC 3157:POWER 3040:TRIPS 3008:Types 2161:from 1266:when 548:adder 203:Adder 90:JSTOR 76:books 4541:ACPI 4274:Glue 4166:FIFO 4109:Core 3847:ASIP 3788:CPLD 3783:FPOA 3778:FPGA 3773:ASIC 3626:SPMD 3621:MIMD 3616:MISD 3609:SWAR 3589:SIMD 3584:SISD 3499:Data 3482:Task 3453:Word 3199:M32R 3144:MIPS 3107:sets 3074:ZISC 3069:NISC 3064:OISC 3059:MISC 3052:EPIC 3047:VLIW 3035:EDGE 3025:RISC 3020:CISC 2929:HUMA 2924:NUMA 2192:< 2134:and 1845:bits 1712:and 1588:The 1391:and 1312:and 1277:< 1163:and 920:< 556:bits 542:– a 538:, a 62:news 4536:APM 4531:PMU 4423:CPU 4380:ROM 4151:Bus 3768:PAL 3443:Bit 3229:LMC 3134:ARM 3129:x86 3119:VAX 2332:out 2267:out 1947:out 1788:out 1725:out 1625:out 1512:out 1482:out 1345:out 1246:out 1219:out 593:), 534:In 490:AGU 485:GPU 480:FPU 398:XOR 388:AND 383:NOT 45:by 4635:: 4470:3D 2469:1 2452:0 2435:0 2418:0 2401:1 2384:1 2367:1 2350:0 2319:in 2281:. 2251:in 2206:in 2147:in 2100:in 2021:in 1974:in 1961:. 1900:in 1739:: 1682:0 1679:0 1676:1 1673:1 1668:0 1665:1 1662:0 1659:1 1654:1 1651:1 1648:1 1645:0 1640:0 1637:0 1634:0 1631:0 969:. 816:. 393:OR 2709:e 2702:t 2695:v 2610:n 2607:i 2603:B 2599:Y 2596:+ 2593:Y 2584:X 2578:+ 2573:n 2570:i 2566:B 2556:X 2550:= 2545:t 2542:u 2539:o 2535:B 2511:n 2508:i 2504:B 2497:Y 2491:X 2488:= 2485:D 2466:1 2463:1 2460:1 2457:1 2449:0 2446:0 2443:1 2440:1 2432:0 2429:1 2426:0 2423:1 2415:1 2412:0 2409:0 2406:1 2398:0 2395:1 2392:1 2389:0 2381:1 2378:0 2375:1 2372:0 2364:1 2361:1 2358:0 2355:0 2347:0 2344:0 2341:0 2338:0 2329:B 2324:D 2316:B 2311:Y 2306:X 2263:B 2259:2 2256:+ 2247:B 2240:Y 2234:X 2231:= 2228:D 2202:B 2198:+ 2195:Y 2189:X 2169:X 2143:B 2122:Y 2096:B 2089:Y 2083:X 2063:Y 2043:X 2017:B 1996:X 1970:B 1943:B 1922:D 1896:B 1875:Y 1855:X 1821:. 1809:Y 1798:X 1793:= 1784:B 1762:Y 1756:X 1753:= 1750:D 1721:B 1700:D 1622:B 1617:D 1612:Y 1607:X 1561:D 1545:. 1533:Y 1522:X 1517:= 1508:B 1478:B 1457:X 1451:Y 1431:Y 1425:X 1405:1 1402:= 1399:Y 1379:0 1376:= 1373:X 1353:1 1350:= 1341:B 1320:Y 1300:X 1280:Y 1274:X 1254:1 1251:= 1242:B 1215:B 1194:D 1174:Y 1151:X 1104:1 1101:+ 1092:B 1086:+ 1083:A 1080:= 1070:) 1067:B 1061:( 1058:+ 1055:A 1052:= 1045:B 1039:A 1011:1 1008:+ 999:B 993:= 990:B 961:, 949:) 944:i 940:B 936:+ 931:i 927:Y 923:( 915:i 911:X 907:= 902:1 899:+ 896:i 892:B 868:i 864:B 855:i 851:Y 841:X 837:= 832:i 828:D 802:i 798:D 794:+ 789:1 786:+ 783:i 779:B 775:2 750:i 746:B 737:i 733:Y 724:i 720:X 697:1 694:+ 691:i 687:B 664:i 660:D 637:i 633:B 610:i 606:Y 597:( 579:i 575:X 566:( 523:e 516:t 509:v 112:) 106:( 101:) 97:( 87:¡ 80:¡ 73:¡ 66:¡ 39:.

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Binary number
Boolean algebra
Logic gate
Ones' complement number
Two's complement number
Signed number representations
Adder
Half adder
Full adder
Ripple-carry adder
Carry-lookahead adder
Brent–Kung adder
Kogge–Stone adder
Ling adder
Carry-save adder
Carry-select adder
Carry-skip adder
Adder–subtractor
Subtractor

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