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60Z",[555,1070,1071],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,1072,1073,1078,1089,1095,1104,1109,1116,1121],{"dataMmlNode":562},[555,1074,1075],{"dataMmlNode":616},[567,1076],{"dataC":620,"xLinkHref":1077},"#MJX-4-TEX-N-3D",[555,1079,1080,1084,1087],{"dataMmlNode":906,"transform":734},[567,1081],{"dataC":1082,"xLinkHref":1083},"34","#MJX-4-TEX-N-34",[567,1085],{"dataC":913,"xLinkHref":1086,"transform":915},"#MJX-4-TEX-N-30",[567,1088],{"dataC":913,"xLinkHref":1086,"transform":918},[555,1090,1092],{"dataMmlNode":616,"transform":1091},"translate(2778,0)",[567,1093],{"dataC":637,"xLinkHref":1094},"#MJX-4-TEX-N-2B",[555,1096,1098,1102],{"dataMmlNode":906,"transform":1097},"translate(3778.2,0)",[567,1099],{"dataC":1100,"xLinkHref":1101},"33","#MJX-4-TEX-N-33",[567,1103],{"dataC":913,"xLinkHref":1086,"transform":915},[555,1105,1107],{"dataMmlNode":616,"transform":1106},"translate(5000.4,0)",[567,1108],{"dataC":637,"xLinkHref":1094},[555,1110,1112],{"dataMmlNode":906,"transform":1111},"translate(6000.7,0)",[567,1113],{"dataC":1114,"xLinkHref":1115},"37","#MJX-4-TEX-N-37",[555,1117,1119],{"dataMmlNode":616,"transform":1118},"translate(6778.4,0)",[567,1120],{"dataC":620,"xLinkHref":1077},[555,1122,1124,1126,1128,1130],{"dataMmlNode":906,"transform":1123},"translate(7834.2,0)",[567,1125],{"dataC":1082,"xLinkHref":1083},[567,1127],{"dataC":1100,"xLinkHref":1101,"transform":915},[567,1129],{"dataC":1114,"xLinkHref":1115,"transform":918},[567,1131],{"dataC":1132,"xLinkHref":1133,"transform":1134},"2E","#MJX-4-TEX-N-2E","translate(1500,0)",[1136,1137,1139],"h5",{"id":1138},"основание-позиционной-системы-счисления","Основание позиционной системы счисления",[406,1141,1142],{},"Основание системы счисления определяет изменение количественного значения(\"во сколько раз\") при изменении положения цифры в числе на один разряд правее\u002Fлевее и равно количеству цифр в алфавите системы счисления.",[406,1144,1145],{},"Теоретически возможно любое значение основания системы счисления, начиная с 2.\nДля системы счисления с основанием p, меньше 10, в качестве знаков алфавита системы счисления используются десятичные цифры от 0 до (p - 1).\nДля систем с основанием p, больше 10, используются все 10 десятичных цифр плюс дополнительные символы(обычно — латинские заглавные буквы, начиная с \"А\").\nНа практике системы счисления с основанием больше 16 практически не используются (за исключением измерения времени и градусной меры углов, основанных на системе счисления с основанием 60).\nОбычно при записи числа значение основания системы счисления записывается в виде нижнего индекса после последней цифры числа.",[1136,1147,1149],{"id":1148},"примеры-наиболее-часто-используемых-систем-счисления","Примеры наиболее часто используемых систем счисления",[426,1151,1152,1167],{},[429,1153,1154],{},[432,1155,1156,1158,1161,1164],{},[435,1157,411],{},[435,1159,1160],{},"Основание(p)",[435,1162,1163],{},"Алфавит системы счисления",[435,1165,1166],{},"Пример записи числа",[460,1168,1169,1183,1197,1210],{},[432,1170,1171,1174,1177,1180],{},[465,1172,1173],{},"Двоичная",[465,1175,1176],{},"2",[465,1178,1179],{},"0,1",[465,1181,1182],{},"101101",[432,1184,1185,1188,1191,1194],{},[465,1186,1187],{},"Восьмеричная",[465,1189,1190],{},"8",[465,1192,1193],{},"0,1,2,3,4,5,6,7",[465,1195,1196],{},"1234567",[432,1198,1199,1202,1204,1207],{},[465,1200,1201],{},"Десятичная",[465,1203,482],{},[465,1205,1206],{},"0,1,2,3,4,5,6,7,8,9",[465,1208,1209],{},"999",[432,1211,1212,1215,1218,1221],{},[465,1213,1214],{},"Шестнадцатеричная",[465,1216,1217],{},"16",[465,1219,1220],{},"0,1,2,3,4,5,6,7,8,9,A=10,B=11,C=12,D=13,E=14,F=15",[465,1222,1223],{},"F4D9",[1136,1225,1227],{"id":1226},"формы-записи-чисел-в-различных-системах-счисления","Формы записи чисел в различных системах счисления",[406,1229,1230,1233],{},[409,1231,1232],{},"Свёрнутая(\"обычная\") форма записи числа"," — привычная запись числа как последовательности цифр, стоящих на своих разрядах.",[406,1235,1236,1239],{},[409,1237,1238],{},"Развёрнутая форма записи числа"," — запись числа в виде суммы произведений его цифр на основание системы счисления в степени, равной значению разряда той или иной цифры числа (для целого числа нумерация разрядов ведётся с нуля справа налево; для дробного числа нумерация разрядов ведётся от десятичной запятой влево по возрастанию, а вправо — по убыванию, при этом разряду единиц присваивается нулевой номер).",[406,1241,1242,1245],{},[409,1243,1244],{},"Формула (схема) Горнера"," — преобразованная запись развёрнутой формы, при которой за счёт использования скобок удаётся избавиться от возведения основания счисления в степени.\nСхема Горнера предполагает рекуррентные вычисления.",[406,1247,1248],{},[1249,1250,1251],"em",{},"Примеры:",[406,1253,1254],{},"а) для целых чисел:",[426,1256,1257,1276],{},[429,1258,1259],{},[432,1260,1261,1264,1267,1270,1273],{},[435,1262,1263],{},"Формы записи",[435,1265,1266],{},"Двоичное",[435,1268,1269],{},"Восьмеричное",[435,1271,1272],{},"Десятичное",[435,1274,1275],{},"Шестнадцатеричное",[460,1277,1278,1459,2080],{},[432,1279,1280,1283,1321,1365,1404],{},[465,1281,1282],{},"Свёрнутая",[465,1284,1285],{},[506,1286,1288],{"className":1287,"jax":510},[509],[512,1289,1294,1302],{"style":1290,"xmlns":515,"width":1291,"height":1292,"role":518,"focusable":519,"viewBox":1293,"xmlnsXLink":521},"vertical-align: -0.05ex;","5.656ex","1.557ex","0 -666 2500 688",[523,1295,1296,1299],{},[526,1297],{"id":1298,"d":883},"MJX-5-TEX-N-31",[526,1300],{"id":1301,"d":876},"MJX-5-TEX-N-30",[555,1303,1304],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,1305,1306],{"dataMmlNode":562},[555,1307,1308,1311,1314,1316,1318],{"dataMmlNode":906},[567,1309],{"dataC":930,"xLinkHref":1310},"#MJX-5-TEX-N-31",[567,1312],{"dataC":913,"xLinkHref":1313,"transform":915},"#MJX-5-TEX-N-30",[567,1315],{"dataC":913,"xLinkHref":1313,"transform":918},[567,1317],{"dataC":930,"xLinkHref":1310,"transform":1134},[567,1319],{"dataC":913,"xLinkHref":1313,"transform":1320},"translate(2000,0)",[465,1322,1323],{},[506,1324,1326],{"className":1325,"jax":510},[509],[512,1327,1331,1346],{"style":1290,"xmlns":515,"width":1328,"height":1329,"role":518,"focusable":519,"viewBox":1330,"xmlnsXLink":521},"4.525ex","1.581ex","0 -677 2000 699",[523,1332,1333,1336,1340,1343],{},[526,1334],{"id":1335,"d":883},"MJX-6-TEX-N-31",[526,1337],{"id":1338,"d":1339},"MJX-6-TEX-N-32","M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 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целого десятичного числа в недесятичную систему счисления",[406,4593,4594],{},"Перевод целого десятичного числа в недесятичную систему счисления выполняется путём последовательного деления числа с остатком на основание системы счисления с последующей записью полученного результата и остатков на каждом шаге деления в порядке, обратном порядку их получения.\nДеление производится до тех пор, пока полученный на очередном шаге результат не будет меньше основания системы счисления.",[406,4596,4597,4598],{},"Пример: перевести число 12345 в троичную систему счисления.\n",[518,4599],{"alt":4600,"src":4601},"Перевод числа 12345 в троичную систему счисления","\u002Fimages\u002Fblog\u002Ftoi\u002Fst5\u002Fimg1.png",[406,4603,4604,4605],{},"В результате:\n",[506,4606,4608],{"className":4607,"jax":510},[509],[512,4609,4614,4640],{"style":4610,"xmlns":515,"width":4611,"height":4612,"role":518,"focusable":519,"viewBox":4613,"xmlnsXLink":521},"vertical-align: -0.375ex;","22.258ex","1.906ex","0 -677 9838.2 842.6",[523,4615,4616,4619,4622,4625,4628,4631,4634,4637],{},[526,4617],{"id":4618,"d":883},"MJX-31-TEX-N-31",[526,4620],{"id":4621,"d":1339},"MJX-31-TEX-N-32",[526,4623],{"id":4624,"d":1060},"MJX-31-TEX-N-33",[526,4626],{"id":4627,"d":1050},"MJX-31-TEX-N-34",[526,4629],{"id":4630,"d":872},"MJX-31-TEX-N-35",[526,4632],{"id":4633,"d":876},"MJX-31-TEX-N-30",[526,4635],{"id":4636,"d":549},"MJX-31-TEX-N-3D",[526,4638],{"id":4639,"d":1068},"MJX-31-TEX-N-2E",[555,4641,4642],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,4643,4644,4673,4679,4711],{"dataMmlNode":562},[555,4645,4646,4663],{"dataMmlNode":3570},[555,4647,4648,4651,4654,4657,4660],{"dataMmlNode":906},[567,4649],{"dataC":930,"xLinkHref":4650},"#MJX-31-TEX-N-31",[567,4652],{"dataC":1357,"xLinkHref":4653,"transform":915},"#MJX-31-TEX-N-32",[567,4655],{"dataC":1100,"xLinkHref":4656,"transform":918},"#MJX-31-TEX-N-33",[567,4658],{"dataC":1082,"xLinkHref":4659,"transform":1134},"#MJX-31-TEX-N-34",[567,4661],{"dataC":909,"xLinkHref":4662,"transform":1320},"#MJX-31-TEX-N-35",[555,4664,4666],{"dataMmlNode":3010,"transform":4665,"dataMjxTexclass":3011},"translate(2533,-150) 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scale(0.707)",[567,4710],{"dataC":1100,"xLinkHref":4656},[555,4712,4714],{"dataMmlNode":616,"transform":4713},"translate(9560.2,0)",[567,4715],{"dataC":1132,"xLinkHref":4716},"#MJX-31-TEX-N-2E",[1136,4718,4720],{"id":4719},"перевод-десятичной-дроби-в-недесятичную-систему-счисления","Перевод десятичной дроби в недесятичную систему счисления",[406,4722,4723],{},"Перевод десятичной дроби в недесятичную систему счисления выполняется путём последовательного умножения числа на основание системы счисления с отбрасыванием получаемых целых частей на каждом шаге умножения и последующей записью полученных значений целых частей по порядку их получения.\nУмножение производится до получения значения с нулевой дробной частью либо до достижения необходимой точности представления дроби(необходимого количества значащих цифр после запятой).",[406,4725,4726,4727,4846,4952,5047,5142,5237,5240],{},"Пример: требуется перевести число 0,123 в пятеричную систему счисления с точностью до 5 значащих цифр после 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5 значащих цифр — прекращаем вычисления.","\nВ результате: 0,123 ≈ 0,03030(в пятеричной системе)",[5242,5243,5244],"blockquote",{},[406,5245,5246],{},"Представление десятичной дроби в недесятичной системе счисления, как правило, является приближённым(за исключением случаев, когда последовательность делений завершается получением нулевой дробной части либо за счёт представления дроби как периодической).",[1136,5248,5250],{"id":5249},"перевод-вещественного-десятичного-числа-в-недесятичную-систему-счисления","Перевод вещественного десятичного числа в недесятичную систему счисления",[406,5252,5253],{},"Перевод вещественного десятичного числа в недесятичную систему счисления выполняется в два этапа:",[5255,5256,5257,5260],"ol",{},[496,5258,5259],{},"Отдельно осуществляется перевод целой части числа путём последовательности делений на основание системы счисления;",[496,5261,5262],{},"Отдельно выполняется перевод дробной части числа путём последовательности умножений на основание системы счисления.",[406,5264,5265],{},"Запись целой части числа в искомой системе счисления дополняется справа запятой и записью дробной части в искомой системе счисления.\nПример: требуется перевести число 15,12 в пятеричную систему счисления с точностью до 5 значащих цифр после запятой:",[5255,5267,5268,5348],{},[496,5269,5270],{},[506,5271,5273],{"className":5272,"jax":510},[509],[512,5274,5277,5298],{"style":2686,"xmlns":515,"width":5275,"height":2688,"role":518,"focusable":519,"viewBox":5276,"xmlnsXLink":521},"10.946ex","0 -666 4838.2 860",[523,5278,5279,5282,5285,5288,5291,5294],{},[526,5280],{"id":5281,"d":883},"MJX-37-TEX-N-31",[526,5283],{"id":5284,"d":872},"MJX-37-TEX-N-35",[526,5286],{"id":5287,"d":876},"MJX-37-TEX-N-30",[526,5289],{"id":5290,"d":549},"MJX-37-TEX-N-3D",[526,5292],{"id":5293,"d":1060},"MJX-37-TEX-N-33",[526,5295],{"id":5296,"d":5297},"MJX-37-TEX-N-3B","M78 370Q78 394 95 412T138 430Q162 430 180 414T199 371Q199 346 182 328T139 310T96 327T78 370ZM78 60Q78 85 94 103T137 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860",[523,5358,5359,5362,5365,5368,5371,5374,5377,5380],{},[526,5360],{"id":5361,"d":876},"MJX-38-TEX-N-30",[526,5363],{"id":5364,"d":2701},"MJX-38-TEX-N-2C",[526,5366],{"id":5367,"d":883},"MJX-38-TEX-N-31",[526,5369],{"id":5370,"d":1339},"MJX-38-TEX-N-32",[526,5372],{"id":5373,"d":549},"MJX-38-TEX-N-3D",[526,5375],{"id":5376,"d":1060},"MJX-38-TEX-N-33",[526,5378],{"id":5379,"d":872},"MJX-38-TEX-N-35",[526,5381],{"id":5382,"d":1068},"MJX-38-TEX-N-2E",[555,5384,5385],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,5386,5387,5392,5397,5415,5421,5426,5431,5446],{"dataMmlNode":562},[555,5388,5389],{"dataMmlNode":906},[567,5390],{"dataC":913,"xLinkHref":5391},"#MJX-38-TEX-N-30",[555,5393,5394],{"dataMmlNode":616,"transform":915},[567,5395],{"dataC":2720,"xLinkHref":5396},"#MJX-38-TEX-N-2C",[555,5398,5399,5407],{"dataMmlNode":3570,"transform":4792},[555,5400,5401,5404],{"dataMmlNode":906},[567,5402],{"dataC":930,"xLinkHref":5403},"#MJX-38-TEX-N-31",[567,5405],{"dataC":1357,"xLinkHref":5406,"transform":915},"#MJX-38-TEX-N-32",[555,5408,5409],{"dataMmlNode":3010,"transform":3579,"dataMjxTexclass":3011},[555,5410,5411,5413],{"dataMmlNode":906},[567,5412],{"dataC":930,"xLinkHref":5403},[567,5414],{"dataC":913,"xLinkHref":5391,"transform":915},[555,5416,5418],{"dataMmlNode":616,"transform":5417},"translate(3012.6,0)",[567,5419],{"dataC":620,"xLinkHref":5420},"#MJX-38-TEX-N-3D",[555,5422,5424],{"dataMmlNode":906,"transform":5423},"translate(4068.3,0)",[567,5425],{"dataC":913,"xLinkHref":5391},[555,5427,5429],{"dataMmlNode":616,"transform":5428},"translate(4568.3,0)",[567,5430],{"dataC":2720,"xLinkHref":5396},[555,5432,5434,5441],{"dataMmlNode":3570,"transform":5433},"translate(5013,0)",[555,5435,5436,5438],{"dataMmlNode":906},[567,5437],{"dataC":913,"xLinkHref":5391},[567,5439],{"dataC":1100,"xLinkHref":5440,"transform":915},"#MJX-38-TEX-N-33",[555,5442,5443],{"dataMmlNode":906,"transform":3579},[567,5444],{"dataC":909,"xLinkHref":5445},"#MJX-38-TEX-N-35",[555,5447,5449],{"dataMmlNode":616,"transform":5448},"translate(6449.5,0)",[567,5450],{"dataC":1132,"xLinkHref":5451},"#MJX-38-TEX-N-2E","\nВ результате: ",[506,5454,5456],{"className":5455,"jax":510},[509],[512,5457,5460,5486],{"style":2686,"xmlns":515,"width":5458,"height":2688,"role":518,"focusable":519,"viewBox":5459,"xmlnsXLink":521},"17.483ex","0 -666 7727.5 860",[523,5461,5462,5465,5468,5471,5474,5477,5480,5483],{},[526,5463],{"id":5464,"d":883},"MJX-39-TEX-N-31",[526,5466],{"id":5467,"d":872},"MJX-39-TEX-N-35",[526,5469],{"id":5470,"d":2701},"MJX-39-TEX-N-2C",[526,5472],{"id":5473,"d":1339},"MJX-39-TEX-N-32",[526,5475],{"id":5476,"d":876},"MJX-39-TEX-N-30",[526,5478],{"id":5479,"d":549},"MJX-39-TEX-N-3D",[526,5481],{"id":5482,"d":1060},"MJX-39-TEX-N-33",[526,5484],{"id":5485,"d":1068},"MJX-39-TEX-N-2E",[555,5487,5488],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,5489,5490,5498,5503,5522,5528,5535,5540,5553],{"dataMmlNode":562},[555,5491,5492,5495],{"dataMmlNode":906},[567,5493],{"dataC":930,"xLinkHref":5494},"#MJX-39-TEX-N-31",[567,5496],{"dataC":909,"xLinkHref":5497,"transform":915},"#MJX-39-TEX-N-35",[555,5499,5500],{"dataMmlNode":616,"transform":918},[567,5501],{"dataC":2720,"xLinkHref":5502},"#MJX-39-TEX-N-2C",[555,5504,5506,5513],{"dataMmlNode":3570,"transform":5505},"translate(1444.7,0)",[555,5507,5508,5510],{"dataMmlNode":906},[567,5509],{"dataC":930,"xLinkHref":5494},[567,5511],{"dataC":1357,"xLinkHref":5512,"transform":915},"#MJX-39-TEX-N-32",[555,5514,5515],{"dataMmlNode":3010,"transform":3579,"dataMjxTexclass":3011},[555,5516,5517,5519],{"dataMmlNode":906},[567,5518],{"dataC":930,"xLinkHref":5494},[567,5520],{"dataC":913,"xLinkHref":5521,"transform":915},"#MJX-39-TEX-N-30",[555,5523,5525],{"dataMmlNode":616,"transform":5524},"translate(3512.6,0)",[567,5526],{"dataC":620,"xLinkHref":5527},"#MJX-39-TEX-N-3D",[555,5529,5530,5533],{"dataMmlNode":906,"transform":5428},[567,5531],{"dataC":1100,"xLinkHref":5532},"#MJX-39-TEX-N-33",[567,5534],{"dataC":913,"xLinkHref":5521,"transform":915},[555,5536,5538],{"dataMmlNode":616,"transform":5537},"translate(5568.3,0)",[567,5539],{"dataC":2720,"xLinkHref":5502},[555,5541,5543,5549],{"dataMmlNode":3570,"transform":5542},"translate(6013,0)",[555,5544,5545,5547],{"dataMmlNode":906},[567,5546],{"dataC":913,"xLinkHref":5521},[567,5548],{"dataC":1100,"xLinkHref":5532,"transform":915},[555,5550,5551],{"dataMmlNode":906,"transform":3579},[567,5552],{"dataC":909,"xLinkHref":5497},[555,5554,5556],{"dataMmlNode":616,"transform":5555},"translate(7449.5,0)",[567,5557],{"dataC":1132,"xLinkHref":5558},"#MJX-39-TEX-N-2E",[1136,5560,5562],{"id":5561},"перевод-чисел-между-недесятичными-системами-счисления","Перевод чисел между недесятичными системами счисления",[406,5564,5565],{},"Перевод чисел между недесятичными системами счисления обычно удобнее всего производить через десятичную систему счисления:",[5255,5567,5568,5571],{},[496,5569,5570],{},"Перевести исходное число в десятичную систему счисления;",[496,5572,5573],{},"Перевести полученное десятичное число в требуемую систему счисления.",[1136,5575,5577],{"id":5576},"перевод-чисел-между-системами-счисления-с-кратными-основаниями","Перевод чисел между системами счисления с кратными основаниями",[406,5579,5580],{},"Если основания исходной и конечной системы кратны друг другу, то перевод чисел между этими системами счисления можно выполнять по упрощённой схеме.",[5582,5583,5585],"h6",{"id":5584},"перевод-двоичного-числа-в-восьмеричную-систему-счисления","Перевод двоичного числа в восьмеричную систему счисления",[406,5587,5588,5589,5592],{},"Перевод двоичного числа в восьмеричную систему счисления производится по ",[1249,5590,5591],{},"триадам"," цифр:",[493,5594,5595,5598],{},[496,5596,5597],{},"Исходное двоичное число разбивается на группы по три цифры(триады) справа налево; при необходимости крайняя слева группа цифр дополняется незначащими нулями слева;",[496,5599,5600],{},"Каждая триада двоичных цифр заменяется соответствующим ей восьмеричным значением согласно таблице:",[426,5602,5603,5633],{},[429,5604,5605],{},[432,5606,5607,5610,5613,5616,5619,5622,5624,5627,5630],{},[435,5608,5609],{},"Двоичная триада",[435,5611,5612],{},"000",[435,5614,5615],{},"001",[435,5617,5618],{},"010",[435,5620,5621],{},"011",[435,5623,476],{},[435,5625,5626],{},"101",[435,5628,5629],{},"110",[435,5631,5632],{},"111",[460,5634,5635],{},[432,5636,5637,5640,5642,5644,5646,5649,5652,5654,5657],{},[465,5638,5639],{},"Восьмеричное значение",[465,5641,558],{},[465,5643,488],{},[465,5645,1176],{},[465,5647,5648],{},"3",[465,5650,5651],{},"4",[465,5653,485],{},[465,5655,5656],{},"6",[465,5658,5659],{},"7",[406,5661,5662,5663,5666,5667],{},"Пример: требуется перевести число 1011010 в восьмеричную систему счисления: 1011010 → ",[409,5664,5665],{},"00","1 011 010 → 1 3 2.\nВ результате: ",[506,5668,5670],{"className":5669,"jax":510},[509],[512,5671,5675,5698],{"style":4610,"xmlns":515,"width":5672,"height":5673,"role":518,"focusable":519,"viewBox":5674,"xmlnsXLink":521},"16.934ex","1.881ex","0 -666 7484.7 831.6",[523,5676,5677,5680,5683,5686,5689,5692,5695],{},[526,5678],{"id":5679,"d":883},"MJX-40-TEX-N-31",[526,5681],{"id":5682,"d":876},"MJX-40-TEX-N-30",[526,5684],{"id":5685,"d":1339},"MJX-40-TEX-N-32",[526,5687],{"id":5688,"d":549},"MJX-40-TEX-N-3D",[526,5690],{"id":5691,"d":1060},"MJX-40-TEX-N-33",[526,5693],{"id":5694,"d":1423},"MJX-40-TEX-N-38",[526,5696],{"id":5697,"d":1068},"MJX-40-TEX-N-2E",[555,5699,5700],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,5701,5702,5728,5734,5752],{"dataMmlNode":562},[555,5703,5704,5722],{"dataMmlNode":3570},[555,5705,5706,5709,5712,5714,5716,5718,5720],{"dataMmlNode":906},[567,5707],{"dataC":930,"xLinkHref":5708},"#MJX-40-TEX-N-31",[567,5710],{"dataC":913,"xLinkHref":5711,"transform":915},"#MJX-40-TEX-N-30",[567,5713],{"dataC":930,"xLinkHref":5708,"transform":918},[567,5715],{"dataC":930,"xLinkHref":5708,"transform":1134},[567,5717],{"dataC":913,"xLinkHref":5711,"transform":1320},[567,5719],{"dataC":930,"xLinkHref":5708,"transform":4696},[567,5721],{"dataC":913,"xLinkHref":5711,"transform":4699},[555,5723,5725],{"dataMmlNode":906,"transform":5724},"translate(3533,-150) scale(0.707)",[567,5726],{"dataC":1357,"xLinkHref":5727},"#MJX-40-TEX-N-32",[555,5729,5731],{"dataMmlNode":616,"transform":5730},"translate(4214.3,0)",[567,5732],{"dataC":620,"xLinkHref":5733},"#MJX-40-TEX-N-3D",[555,5735,5737,5746],{"dataMmlNode":3570,"transform":5736},"translate(5270.1,0)",[555,5738,5739,5741,5744],{"dataMmlNode":906},[567,5740],{"dataC":930,"xLinkHref":5708},[567,5742],{"dataC":1100,"xLinkHref":5743,"transform":915},"#MJX-40-TEX-N-33",[567,5745],{"dataC":1357,"xLinkHref":5727,"transform":918},[555,5747,5749],{"dataMmlNode":906,"transform":5748},"translate(1533,-150) scale(0.707)",[567,5750],{"dataC":1445,"xLinkHref":5751},"#MJX-40-TEX-N-38",[555,5753,5755],{"dataMmlNode":616,"transform":5754},"translate(7206.7,0)",[567,5756],{"dataC":1132,"xLinkHref":5757},"#MJX-40-TEX-N-2E",[5582,5759,5761],{"id":5760},"перевод-восьмеричного-числа-в-двоичную-систему-счисления","Перевод восьмеричного числа в двоичную систему счисления",[406,5763,5764],{},"Перевод восьмеричного числа в двоичную систему счисления также производится по триадам цифр:",[493,5766,5767,5770,5773],{},[496,5768,5769],{},"Исходное восьмеричное число разбивается на отдельные цифры;",[496,5771,5772],{},"Каждая восьмеричная цифра заменяется соответствующей её триадой двоичных цифр по таблице(см. выше);",[496,5774,5775,5776,5778,5779],{},"Искомое двоичное число составляется из полученных триад; Незначащие нули слева отбрасываются.\nПример: требуется перевести число 12345 из восьмеричной системы в двоичную систему счисления:\n1 2 3 4 5 → ",[409,5777,5665],{},"1 010 011 100 101 → 1010011100101.\nВ результате: ",[506,5780,5782],{"className":5781,"jax":510},[509],[512,5783,5786,5815],{"style":4610,"xmlns":515,"width":5784,"height":4612,"role":518,"focusable":519,"viewBox":5785,"xmlnsXLink":521},"25.983ex","0 -677 11484.7 842.6",[523,5787,5788,5791,5794,5797,5800,5803,5806,5809,5812],{},[526,5789],{"id":5790,"d":883},"MJX-41-TEX-N-31",[526,5792],{"id":5793,"d":1339},"MJX-41-TEX-N-32",[526,5795],{"id":5796,"d":1060},"MJX-41-TEX-N-33",[526,5798],{"id":5799,"d":1050},"MJX-41-TEX-N-34",[526,5801],{"id":5802,"d":872},"MJX-41-TEX-N-35",[526,5804],{"id":5805,"d":1423},"MJX-41-TEX-N-38",[526,5807],{"id":5808,"d":549},"MJX-41-TEX-N-3D",[526,5810],{"id":5811,"d":876},"MJX-41-TEX-N-30",[526,5813],{"id":5814,"d":1068},"MJX-41-TEX-N-2E",[555,5816,5817],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,5818,5819,5843,5849,5890],{"dataMmlNode":562},[555,5820,5821,5838],{"dataMmlNode":3570},[555,5822,5823,5826,5829,5832,5835],{"dataMmlNode":906},[567,5824],{"dataC":930,"xLinkHref":5825},"#MJX-41-TEX-N-31",[567,5827],{"dataC":1357,"xLinkHref":5828,"transform":915},"#MJX-41-TEX-N-32",[567,5830],{"dataC":1100,"xLinkHref":5831,"transform":918},"#MJX-41-TEX-N-33",[567,5833],{"dataC":1082,"xLinkHref":5834,"transform":1134},"#MJX-41-TEX-N-34",[567,5836],{"dataC":909,"xLinkHref":5837,"transform":1320},"#MJX-41-TEX-N-35",[555,5839,5840],{"dataMmlNode":906,"transform":4665},[567,5841],{"dataC":1445,"xLinkHref":5842},"#MJX-41-TEX-N-38",[555,5844,5846],{"dataMmlNode":616,"transform":5845},"translate(3214.3,0)",[567,5847],{"dataC":620,"xLinkHref":5848},"#MJX-41-TEX-N-3D",[555,5850,5852,5885],{"dataMmlNode":3570,"transform":5851},"translate(4270.1,0)",[555,5853,5854,5856,5859,5861,5863,5865,5867,5869,5871,5873,5876,5879,5882],{"dataMmlNode":906},[567,5855],{"dataC":930,"xLinkHref":5825},[567,5857],{"dataC":913,"xLinkHref":5858,"transform":915},"#MJX-41-TEX-N-30",[567,5860],{"dataC":930,"xLinkHref":5825,"transform":918},[567,5862],{"dataC":913,"xLinkHref":5858,"transform":1134},[567,5864],{"dataC":913,"xLinkHref":5858,"transform":1320},[567,5866],{"dataC":930,"xLinkHref":5825,"transform":4696},[567,5868],{"dataC":930,"xLinkHref":5825,"transform":4699},[567,5870],{"dataC":930,"xLinkHref":5825,"transform":4702},[567,5872],{"dataC":913,"xLinkHref":5858,"transform":4705},[567,5874],{"dataC":913,"xLinkHref":5858,"transform":5875},"translate(4500,0)",[567,5877],{"dataC":930,"xLinkHref":5825,"transform":5878},"translate(5000,0)",[567,5880],{"dataC":913,"xLinkHref":5858,"transform":5881},"translate(5500,0)",[567,5883],{"dataC":930,"xLinkHref":5825,"transform":5884},"translate(6000,0)",[555,5886,5888],{"dataMmlNode":906,"transform":5887},"translate(6533,-150) scale(0.707)",[567,5889],{"dataC":1357,"xLinkHref":5828},[555,5891,5893],{"dataMmlNode":616,"transform":5892},"translate(11206.7,0)",[567,5894],{"dataC":1132,"xLinkHref":5895},"#MJX-41-TEX-N-2E",[5582,5897,5899],{"id":5898},"перевод-двоичного-числа-в-шестнадцатеричную-систему-счисления","Перевод двоичного числа в шестнадцатеричную систему счисления",[406,5901,5902],{},"Перевод двоичного числа в шестнадцатеричную систему счисления производится по тетрадам цифр:",[493,5904,5905,5908],{},[496,5906,5907],{},"Исходное двоичное число разбивается на группы по четыре цифры (\"тетрады\") справа налево; При необходимости крайняя слева группа цифр дополняется незначащими нулями слева;",[496,5909,5910],{},"Каждая тетрада двоичных цифр заменяется соответствующим ей шестнадцатеричным значением согласно таблице:",[426,5912,5913,5966],{},[429,5914,5915],{},[432,5916,5917,5919,5922,5925,5928,5931,5934,5937,5940,5943,5945,5948,5951,5954,5957,5960,5963],{},[435,5918,5609],{},[435,5920,5921],{},"0000",[435,5923,5924],{},"0001",[435,5926,5927],{},"0010",[435,5929,5930],{},"0011",[435,5932,5933],{},"0100",[435,5935,5936],{},"0101",[435,5938,5939],{},"0110",[435,5941,5942],{},"0111",[435,5944,470],{},[435,5946,5947],{},"1001",[435,5949,5950],{},"1010",[435,5952,5953],{},"1011",[435,5955,5956],{},"1100",[435,5958,5959],{},"1101",[435,5961,5962],{},"1110",[435,5964,5965],{},"1111",[460,5967,5968],{},[432,5969,5970,5973,5975,5977,5979,5981,5983,5985,5987,5989,5991,5994,5997,6000,6002,6004,6007],{},[465,5971,5972],{},"Шестнадцатеричное значение",[465,5974,558],{},[465,5976,488],{},[465,5978,1176],{},[465,5980,5648],{},[465,5982,5651],{},[465,5984,485],{},[465,5986,5656],{},[465,5988,5659],{},[465,5990,1190],{},[465,5992,5993],{},"9",[465,5995,5996],{},"A",[465,5998,5999],{},"B",[465,6001,446],{},[465,6003,443],{},[465,6005,6006],{},"E",[465,6008,6009],{},"F",[406,6011,6012,6013],{},"Пример: требуется перевести число 1011010 из двоичной системы счисления в шестнадцатеричную: 1011010 → 0101 1010 → 5 А. В результате:\n",[506,6014,6016],{"className":6015,"jax":510},[509],[512,6017,6021,6047],{"style":4610,"xmlns":515,"width":6018,"height":6019,"role":518,"focusable":519,"viewBox":6020,"xmlnsXLink":521},"17.168ex","1.994ex","0 -716 7588.2 881.6",[523,6022,6023,6026,6029,6032,6035,6038,6041,6044],{},[526,6024],{"id":6025,"d":883},"MJX-42-TEX-N-31",[526,6027],{"id":6028,"d":876},"MJX-42-TEX-N-30",[526,6030],{"id":6031,"d":1339},"MJX-42-TEX-N-32",[526,6033],{"id":6034,"d":549},"MJX-42-TEX-N-3D",[526,6036],{"id":6037,"d":872},"MJX-42-TEX-N-35",[526,6039],{"id":6040,"d":1419},"MJX-42-TEX-I-1D434",[526,6042],{"id":6043,"d":1940},"MJX-42-TEX-N-36",[526,6045],{"id":6046,"d":1068},"MJX-42-TEX-N-2E",[555,6048,6049],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,6050,6051,6076,6081,6086,6104],{"dataMmlNode":562},[555,6052,6053,6071],{"dataMmlNode":3570},[555,6054,6055,6058,6061,6063,6065,6067,6069],{"dataMmlNode":906},[567,6056],{"dataC":930,"xLinkHref":6057},"#MJX-42-TEX-N-31",[567,6059],{"dataC":913,"xLinkHref":6060,"transform":915},"#MJX-42-TEX-N-30",[567,6062],{"dataC":930,"xLinkHref":6057,"transform":918},[567,6064],{"dataC":930,"xLinkHref":6057,"transform":1134},[567,6066],{"dataC":913,"xLinkHref":6060,"transform":1320},[567,6068],{"dataC":930,"xLinkHref":6057,"transform":4696},[567,6070],{"dataC":913,"xLinkHref":6060,"transform":4699},[555,6072,6073],{"dataMmlNode":906,"transform":5724},[567,6074],{"dataC":1357,"xLinkHref":6075},"#MJX-42-TEX-N-32",[555,6077,6078],{"dataMmlNode":616,"transform":5730},[567,6079],{"dataC":620,"xLinkHref":6080},"#MJX-42-TEX-N-3D",[555,6082,6083],{"dataMmlNode":906,"transform":5736},[567,6084],{"dataC":909,"xLinkHref":6085},"#MJX-42-TEX-N-35",[555,6087,6089,6094],{"dataMmlNode":3570,"transform":6088},"translate(5770.1,0)",[555,6090,6091],{"dataMmlNode":565},[567,6092],{"dataC":1438,"xLinkHref":6093},"#MJX-42-TEX-I-1D434",[555,6095,6097],{"dataMmlNode":3010,"transform":6096,"dataMjxTexclass":3011},"translate(783,-150) scale(0.707)",[555,6098,6099,6101],{"dataMmlNode":906},[567,6100],{"dataC":930,"xLinkHref":6057},[567,6102],{"dataC":1984,"xLinkHref":6103,"transform":915},"#MJX-42-TEX-N-36",[555,6105,6107],{"dataMmlNode":616,"transform":6106},"translate(7310.2,0)",[567,6108],{"dataC":1132,"xLinkHref":6109},"#MJX-42-TEX-N-2E",[5582,6111,6113],{"id":6112},"перевод-шестнадцатеричного-числа-в-двоичную-систему-счисления","Перевод шестнадцатеричного числа в двоичную систему счисления",[406,6115,6116],{},"Перевод шестнадцатеричного числа в двоичную систему счисления также производится по тетрадам цифр:",[493,6118,6119,6122,6125],{},[496,6120,6121],{},"Исходное шестнадцатеричное число разбивается на отдельные цифры;",[496,6123,6124],{},"Каждая шестнадцатеричная цифра заменяется соответствующей ей тетрадой двоичных цифр по таблице (см. выше);",[496,6126,6127],{},"Искомое двоичное число составляется из полученных тетрад; Незначащие нули слева отбрасываются.",[406,6129,6130,6131,6133,6134],{},"Пример: требуется перевести число 1ADA из шестнадцатеричной системы счисления в двоичную: 1 A D A → ",[409,6132,5612],{},"1 1010 1101 1010 → 1101011011010. В результате:\n",[506,6135,6137],{"className":6136,"jax":510},[509],[512,6138,6141,6167],{"style":4610,"xmlns":515,"width":6139,"height":6019,"role":518,"focusable":519,"viewBox":6140,"xmlnsXLink":521},"27.525ex","0 -716 12166.2 881.6",[523,6142,6143,6146,6149,6152,6155,6158,6161,6164],{},[526,6144],{"id":6145,"d":883},"MJX-43-TEX-N-31",[526,6147],{"id":6148,"d":1419},"MJX-43-TEX-I-1D434",[526,6150],{"id":6151,"d":533},"MJX-43-TEX-I-1D437",[526,6153],{"id":6154,"d":1940},"MJX-43-TEX-N-36",[526,6156],{"id":6157,"d":549},"MJX-43-TEX-N-3D",[526,6159],{"id":6160,"d":876},"MJX-43-TEX-N-30",[526,6162],{"id":6163,"d":1339},"MJX-43-TEX-N-32",[526,6165],{"id":6166,"d":1068},"MJX-43-TEX-N-2E",[555,6168,6169],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,6170,6171,6176,6181,6186,6201,6207,6244],{"dataMmlNode":562},[555,6172,6173],{"dataMmlNode":906},[567,6174],{"dataC":930,"xLinkHref":6175},"#MJX-43-TEX-N-31",[555,6177,6178],{"dataMmlNode":565,"transform":915},[567,6179],{"dataC":1438,"xLinkHref":6180},"#MJX-43-TEX-I-1D434",[555,6182,6183],{"dataMmlNode":565,"transform":1449},[567,6184],{"dataC":576,"xLinkHref":6185},"#MJX-43-TEX-I-1D437",[555,6187,6188,6192],{"dataMmlNode":3570,"transform":1455},[555,6189,6190],{"dataMmlNode":565},[567,6191],{"dataC":1438,"xLinkHref":6180},[555,6193,6194],{"dataMmlNode":3010,"transform":6096,"dataMjxTexclass":3011},[555,6195,6196,6198],{"dataMmlNode":906},[567,6197],{"dataC":930,"xLinkHref":6175},[567,6199],{"dataC":1984,"xLinkHref":6200,"transform":915},"#MJX-43-TEX-N-36",[555,6202,6204],{"dataMmlNode":616,"transform":6203},"translate(3895.9,0)",[567,6205],{"dataC":620,"xLinkHref":6206},"#MJX-43-TEX-N-3D",[555,6208,6210,6239],{"dataMmlNode":3570,"transform":6209},"translate(4951.7,0)",[555,6211,6212,6214,6216,6219,6221,6223,6225,6227,6229,6231,6233,6235,6237],{"dataMmlNode":906},[567,6213],{"dataC":930,"xLinkHref":6175},[567,6215],{"dataC":930,"xLinkHref":6175,"transform":915},[567,6217],{"dataC":913,"xLinkHref":6218,"transform":918},"#MJX-43-TEX-N-30",[567,6220],{"dataC":930,"xLinkHref":6175,"transform":1134},[567,6222],{"dataC":913,"xLinkHref":6218,"transform":1320},[567,6224],{"dataC":930,"xLinkHref":6175,"transform":4696},[567,6226],{"dataC":930,"xLinkHref":6175,"transform":4699},[567,6228],{"dataC":913,"xLinkHref":6218,"transform":4702},[567,6230],{"dataC":930,"xLinkHref":6175,"transform":4705},[567,6232],{"dataC":930,"xLinkHref":6175,"transform":5875},[567,6234],{"dataC":913,"xLinkHref":6218,"transform":5878},[567,6236],{"dataC":930,"xLinkHref":6175,"transform":5881},[567,6238],{"dataC":913,"xLinkHref":6218,"transform":5884},[555,6240,6241],{"dataMmlNode":906,"transform":5887},[567,6242],{"dataC":1357,"xLinkHref":6243},"#MJX-43-TEX-N-32",[555,6245,6247],{"dataMmlNode":616,"transform":6246},"translate(11888.2,0)",[567,6248],{"dataC":1132,"xLinkHref":6249},"#MJX-43-TEX-N-2E",[5242,6251,6252],{},[406,6253,6254],{},"При преобразовании чисел по триадам и тетрадам не забывайте дополнять триады(тетрады) незначащими нулями слева до трёх(четырёх) знаков, а также отбрасывать незначащие нули после завершения преобразования.",[1136,6256,6258],{"id":6257},"таблицы-степеней","Таблицы степеней",[406,6260,6261],{},"Существенную помощь при вычислениях, связанных с переводом чисел в десятичную систему счисления, могут оказать таблицы значений степеней оснований системы счисления. В качестве примера приведена такая таблица для основания системы счисления, равного 2(рекомендуется выучить её наизусть). Аналогично можно составить подобные таблицы и для других оснований систем счисления.",[426,6263,6264,6887],{},[429,6265,6266],{},[432,6267,6268,6305,6339,6370,6397,6430,6463,6494,6525,6558,6589,6620,6661,6696,6731,6770,6810,6849,6852],{},[435,6269,6270],{},[506,6271,6273],{"className":6272,"jax":510},[509],[512,6274,6279,6288],{"style":6275,"xmlns":515,"width":6276,"height":6277,"role":518,"focusable":519,"viewBox":6278,"xmlnsXLink":521},"vertical-align: 0;","2.279ex","1.528ex","0 -675.5 1007.3 675.5",[523,6280,6281,6284],{},[526,6282],{"id":6283,"d":1339},"MJX-44-TEX-N-32",[526,6285],{"id":6286,"d":6287},"MJX-44-TEX-I-1D45B","M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",[555,6289,6290],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,6291,6292],{"dataMmlNode":562},[555,6293,6294,6299],{"dataMmlNode":1516},[555,6295,6296],{"dataMmlNode":906},[567,6297],{"dataC":1357,"xLinkHref":6298},"#MJX-44-TEX-N-32",[555,6300,6301],{"dataMmlNode":565,"transform":1525},[567,6302],{"dataC":6303,"xLinkHref":6304},"1D45B","#MJX-44-TEX-I-1D45B",[435,6306,6307],{},[506,6308,6310],{"className":6309,"jax":510},[509],[512,6311,6315,6323],{"style":6275,"xmlns":515,"width":6312,"height":6313,"role":518,"focusable":519,"viewBox":6314,"xmlnsXLink":521},"2.119ex","1.887ex","0 -833.9 936.6 833.9",[523,6316,6317,6320],{},[526,6318],{"id":6319,"d":1339},"MJX-45-TEX-N-32",[526,6321],{"id":6322,"d":876},"MJX-45-TEX-N-30",[555,6324,6325],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,6326,6327],{"dataMmlNode":562},[555,6328,6329,6334],{"dataMmlNode":1516},[555,6330,6331],{"dataMmlNode":906},[567,6332],{"dataC":1357,"xLinkHref":6333},"#MJX-45-TEX-N-32",[555,6335,6336],{"dataMmlNode":906,"transform":1525},[567,6337],{"dataC":913,"xLinkHref":6338},"#MJX-45-TEX-N-30",[435,6340,6341],{},[506,6342,6344],{"className":6343,"jax":510},[509],[512,6345,6346,6354],{"style":6275,"xmlns":515,"width":6312,"height":6313,"role":518,"focusable":519,"viewBox":6314,"xmlnsXLink":521},[523,6347,6348,6351],{},[526,6349],{"id":6350,"d":1339},"MJX-46-TEX-N-32",[526,6352],{"id":6353,"d":883},"MJX-46-TEX-N-31",[555,6355,6356],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,6357,6358],{"dataMmlNode":562},[555,6359,6360,6365],{"dataMmlNode":1516},[555,6361,6362],{"dataMmlNode":906},[567,6363],{"dataC":1357,"xLinkHref":6364},"#MJX-46-TEX-N-32",[555,6366,6367],{"dataMmlNode":906,"transform":1525},[567,6368],{"dataC":930,"xLinkHref":6369},"#MJX-46-TEX-N-31",[435,6371,6372],{},[506,6373,6375],{"className":6374,"jax":510},[509],[512,6376,6377,6382],{"style":6275,"xmlns":515,"width":6312,"height":6313,"role":518,"focusable":519,"viewBox":6314,"xmlnsXLink":521},[523,6378,6379],{},[526,6380],{"id":6381,"d":1339},"MJX-47-TEX-N-32",[555,6383,6384],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,6385,6386],{"dataMmlNode":562},[555,6387,6388,6393],{"dataMmlNode":1516},[555,6389,6390],{"dataMmlNode":906},[567,6391],{"dataC":1357,"xLinkHref":6392},"#MJX-47-TEX-N-32",[555,6394,6395],{"dataMmlNode":906,"transform":1525},[567,6396],{"dataC":1357,"xLinkHref":6392},[435,6398,6399],{},[506,6400,6402],{"className":6401,"jax":510},[509],[512,6403,6406,6414],{"style":6275,"xmlns":515,"width":6312,"height":6404,"role":518,"focusable":519,"viewBox":6405,"xmlnsXLink":521},"1.885ex","0 -833.2 936.6 833.2",[523,6407,6408,6411],{},[526,6409],{"id":6410,"d":1339},"MJX-48-TEX-N-32",[526,6412],{"id":6413,"d":1060},"MJX-48-TEX-N-33",[555,6415,6416],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,6417,6418],{"dataMmlNode":562},[555,6419,6420,6425],{"dataMmlNode":1516},[555,6421,6422],{"dataMmlNode":906},[567,6423],{"dataC":1357,"xLinkHref":6424},"#MJX-48-TEX-N-32",[555,6426,6427],{"dataMmlNode":906,"transform":1525},[567,6428],{"dataC":1100,"xLinkHref":6429},"#MJX-48-TEX-N-33",[435,6431,6432],{},[506,6433,6435],{"className":6434,"jax":510},[509],[512,6436,6439,6447],{"style":6275,"xmlns":515,"width":6312,"height":6437,"role":518,"focusable":519,"viewBox":6438,"xmlnsXLink":521},"1.904ex","0 -841.7 936.6 841.7",[523,6440,6441,6444],{},[526,6442],{"id":6443,"d":1339},"MJX-49-TEX-N-32",[526,6445],{"id":6446,"d":1050},"MJX-49-TEX-N-34",[555,6448,6449],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,6450,6451],{"dataMmlNode":562},[555,6452,6453,6458],{"dataMmlNode":1516},[555,6454,6455],{"dataMmlNode":906},[567,6456],{"dataC":1357,"xLinkHref":6457},"#MJX-49-TEX-N-32",[555,6459,6460],{"dataMmlNode":906,"transform":1525},[567,6461],{"dataC":1082,"xLinkHref":6462},"#MJX-49-TEX-N-34",[435,6464,6465],{},[506,6466,6468],{"className":6467,"jax":510},[509],[512,6469,6470,6478],{"style":6275,"xmlns":515,"width":6312,"height":6313,"role":518,"focusable":519,"viewBox":6314,"xmlnsXLink":521},[523,6471,6472,6475],{},[526,6473],{"id":6474,"d":1339},"MJX-50-TEX-N-32",[526,6476],{"id":6477,"d":872},"MJX-50-TEX-N-35",[555,6479,6480],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,6481,6482],{"dataMmlNode":562},[555,6483,6484,6489],{"dataMmlNode":1516},[555,6485,6486],{"dataMmlNode":906},[567,6487],{"dataC":1357,"xLinkHref":6488},"#MJX-50-TEX-N-32",[555,6490,6491],{"dataMmlNode":906,"transform":1525},[567,6492],{"dataC":909,"xLinkHref":6493},"#MJX-50-TEX-N-35",[435,6495,6496],{},[506,6497,6499],{"className":6498,"jax":510},[509],[512,6500,6501,6509],{"style":6275,"xmlns":515,"width":6312,"height":6313,"role":518,"focusable":519,"viewBox":6314,"xmlnsXLink":521},[523,6502,6503,6506],{},[526,6504],{"id":6505,"d":1339},"MJX-51-TEX-N-32",[526,6507],{"id":6508,"d":1940},"MJX-51-TEX-N-36",[555,6510,6511],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,6512,6513],{"dataMmlNode":562},[555,6514,6515,6520],{"dataMmlNode":1516},[555,6516,6517],{"dataMmlNode":906},[567,6518],{"dataC":1357,"xLinkHref":6519},"#MJX-51-TEX-N-32",[555,6521,6522],{"dataMmlNode":906,"transform":1525},[567,6523],{"dataC":1984,"xLinkHref":6524},"#MJX-51-TEX-N-36",[435,6526,6527],{},[506,6528,6530],{"className":6529,"jax":510},[509],[512,6531,6534,6542],{"style":6275,"xmlns":515,"width":6312,"height":6532,"role":518,"focusable":519,"viewBox":6533,"xmlnsXLink":521},"1.903ex","0 -841 936.6 841",[523,6535,6536,6539],{},[526,6537],{"id":6538,"d":1339},"MJX-52-TEX-N-32",[526,6540],{"id":6541,"d":1064},"MJX-52-TEX-N-37",[555,6543,6544],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,6545,6546],{"dataMmlNode":562},[555,6547,6548,6553],{"dataMmlNode":1516},[555,6549,6550],{"dataMmlNode":906},[567,6551],{"dataC":1357,"xLinkHref":6552},"#MJX-52-TEX-N-32",[555,6554,6555],{"dataMmlNode":906,"transform":1525},[567,6556],{"dataC":1114,"xLinkHref":6557},"#MJX-52-TEX-N-37",[435,6559,6560],{},[506,6561,6563],{"className":6562,"jax":510},[509],[512,6564,6565,6573],{"style":6275,"xmlns":515,"width":6312,"height":6313,"role":518,"focusable":519,"viewBox":6314,"xmlnsXLink":521},[523,6566,6567,6570],{},[526,6568],{"id":6569,"d":1339},"MJX-53-TEX-N-32",[526,6571],{"id":6572,"d":1423},"MJX-53-TEX-N-38",[555,6574,6575],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,6576,6577],{"dataMmlNode":562},[555,6578,6579,6584],{"dataMmlNode":1516},[555,6580,6581],{"dataMmlNode":906},[567,6582],{"dataC":1357,"xLinkHref":6583},"#MJX-53-TEX-N-32",[555,6585,6586],{"dataMmlNode":906,"transform":1525},[567,6587],{"dataC":1445,"xLinkHref":6588},"#MJX-53-TEX-N-38",[435,6590,6591],{},[506,6592,6594],{"className":6593,"jax":510},[509],[512,6595,6596,6604],{"style":6275,"xmlns":515,"width":6312,"height":6313,"role":518,"focusable":519,"viewBox":6314,"xmlnsXLink":521},[523,6597,6598,6601],{},[526,6599],{"id":6600,"d":1339},"MJX-54-TEX-N-32",[526,6602],{"id":6603,"d":4474},"MJX-54-TEX-N-39",[555,6605,6606],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,6607,6608],{"dataMmlNode":562},[555,6609,6610,6615],{"dataMmlNode":1516},[555,6611,6612],{"dataMmlNode":906},[567,6613],{"dataC":1357,"xLinkHref":6614},"#MJX-54-TEX-N-32",[555,6616,6617],{"dataMmlNode":906,"transform":1525},[567,6618],{"dataC":4566,"xLinkHref":6619},"#MJX-54-TEX-N-39",[435,6621,6622],{},[506,6623,6625],{"className":6624,"jax":510},[509],[512,6626,6629,6640],{"style":6275,"xmlns":515,"width":6627,"height":6313,"role":518,"focusable":519,"viewBox":6628,"xmlnsXLink":521},"2.919ex","0 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833.9",[523,6630,6631,6634,6637],{},[526,6632],{"id":6633,"d":1339},"MJX-55-TEX-N-32",[526,6635],{"id":6636,"d":883},"MJX-55-TEX-N-31",[526,6638],{"id":6639,"d":876},"MJX-55-TEX-N-30",[555,6641,6642],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,6643,6644],{"dataMmlNode":562},[555,6645,6646,6651],{"dataMmlNode":1516},[555,6647,6648],{"dataMmlNode":906},[567,6649],{"dataC":1357,"xLinkHref":6650},"#MJX-55-TEX-N-32",[555,6652,6653],{"dataMmlNode":3010,"transform":1525,"dataMjxTexclass":3011},[555,6654,6655,6658],{"dataMmlNode":906},[567,6656],{"dataC":930,"xLinkHref":6657},"#MJX-55-TEX-N-31",[567,6659],{"dataC":913,"xLinkHref":6660,"transform":915},"#MJX-55-TEX-N-30",[435,6662,6663],{},[506,6664,6666],{"className":6665,"jax":510},[509],[512,6667,6668,6676],{"style":6275,"xmlns":515,"width":6627,"height":6313,"role":518,"focusable":519,"viewBox":6628,"xmlnsXLink":521},[523,6669,6670,6673],{},[526,6671],{"id":6672,"d":1339},"MJX-56-TEX-N-32",[526,6674],{"id":6675,"d":883},"MJX-56-TEX-N-31",[555,6677,6678],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,6679,6680],{"dataMmlNode":562},[555,6681,6682,6687],{"dataMmlNode":1516},[555,6683,6684],{"dataMmlNode":906},[567,6685],{"dataC":1357,"xLinkHref":6686},"#MJX-56-TEX-N-32",[555,6688,6689],{"dataMmlNode":3010,"transform":1525,"dataMjxTexclass":3011},[555,6690,6691,6694],{"dataMmlNode":906},[567,6692],{"dataC":930,"xLinkHref":6693},"#MJX-56-TEX-N-31",[567,6695],{"dataC":930,"xLinkHref":6693,"transform":915},[435,6697,6698],{},[506,6699,6701],{"className":6700,"jax":510},[509],[512,6702,6703,6711],{"style":6275,"xmlns":515,"width":6627,"height":6313,"role":518,"focusable":519,"viewBox":6628,"xmlnsXLink":521},[523,6704,6705,6708],{},[526,6706],{"id":6707,"d":1339},"MJX-57-TEX-N-32",[526,6709],{"id":6710,"d":883},"MJX-57-TEX-N-31",[555,6712,6713],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,6714,6715],{"dataMmlNode":562},[555,6716,6717,6722],{"dataMmlNode":1516},[555,6718,6719],{"dataMmlNode":906},[567,6720],{"dataC":1357,"xLinkHref":6721},"#MJX-57-TEX-N-32",[555,6723,6724],{"dataMmlNode":3010,"transform":1525,"dataMjxTexclass":3011},[555,6725,6726,6729],{"dataMmlNode":906},[567,6727],{"dataC":930,"xLinkHref":6728},"#MJX-57-TEX-N-31",[567,6730],{"dataC":1357,"xLinkHref":6721,"transform":915},[435,6732,6733],{},[506,6734,6736],{"className":6735,"jax":510},[509],[512,6737,6738,6749],{"style":6275,"xmlns":515,"width":6627,"height":6313,"role":518,"focusable":519,"viewBox":6628,"xmlnsXLink":521},[523,6739,6740,6743,6746],{},[526,6741],{"id":6742,"d":1339},"MJX-58-TEX-N-32",[526,6744],{"id":6745,"d":883},"MJX-58-TEX-N-31",[526,6747],{"id":6748,"d":1060},"MJX-58-TEX-N-33",[555,6750,6751],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,6752,6753],{"dataMmlNode":562},[555,6754,6755,6760],{"dataMmlNode":1516},[555,6756,6757],{"dataMmlNode":906},[567,6758],{"dataC":1357,"xLinkHref":6759},"#MJX-58-TEX-N-32",[555,6761,6762],{"dataMmlNode":3010,"transform":1525,"dataMjxTexclass":3011},[555,6763,6764,6767],{"dataMmlNode":906},[567,6765],{"dataC":930,"xLinkHref":6766},"#MJX-58-TEX-N-31",[567,6768],{"dataC":1100,"xLinkHref":6769,"transform":915},"#MJX-58-TEX-N-33",[435,6771,6772],{},[506,6773,6775],{"className":6774,"jax":510},[509],[512,6776,6778,6789],{"style":6275,"xmlns":515,"width":6627,"height":6437,"role":518,"focusable":519,"viewBox":6777,"xmlnsXLink":521},"0 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841.7",[523,6779,6780,6783,6786],{},[526,6781],{"id":6782,"d":1339},"MJX-59-TEX-N-32",[526,6784],{"id":6785,"d":883},"MJX-59-TEX-N-31",[526,6787],{"id":6788,"d":1050},"MJX-59-TEX-N-34",[555,6790,6791],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,6792,6793],{"dataMmlNode":562},[555,6794,6795,6800],{"dataMmlNode":1516},[555,6796,6797],{"dataMmlNode":906},[567,6798],{"dataC":1357,"xLinkHref":6799},"#MJX-59-TEX-N-32",[555,6801,6802],{"dataMmlNode":3010,"transform":1525,"dataMjxTexclass":3011},[555,6803,6804,6807],{"dataMmlNode":906},[567,6805],{"dataC":930,"xLinkHref":6806},"#MJX-59-TEX-N-31",[567,6808],{"dataC":1082,"xLinkHref":6809,"transform":915},"#MJX-59-TEX-N-34",[435,6811,6812],{},[506,6813,6815],{"className":6814,"jax":510},[509],[512,6816,6817,6828],{"style":6275,"xmlns":515,"width":6627,"height":6313,"role":518,"focusable":519,"viewBox":6628,"xmlnsXLink":521},[523,6818,6819,6822,6825],{},[526,6820],{"id":6821,"d":1339},"MJX-60-TEX-N-32",[526,6823],{"id":6824,"d":883},"MJX-60-TEX-N-31",[526,6826],{"id":6827,"d":872},"MJX-60-TEX-N-35",[555,6829,6830],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,6831,6832],{"dataMmlNode":562},[555,6833,6834,6839],{"dataMmlNode":1516},[555,6835,6836],{"dataMmlNode":906},[567,6837],{"dataC":1357,"xLinkHref":6838},"#MJX-60-TEX-N-32",[555,6840,6841],{"dataMmlNode":3010,"transform":1525,"dataMjxTexclass":3011},[555,6842,6843,6846],{"dataMmlNode":906},[567,6844],{"dataC":930,"xLinkHref":6845},"#MJX-60-TEX-N-31",[567,6847],{"dataC":909,"xLinkHref":6848,"transform":915},"#MJX-60-TEX-N-35",[435,6850,6851],{},"...",[435,6853,6854],{},[506,6855,6857],{"className":6856,"jax":510},[509],[512,6858,6859,6867],{"style":6275,"xmlns":515,"width":6627,"height":6313,"role":518,"focusable":519,"viewBox":6628,"xmlnsXLink":521},[523,6860,6861,6864],{},[526,6862],{"id":6863,"d":1339},"MJX-61-TEX-N-32",[526,6865],{"id":6866,"d":876},"MJX-61-TEX-N-30",[555,6868,6869],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,6870,6871],{"dataMmlNode":562},[555,6872,6873,6878],{"dataMmlNode":1516},[555,6874,6875],{"dataMmlNode":906},[567,6876],{"dataC":1357,"xLinkHref":6877},"#MJX-61-TEX-N-32",[555,6879,6880],{"dataMmlNode":3010,"transform":1525,"dataMjxTexclass":3011},[555,6881,6882,6884],{"dataMmlNode":906},[567,6883],{"dataC":1357,"xLinkHref":6877},[567,6885],{"dataC":913,"xLinkHref":6886,"transform":915},"#MJX-61-TEX-N-30",[460,6888,6889],{},[432,6890,6891,6893,6895,6897,6899,6901,6903,6905,6908,6911,6914,6917,6920,6923,6926,6929,6932,6935,6937],{},[465,6892,467],{},[465,6894,488],{},[465,6896,1176],{},[465,6898,5651],{},[465,6900,1190],{},[465,6902,1217],{},[465,6904,1357],{},[465,6906,6907],{},"64",[465,6909,6910],{},"128",[465,6912,6913],{},"256",[465,6915,6916],{},"512",[465,6918,6919],{},"1024",[465,6921,6922],{},"2048",[465,6924,6925],{},"4096",[465,6927,6928],{},"8192",[465,6930,6931],{},"16384",[465,6933,6934],{},"32768",[465,6936,6851],{},[465,6938,6939],{},"1048576",[1136,6941,6943,6944],{"id":6942},"арифметика-в-недесятичных-системах-счисления-на-примере-двоичной-арифметики","Арифметика в недесятичных системах счисления ",[1249,6945,6946],{},"(на примере двоичной арифметики)",[406,6948,6949],{},"Правила арифметических вычислений в общем едины для любой позиционной системы счисления. Необходима только внимательность при отслеживании переносов между разрядами, возникающих при непривычном недесятичном значении основания системы счисления.",[5582,6951,6953],{"id":6952},"сложение-одноразрядных-двоичных-чисел","Сложение одноразрядных двоичных чисел",[406,6955,6956],{},[518,6957],{"alt":6953,"src":6958},"\u002Fimages\u002Fblog\u002Ftoi\u002Fst5\u002Fimg2.png",[5582,6960,6962],{"id":6961},"умножение-одноразрядных-двоичных-чисел","Умножение одноразрядных двоичных чисел",[406,6964,6965],{},[518,6966],{"alt":6962,"src":6967},"\u002Fimages\u002Fblog\u002Ftoi\u002Fst5\u002Fimg3.png",[5582,6969,6971],{"id":6970},"вычитание-одноразрядных-двоичных-чисел","Вычитание одноразрядных двоичных чисел",[406,6973,6974],{},[518,6975],{"alt":6971,"src":6976},"\u002Fimages\u002Fblog\u002Ftoi\u002Fst5\u002Fimg4.png",[5582,6978,6980],{"id":6979},"сложение-многоразрядных-двоичных-чисел","Сложение многоразрядных двоичных чисел",[406,6982,6983],{},"Выполняется в столбик. Пример: требуется сложить 1111 и 111.",[1136,6985,6987],{"id":6986},"",[506,6988,6990],{"className":6989,"jax":510},[509],[512,6991,6996,7007],{"style":6992,"xmlns":515,"width":6993,"height":6994,"role":518,"focusable":519,"viewBox":6995,"xmlnsXLink":521},"vertical-align: -4.589ex;","7.085ex","10.31ex","0 -2528.5 3131.6 4556.9",[523,6997,6998,7001,7004],{},[526,6999],{"id":7000,"d":553},"MJX-62-TEX-N-2B",[526,7002],{"id":7003,"d":883},"MJX-62-TEX-N-31",[526,7005],{"id":7006,"d":876},"MJX-62-TEX-N-30",[555,7008,7009],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,7010,7011],{"dataMmlNode":562},[555,7012,7014,7115,7140],{"dataMmlNode":7013},"mtable",[555,7015,7018],{"dataMmlNode":7016,"transform":7017},"mtr","translate(0,735)",[555,7019,7021,7026],{"dataMmlNode":7020},"mtd",[555,7022,7023],{"dataMmlNode":616},[567,7024],{"dataC":637,"xLinkHref":7025},"#MJX-62-TEX-N-2B",[555,7027,7028,7102],{"dataMmlNode":7013,"transform":2133},[555,7029,7031],{"dataMmlNode":7016,"transform":7030},"translate(0,356.5)",[555,7032,7033,7051,7067,7082,7097],{"dataMmlNode":7020},[555,7034,7036,7040],{"dataMmlNode":7035},"mover",[555,7037],{"dataMmlNode":7038,"transform":7039},"mrow","translate(176.8,0)",[555,7041,7044],{"dataMmlNode":7042,"transform":7043},"mstyle","translate(0,200) scale(0.707)",[555,7045,7046],{"dataMmlNode":3010,"dataMjxTexclass":3011},[555,7047,7048],{"dataMmlNode":906},[567,7049],{"dataC":930,"xLinkHref":7050},"#MJX-62-TEX-N-31",[555,7052,7054,7058],{"dataMmlNode":7035,"transform":7053},"translate(353.6,0)",[555,7055,7056],{"dataMmlNode":906},[567,7057],{"dataC":930,"xLinkHref":7050},[555,7059,7061],{"dataMmlNode":7042,"transform":7060},"translate(73.2,866) scale(0.707)",[555,7062,7063],{"dataMmlNode":3010,"dataMjxTexclass":3011},[555,7064,7065],{"dataMmlNode":906},[567,7066],{"dataC":930,"xLinkHref":7050},[555,7068,7070,7074],{"dataMmlNode":7035,"transform":7069},"translate(853.6,0)",[555,7071,7072],{"dataMmlNode":906},[567,7073],{"dataC":930,"xLinkHref":7050},[555,7075,7076],{"dataMmlNode":7042,"transform":7060},[555,7077,7078],{"dataMmlNode":3010,"dataMjxTexclass":3011},[555,7079,7080],{"dataMmlNode":906},[567,7081],{"dataC":930,"xLinkHref":7050},[555,7083,7085,7089],{"dataMmlNode":7035,"transform":7084},"translate(1353.6,0)",[555,7086,7087],{"dataMmlNode":906},[567,7088],{"dataC":930,"xLinkHref":7050},[555,7090,7091],{"dataMmlNode":7042,"transform":7060},[555,7092,7093],{"dataMmlNode":3010,"dataMjxTexclass":3011},[555,7094,7095],{"dataMmlNode":906},[567,7096],{"dataC":930,"xLinkHref":7050},[555,7098,7100],{"dataMmlNode":906,"transform":7099},"translate(1853.6,0)",[567,7101],{"dataC":930,"xLinkHref":7050},[555,7103,7105],{"dataMmlNode":7016,"transform":7104},"translate(0,-1043.5)",[555,7106,7107],{"dataMmlNode":7020,"transform":7069},[555,7108,7109,7111,7113],{"dataMmlNode":906},[567,7110],{"dataC":930,"xLinkHref":7050},[567,7112],{"dataC":930,"xLinkHref":7050,"transform":915},[567,7114],{"dataC":930,"xLinkHref":7050,"transform":918},[555,7116,7118],{"dataMmlNode":7016,"transform":7117},"translate(0,-1778.5)",[555,7119,7121],{"dataMmlNode":7020,"transform":7120},"translate(631.6,0)",[555,7122,7123],{"dataMmlNode":7013},[555,7124,7125],{"dataMmlNode":7016},[555,7126,7127],{"dataMmlNode":7020},[555,7128,7129,7131,7134,7136,7138],{"dataMmlNode":906},[567,7130],{"dataC":930,"xLinkHref":7050},[567,7132],{"dataC":913,"xLinkHref":7133,"transform":915},"#MJX-62-TEX-N-30",[567,7135],{"dataC":930,"xLinkHref":7050,"transform":918},[567,7137],{"dataC":930,"xLinkHref":7050,"transform":1134},[567,7139],{"dataC":913,"xLinkHref":7133,"transform":1320},[7141,7142],"line",{"dataLine":7143,"className":7144,"x1":558,"y1":7146,"x2":7147,"y2":7146},"h",[7145],"mjx-solid","-793.5","3131.6",[406,7149,7150],{},"Распишем поразрядно действия при сложении в столбик:",[493,7152,7153,7156,7159,7162,7165],{},[496,7154,7155],{},"Первый: 1 + 1 = 0 — единица переходит в следующий разряд.",[496,7157,7158],{},"Второй: 1 + 1 + 1 = 1 — единица переходит в следующий разряд.",[496,7160,7161],{},"Третий: 1 + 1 + 1 = 1 — единица переходит в следующий разряд.",[496,7163,7164],{},"Четвёртый: 1 + 0 + 1 = 0 — единица переходит в следующий разряд.",[496,7166,7167],{},"Пятый: 1 + 0 + 0 = 1.",[5582,7169,7171],{"id":7170},"вычитание-многоразрядных-двоичных-чисел","Вычитание многоразрядных двоичных чисел",[406,7173,7174],{},"Выполняется в столбик, при этом возможен заём единицы из старшего разряда. Пример: требуется вычислить значение выражения 110101 - 1001:",[1136,7176,7178],{"id":7177},"_1",[506,7179,7181],{"className":7180,"jax":510},[509],[512,7182,7185,7196],{"style":6992,"xmlns":515,"width":7183,"height":6994,"role":518,"focusable":519,"viewBox":7184,"xmlnsXLink":521},"8.548ex","0 -2528.5 3778 4556.9",[523,7186,7187,7190,7193],{},[526,7188],{"id":7189,"d":703},"MJX-63-TEX-N-2212",[526,7191],{"id":7192,"d":883},"MJX-63-TEX-N-31",[526,7194],{"id":7195,"d":876},"MJX-63-TEX-N-30",[555,7197,7198],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,7199,7200],{"dataMmlNode":562},[555,7201,7202,7261,7285],{"dataMmlNode":7013},[555,7203,7204],{"dataMmlNode":7016,"transform":7017},[555,7205,7206,7211],{"dataMmlNode":7020},[555,7207,7208],{"dataMmlNode":616},[567,7209],{"dataC":750,"xLinkHref":7210},"#MJX-63-TEX-N-2212",[555,7212,7213,7247],{"dataMmlNode":7013,"transform":2133},[555,7214,7215],{"dataMmlNode":7016,"transform":7030},[555,7216,7217,7222,7236],{"dataMmlNode":7020},[555,7218,7219],{"dataMmlNode":906},[567,7220],{"dataC":930,"xLinkHref":7221},"#MJX-63-TEX-N-31",[555,7223,7224,7228],{"dataMmlNode":7035,"transform":915},[555,7225,7226],{"dataMmlNode":906},[567,7227],{"dataC":930,"xLinkHref":7221},[555,7229,7230],{"dataMmlNode":7042,"transform":7060},[555,7231,7232],{"dataMmlNode":3010,"dataMjxTexclass":3011},[555,7233,7234],{"dataMmlNode":906},[567,7235],{"dataC":930,"xLinkHref":7221},[555,7237,7238,7241,7243,7245],{"dataMmlNode":906,"transform":918},[567,7239],{"dataC":913,"xLinkHref":7240},"#MJX-63-TEX-N-30",[567,7242],{"dataC":930,"xLinkHref":7221,"transform":915},[567,7244],{"dataC":913,"xLinkHref":7240,"transform":918},[567,7246],{"dataC":930,"xLinkHref":7221,"transform":1134},[555,7248,7249],{"dataMmlNode":7016,"transform":7104},[555,7250,7251],{"dataMmlNode":7020,"transform":918},[555,7252,7253,7255,7257,7259],{"dataMmlNode":906},[567,7254],{"dataC":930,"xLinkHref":7221},[567,7256],{"dataC":913,"xLinkHref":7240,"transform":915},[567,7258],{"dataC":913,"xLinkHref":7240,"transform":918},[567,7260],{"dataC":930,"xLinkHref":7221,"transform":1134},[555,7262,7263],{"dataMmlNode":7016,"transform":7117},[555,7264,7265],{"dataMmlNode":7020,"transform":2133},[555,7266,7267],{"dataMmlNode":7013},[555,7268,7269],{"dataMmlNode":7016},[555,7270,7271],{"dataMmlNode":7020},[555,7272,7273,7275,7277,7279,7281,7283],{"dataMmlNode":906},[567,7274],{"dataC":930,"xLinkHref":7221},[567,7276],{"dataC":913,"xLinkHref":7240,"transform":915},[567,7278],{"dataC":930,"xLinkHref":7221,"transform":918},[567,7280],{"dataC":930,"xLinkHref":7221,"transform":1134},[567,7282],{"dataC":930,"xLinkHref":7221,"transform":1320},[567,7284],{"dataC":913,"xLinkHref":7240,"transform":4696},[7141,7286],{"dataLine":7143,"className":7287,"x1":558,"y1":7146,"x2":7288,"y2":7146},[7145],"3778",[5582,7290,7292],{"id":7291},"умножение-многоразрядных-двоичных-чисел","Умножение многоразрядных двоичных чисел",[406,7294,7295],{},"Выполняется в столбик аналогично умножению десятичных чисел. Однако при этом для двоичной системы счисления можно воспользоваться следующими простыми правилами:",[493,7297,7298,7301],{},[496,7299,7300],{},"Всегда умножать большее число на меньшее;",[496,7302,7303],{},"Умножение заменяется сложением копий множимого числа, записанных друг под другом со сдвигом каждый раз на одну позицию влево для каждого единичного разряда множителя (для нулевых разрядов множителя копии множимого в искомой сумме пропускаются).",[406,7305,7306],{},"Пример: требуется вычислить значение выражения 110101 × 1101(для 2-го нулевого разряда копия множимого пропускается):",[1136,7308,7310],{"id":7309},"_2",[506,7311,7313],{"className":7312,"jax":510},[509],[512,7314,7319,7337],{"style":7315,"xmlns":515,"width":7316,"height":7317,"role":518,"focusable":519,"viewBox":7318,"xmlnsXLink":521},"vertical-align: -8.643ex;","11.941ex","18.416ex","0 -4320 5278 8140",[523,7320,7321,7325,7328,7331,7334],{},[526,7322],{"id":7323,"d":7324},"MJX-64-TEX-I-D7","M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z",[526,7326],{"id":7327,"d":883},"MJX-64-TEX-N-31",[526,7329],{"id":7330,"d":876},"MJX-64-TEX-N-30",[526,7332],{"id":7333,"d":553},"MJX-64-TEX-N-2B",[526,7335],{"id":7336,"d":6986},"MJX-64-TEX-N-A0",[555,7338,7339],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,7340,7341],{"dataMmlNode":562},[555,7342,7343,7392,7541],{"dataMmlNode":7013},[555,7344,7346],{"dataMmlNode":7016,"transform":7345},"translate(0,2870)",[555,7347,7348,7354],{"dataMmlNode":7020,"transform":1134},[555,7349,7350],{"dataMmlNode":565},[567,7351],{"dataC":7352,"xLinkHref":7353},"D7","#MJX-64-TEX-I-D7",[555,7355,7356,7377],{"dataMmlNode":7013,"transform":2133},[555,7357,7359],{"dataMmlNode":7016,"transform":7358},"translate(0,700)",[555,7360,7361],{"dataMmlNode":7020},[555,7362,7363,7366,7368,7371,7373,7375],{"dataMmlNode":906},[567,7364],{"dataC":930,"xLinkHref":7365},"#MJX-64-TEX-N-31",[567,7367],{"dataC":930,"xLinkHref":7365,"transform":915},[567,7369],{"dataC":913,"xLinkHref":7370,"transform":918},"#MJX-64-TEX-N-30",[567,7372],{"dataC":930,"xLinkHref":7365,"transform":1134},[567,7374],{"dataC":913,"xLinkHref":7370,"transform":1320},[567,7376],{"dataC":930,"xLinkHref":7365,"transform":4696},[555,7378,7380],{"dataMmlNode":7016,"transform":7379},"translate(0,-700)",[555,7381,7382],{"dataMmlNode":7020,"transform":918},[555,7383,7384,7386,7388,7390],{"dataMmlNode":906},[567,7385],{"dataC":930,"xLinkHref":7365},[567,7387],{"dataC":930,"xLinkHref":7365,"transform":915},[567,7389],{"dataC":913,"xLinkHref":7370,"transform":918},[567,7391],{"dataC":930,"xLinkHref":7365,"transform":1134},[555,7393,7395],{"dataMmlNode":7016,"transform":7394},"translate(0,-1435)",[555,7396,7397],{"dataMmlNode":7020},[555,7398,7399,7452],{"dataMmlNode":7013},[555,7400,7402],{"dataMmlNode":7016,"transform":7401},"translate(0,1435)",[555,7403,7404,7409],{"dataMmlNode":7020,"transform":915},[555,7405,7406],{"dataMmlNode":616},[567,7407],{"dataC":637,"xLinkHref":7408},"#MJX-64-TEX-N-2B",[555,7410,7411,7429],{"dataMmlNode":7013,"transform":2133},[555,7412,7413],{"dataMmlNode":7016,"transform":7358},[555,7414,7415],{"dataMmlNode":7020,"transform":918},[555,7416,7417,7419,7421,7423,7425,7427],{"dataMmlNode":906},[567,7418],{"dataC":930,"xLinkHref":7365},[567,7420],{"dataC":930,"xLinkHref":7365,"transform":915},[567,7422],{"dataC":913,"xLinkHref":7370,"transform":918},[567,7424],{"dataC":930,"xLinkHref":7365,"transform":1134},[567,7426],{"dataC":913,"xLinkHref":7370,"transform":1320},[567,7428],{"dataC":930,"xLinkHref":7365,"transform":4696},[555,7430,7431],{"dataMmlNode":7016,"transform":7379},[555,7432,7433,7447],{"dataMmlNode":7020},[555,7434,7435,7437,7439,7441,7443,7445],{"dataMmlNode":906},[567,7436],{"dataC":930,"xLinkHref":7365},[567,7438],{"dataC":930,"xLinkHref":7365,"transform":915},[567,7440],{"dataC":913,"xLinkHref":7370,"transform":918},[567,7442],{"dataC":930,"xLinkHref":7365,"transform":1134},[567,7444],{"dataC":913,"xLinkHref":7370,"transform":1320},[567,7446],{"dataC":930,"xLinkHref":7365,"transform":4696},[555,7448,7449],{"dataMmlNode":7042,"transform":4699},[555,7450],{"dataMmlNode":7451},"mspace",[555,7453,7455],{"dataMmlNode":7016,"transform":7454},"translate(0,-1400)",[555,7456,7457],{"dataMmlNode":7020},[555,7458,7459,7502,7536],{"dataMmlNode":7013},[555,7460,7461],{"dataMmlNode":7016,"transform":7017},[555,7462,7463,7467],{"dataMmlNode":7020},[555,7464,7465],{"dataMmlNode":616},[567,7466],{"dataC":637,"xLinkHref":7408},[555,7468,7469],{"dataMmlNode":7013,"transform":2133},[555,7470,7471],{"dataMmlNode":7016},[555,7472,7473,7487,7491,7497],{"dataMmlNode":7020},[555,7474,7475,7477,7479,7481,7483,7485],{"dataMmlNode":906},[567,7476],{"dataC":930,"xLinkHref":7365},[567,7478],{"dataC":930,"xLinkHref":7365,"transform":915},[567,7480],{"dataC":913,"xLinkHref":7370,"transform":918},[567,7482],{"dataC":930,"xLinkHref":7365,"transform":1134},[567,7484],{"dataC":913,"xLinkHref":7370,"transform":1320},[567,7486],{"dataC":930,"xLinkHref":7365,"transform":4696},[555,7488,7489],{"dataMmlNode":7042,"transform":4699},[555,7490],{"dataMmlNode":7451},[555,7492,7493],{"dataMmlNode":4822,"transform":4705},[567,7494],{"dataC":7495,"xLinkHref":7496},"A0","#MJX-64-TEX-N-A0",[555,7498,7500],{"dataMmlNode":4822,"transform":7499},"translate(4250,0)",[567,7501],{"dataC":7495,"xLinkHref":7496},[555,7503,7505],{"dataMmlNode":7016,"transform":7504},"translate(0,-735)",[555,7506,7508],{"dataMmlNode":7020,"transform":7507},"translate(278,0)",[555,7509,7510],{"dataMmlNode":7013},[555,7511,7512],{"dataMmlNode":7016},[555,7513,7514],{"dataMmlNode":7020},[555,7515,7516,7518,7520,7522,7524,7526,7528,7530,7532,7534],{"dataMmlNode":906},[567,7517],{"dataC":930,"xLinkHref":7365},[567,7519],{"dataC":913,"xLinkHref":7370,"transform":915},[567,7521],{"dataC":930,"xLinkHref":7365,"transform":918},[567,7523],{"dataC":913,"xLinkHref":7370,"transform":1134},[567,7525],{"dataC":930,"xLinkHref":7365,"transform":1320},[567,7527],{"dataC":930,"xLinkHref":7365,"transform":4696},[567,7529],{"dataC":913,"xLinkHref":7370,"transform":4699},[567,7531],{"dataC":913,"xLinkHref":7370,"transform":4702},[567,7533],{"dataC":913,"xLinkHref":7370,"transform":4705},[567,7535],{"dataC":930,"xLinkHref":7365,"transform":5875},[7141,7537],{"dataLine":7143,"className":7538,"x1":558,"y1":7539,"x2":7540,"y2":7539},[7145],"250","5278",[7141,7542],{"dataLine":7143,"className":7543,"x1":558,"y1":7544,"x2":7540,"y2":7544},[7145],"1685",[5582,7546,7548],{"id":7547},"деление-многоразрядных-двоичных-чисел","Деление многоразрядных двоичных чисел",[406,7550,7551],{},"Выполняется аналогично делению в столбик десятичных чисел. При этом на каждом шаге деления выполняется последовательное вычитание делителя из очередного делимого до получения остатка, равного 0 или 1, а подсчитанное количество вычитаний записывается как очередное значение частного.",[406,7553,7554],{},"Пример: требуется вычислить значение выражения 10010 \u002F 110.",[406,7556,7557],{},[518,7558],{"alt":7548,"src":7559},"\u002Fimages\u002Fblog\u002Ftoi\u002Fst5\u002Fimg5.png",[406,7561,7562],{},"Пошаговый алгоритм:",[493,7564,7565,7568,7571],{},[496,7566,7567],{},"Первые три числа делимого меньше, чем делитель — значит, умножаем делитель на 0 и вычитаем. Получаем 100.",[496,7569,7570],{},"Дописываем 1 справа от 100, видим, что 1001 больше, чем 110, поэтому умножаем делитель на 1 и вычитаем его из 1001. Получаем 11.",[496,7572,7573],{},"Дописываем 0 справа. Полученное 110 равно делителю, поэтому тоже умножаем его на 1, получаем конечный результат.",[406,7575,7576],{},"В результате: 10010 \u002F 110 = 11.",[406,7578,7579],{},"Ещё пример: требуется вычислить значение выражения 1100 \u002F 10.",[406,7581,7562],{},[493,7583,7584,7587,7590,7593],{},[496,7585,7586],{},"Смотрим на делимое, видим, что первые две его цифры — 11. Умножаем делитель на 1 и вычитаем из 11 число 10.",[496,7588,7589],{},"Получили 1, дописываем справа следующую по порядку цифру — 0. Теперь 10 равно делителю, значит, тоже умножаем его на 1 и вычитаем.",[496,7591,7592],{},"Получаем 0. Но у нас ещё остался один 0 у делимого — дописываем его справа от полученного 0.",[496,7594,7595],{},"Число 0 меньше, чем 10, поэтому умножаем делитель на 0.",[406,7597,7598],{},"В результате: 1100 \u002F 10 = 110.",[402,7600,7602],{"id":7601},"арифметические-операции-в-восьмеричной-системе-счисления","Арифметические операции в восьмеричной системе счисления",[406,7604,7605],{},[518,7606],{"alt":7607,"src":7608},"Таблица сложения восьмеричных чисел","\u002Fimages\u002Fblog\u002Ftoi\u002Fst5\u002Fimg6.png",[406,7610,7611],{},"Аналогично можно записать правила арифметических операций и для других систем счисления.\nРассмотрим восьмеричную систему счисления, в которой используется 8 символов: 0, 1, 2, 3, 4, 5, 6, 7.\nПравил сложения и умножения очень много, удобнее представить их с помощью таблиц.\nРассмотрим три операции: умножение, вычитание и сложение.",[1136,7613,7615],{"id":7614},"сложение-в-восьмеричной-системе","Сложение в восьмеричной системе",[406,7617,7618],{},"☑️Примеры сложения в восьмеричной системе:\n1000 + 11 = 1011;\n111 + 1 = 112;",[406,7620,7621],{},"Выполним сложение в восьмеричной системе в столбик:",[406,7623,7624],{},[506,7625,7627],{"className":7626,"jax":510},[509],[512,7628,7633,7659],{"style":7629,"xmlns":515,"width":7630,"height":7631,"role":518,"focusable":519,"viewBox":7632,"xmlnsXLink":521},"vertical-align: -3.812ex;","6.285ex","8.756ex","0 -2185 2778 3870",[523,7634,7635,7638,7641,7644,7647,7650,7653,7656],{},[526,7636],{"id":7637,"d":553},"MJX-65-TEX-N-2B",[526,7639],{"id":7640,"d":1060},"MJX-65-TEX-N-33",[526,7642],{"id":7643,"d":1050},"MJX-65-TEX-N-34",[526,7645],{"id":7646,"d":1339},"MJX-65-TEX-N-32",[526,7648],{"id":7649,"d":883},"MJX-65-TEX-N-31",[526,7651],{"id":7652,"d":872},"MJX-65-TEX-N-35",[526,7654],{"id":7655,"d":876},"MJX-65-TEX-N-30",[526,7657],{"id":7658,"d":1940},"MJX-65-TEX-N-36",[555,7660,7661],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,7662,7663],{"dataMmlNode":562},[555,7664,7665,7708,7731],{"dataMmlNode":7013},[555,7666,7667],{"dataMmlNode":7016,"transform":7017},[555,7668,7669,7674],{"dataMmlNode":7020},[555,7670,7671],{"dataMmlNode":616},[567,7672],{"dataC":637,"xLinkHref":7673},"#MJX-65-TEX-N-2B",[555,7675,7676,7694],{"dataMmlNode":7013,"transform":2133},[555,7677,7678],{"dataMmlNode":7016,"transform":7358},[555,7679,7680],{"dataMmlNode":7020},[555,7681,7682,7685,7688,7691],{"dataMmlNode":906},[567,7683],{"dataC":1100,"xLinkHref":7684},"#MJX-65-TEX-N-33",[567,7686],{"dataC":1082,"xLinkHref":7687,"transform":915},"#MJX-65-TEX-N-34",[567,7689],{"dataC":1357,"xLinkHref":7690,"transform":918},"#MJX-65-TEX-N-32",[567,7692],{"dataC":930,"xLinkHref":7693,"transform":1134},"#MJX-65-TEX-N-31",[555,7695,7696],{"dataMmlNode":7016,"transform":7379},[555,7697,7698],{"dataMmlNode":7020},[555,7699,7700,7702,7704,7706],{"dataMmlNode":906},[567,7701],{"dataC":930,"xLinkHref":7693},[567,7703],{"dataC":1082,"xLinkHref":7687,"transform":915},[567,7705],{"dataC":1357,"xLinkHref":7690,"transform":918},[567,7707],{"dataC":1357,"xLinkHref":7690,"transform":1134},[555,7709,7710],{"dataMmlNode":7016,"transform":7394},[555,7711,7712],{"dataMmlNode":7020,"transform":2133},[555,7713,7714],{"dataMmlNode":7013},[555,7715,7716],{"dataMmlNode":7016},[555,7717,7718],{"dataMmlNode":7020},[555,7719,7720,7723,7726,7729],{"dataMmlNode":906},[567,7721],{"dataC":909,"xLinkHref":7722},"#MJX-65-TEX-N-35",[567,7724],{"dataC":913,"xLinkHref":7725,"transform":915},"#MJX-65-TEX-N-30",[567,7727],{"dataC":1984,"xLinkHref":7728,"transform":918},"#MJX-65-TEX-N-36",[567,7730],{"dataC":1100,"xLinkHref":7684,"transform":1134},[7141,7732],{"dataLine":7143,"className":7733,"x1":558,"y1":7734,"x2":7735,"y2":7734},[7145],"-450","2778",[406,7737,7738],{},"В третьем столбце получилось значение 0, т.к. 4+4=10 в восьмеричной системе, поэтому записываем 0, а 1 переносим в следующий разряд.",[1136,7740,7742],{"id":7741},"вычитание-в-восьмеричной-системе","Вычитание в восьмеричной системе",[406,7744,7745],{},"☑️Вычесть 3546 - 1271",[406,7747,7748],{},[506,7749,7751],{"className":7750,"jax":510},[509],[512,7752,7753,7779],{"style":7629,"xmlns":515,"width":7630,"height":7631,"role":518,"focusable":519,"viewBox":7632,"xmlnsXLink":521},[523,7754,7755,7758,7761,7764,7767,7770,7773,7776],{},[526,7756],{"id":7757,"d":703},"MJX-66-TEX-N-2212",[526,7759],{"id":7760,"d":1060},"MJX-66-TEX-N-33",[526,7762],{"id":7763,"d":872},"MJX-66-TEX-N-35",[526,7765],{"id":7766,"d":1050},"MJX-66-TEX-N-34",[526,7768],{"id":7769,"d":1940},"MJX-66-TEX-N-36",[526,7771],{"id":7772,"d":883},"MJX-66-TEX-N-31",[526,7774],{"id":7775,"d":1339},"MJX-66-TEX-N-32",[526,7777],{"id":7778,"d":1064},"MJX-66-TEX-N-37",[555,7780,7781],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,7782,7783],{"dataMmlNode":562},[555,7784,7785,7831,7851],{"dataMmlNode":7013},[555,7786,7787],{"dataMmlNode":7016,"transform":7017},[555,7788,7789,7794],{"dataMmlNode":7020},[555,7790,7791],{"dataMmlNode":616},[567,7792],{"dataC":750,"xLinkHref":7793},"#MJX-66-TEX-N-2212",[555,7795,7796,7814],{"dataMmlNode":7013,"transform":2133},[555,7797,7798],{"dataMmlNode":7016,"transform":7358},[555,7799,7800],{"dataMmlNode":7020},[555,7801,7802,7805,7808,7811],{"dataMmlNode":906},[567,7803],{"dataC":1100,"xLinkHref":7804},"#MJX-66-TEX-N-33",[567,7806],{"dataC":909,"xLinkHref":7807,"transform":915},"#MJX-66-TEX-N-35",[567,7809],{"dataC":1082,"xLinkHref":7810,"transform":918},"#MJX-66-TEX-N-34",[567,7812],{"dataC":1984,"xLinkHref":7813,"transform":1134},"#MJX-66-TEX-N-36",[555,7815,7816],{"dataMmlNode":7016,"transform":7379},[555,7817,7818],{"dataMmlNode":7020},[555,7819,7820,7823,7826,7829],{"dataMmlNode":906},[567,7821],{"dataC":930,"xLinkHref":7822},"#MJX-66-TEX-N-31",[567,7824],{"dataC":1357,"xLinkHref":7825,"transform":915},"#MJX-66-TEX-N-32",[567,7827],{"dataC":1114,"xLinkHref":7828,"transform":918},"#MJX-66-TEX-N-37",[567,7830],{"dataC":930,"xLinkHref":7822,"transform":1134},[555,7832,7833],{"dataMmlNode":7016,"transform":7394},[555,7834,7835],{"dataMmlNode":7020,"transform":2133},[555,7836,7837],{"dataMmlNode":7013},[555,7838,7839],{"dataMmlNode":7016},[555,7840,7841],{"dataMmlNode":7020},[555,7842,7843,7845,7847,7849],{"dataMmlNode":906},[567,7844],{"dataC":1357,"xLinkHref":7825},[567,7846],{"dataC":1357,"xLinkHref":7825,"transform":915},[567,7848],{"dataC":909,"xLinkHref":7807,"transform":918},[567,7850],{"dataC":909,"xLinkHref":7807,"transform":1134},[7141,7852],{"dataLine":7143,"className":7853,"x1":558,"y1":7734,"x2":7735,"y2":7734},[7145],[1136,7855,7857],{"id":7856},"умножение-в-восьмеричной-системе","Умножение в восьмеричной системе",[406,7859,7860],{},"☑️Умножить 17 на 16\nСначала умножаем поразрядно 1 7 на 6, затем 1 7 на 1",[406,7862,7863],{},[506,7864,7866],{"className":7865,"jax":510},[509],[512,7867,7872,7895],{"style":7868,"xmlns":515,"width":7869,"height":7870,"role":518,"focusable":519,"viewBox":7871,"xmlnsXLink":521},"vertical-align: -7.059ex;","5.154ex","15.249ex","0 -3620 2278 6740",[523,7873,7874,7877,7880,7883,7886,7889,7892],{},[526,7875],{"id":7876,"d":7324},"MJX-67-TEX-I-D7",[526,7878],{"id":7879,"d":883},"MJX-67-TEX-N-31",[526,7881],{"id":7882,"d":1064},"MJX-67-TEX-N-37",[526,7884],{"id":7885,"d":1940},"MJX-67-TEX-N-36",[526,7887],{"id":7888,"d":553},"MJX-67-TEX-N-2B",[526,7890],{"id":7891,"d":1060},"MJX-67-TEX-N-33",[526,7893],{"id":7894,"d":1339},"MJX-67-TEX-N-32",[555,7896,7897],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,7898,7899],{"dataMmlNode":562},[555,7900,7901,7936,7999],{"dataMmlNode":7013},[555,7902,7904],{"dataMmlNode":7016,"transform":7903},"translate(0,2170)",[555,7905,7906,7911],{"dataMmlNode":7020,"transform":915},[555,7907,7908],{"dataMmlNode":565},[567,7909],{"dataC":7352,"xLinkHref":7910},"#MJX-67-TEX-I-D7",[555,7912,7913,7925],{"dataMmlNode":7013,"transform":2133},[555,7914,7915],{"dataMmlNode":7016,"transform":7358},[555,7916,7917],{"dataMmlNode":7020},[555,7918,7919,7922],{"dataMmlNode":906},[567,7920],{"dataC":930,"xLinkHref":7921},"#MJX-67-TEX-N-31",[567,7923],{"dataC":1114,"xLinkHref":7924,"transform":915},"#MJX-67-TEX-N-37",[555,7926,7927],{"dataMmlNode":7016,"transform":7379},[555,7928,7929],{"dataMmlNode":7020},[555,7930,7931,7933],{"dataMmlNode":906},[567,7932],{"dataC":930,"xLinkHref":7921},[567,7934],{"dataC":1984,"xLinkHref":7935,"transform":915},"#MJX-67-TEX-N-36",[555,7937,7938],{"dataMmlNode":7016,"transform":7394},[555,7939,7940],{"dataMmlNode":7020},[555,7941,7942,7977,7995],{"dataMmlNode":7013},[555,7943,7944],{"dataMmlNode":7016,"transform":7017},[555,7945,7946,7951],{"dataMmlNode":7020},[555,7947,7948],{"dataMmlNode":616},[567,7949],{"dataC":637,"xLinkHref":7950},"#MJX-67-TEX-N-2B",[555,7952,7953,7967],{"dataMmlNode":7013,"transform":2133},[555,7954,7955],{"dataMmlNode":7016,"transform":7358},[555,7956,7957],{"dataMmlNode":7020},[555,7958,7959,7961,7964],{"dataMmlNode":906},[567,7960],{"dataC":930,"xLinkHref":7921},[567,7962],{"dataC":1100,"xLinkHref":7963,"transform":915},"#MJX-67-TEX-N-33",[567,7965],{"dataC":1357,"xLinkHref":7966,"transform":918},"#MJX-67-TEX-N-32",[555,7968,7969],{"dataMmlNode":7016,"transform":7379},[555,7970,7971],{"dataMmlNode":7020,"transform":915},[555,7972,7973,7975],{"dataMmlNode":906},[567,7974],{"dataC":930,"xLinkHref":7921},[567,7976],{"dataC":1114,"xLinkHref":7924,"transform":915},[555,7978,7979],{"dataMmlNode":7016,"transform":7394},[555,7980,7981],{"dataMmlNode":7020,"transform":2133},[555,7982,7983],{"dataMmlNode":7013},[555,7984,7985],{"dataMmlNode":7016},[555,7986,7987],{"dataMmlNode":7020},[555,7988,7989,7991,7993],{"dataMmlNode":906},[567,7990],{"dataC":1100,"xLinkHref":7963},[567,7992],{"dataC":1357,"xLinkHref":7966,"transform":915},[567,7994],{"dataC":1357,"xLinkHref":7966,"transform":918},[7141,7996],{"dataLine":7143,"className":7997,"x1":558,"y1":7734,"x2":7998,"y2":7734},[7145],"2278",[7141,8000],{"dataLine":7143,"className":8001,"x1":558,"y1":8002,"x2":7998,"y2":8002},[7145],"985",[406,8004,8005],{},"Восьмеричная система обычно используется в областях, связанных с использованием цифровых устройств, применяется при предоставлении прав доступа к файлам в работе с битовыми флагами и масками.",[402,8007,8009],{"id":8008},"арифметические-операции-в-шестнадцатеричной-системе","Арифметические операции в шестнадцатеричной системе",[406,8011,8012],{},"Рассмотрим операции сложения и вычитания в шестнадцатеричной системе счисления.\nПри выполнении операций сложения необходимо помнить, что перенос числа появляется тогда, когда сумма в очередном разряде превышает 15.\nБывает удобно, если плохо помнится что значит, например, C в 16-ичной системе, переписать в столбик исходные 16-ичные числа на числа в 10-ичной системе счисления и после этого выполнить сложение.\nПри вычитании заём из старшего разряда равен 16, а все промежуточные разряды(если не получилось у соседнего сразу занять) заполняются старшей цифрой F или 15.",[1136,8014,8016],{"id":8015},"сложение-в-шестнадцатеричной-системе","Сложение в шестнадцатеричной системе",[406,8018,8019],{},"☑️Сложить A5B + C7E",[406,8021,8022],{},[506,8023,8025],{"className":8024,"jax":510},[509],[512,8026,8029,8061],{"style":7629,"xmlns":515,"width":8027,"height":7631,"role":518,"focusable":519,"viewBox":8028,"xmlnsXLink":521},"7.416ex","0 -2185 3278 3870",[523,8030,8031,8034,8037,8040,8043,8046,8049,8052,8055,8058],{},[526,8032],{"id":8033,"d":553},"MJX-68-TEX-N-2B",[526,8035],{"id":8036,"d":883},"MJX-68-TEX-N-31",[526,8038],{"id":8039,"d":876},"MJX-68-TEX-N-30",[526,8041],{"id":8042,"d":872},"MJX-68-TEX-N-35",[526,8044],{"id":8045,"d":1339},"MJX-68-TEX-N-32",[526,8047],{"id":8048,"d":1064},"MJX-68-TEX-N-37",[526,8050],{"id":8051,"d":1050},"MJX-68-TEX-N-34",[526,8053],{"id":8054,"d":1940},"MJX-68-TEX-N-36",[526,8056],{"id":8057,"d":1060},"MJX-68-TEX-N-33",[526,8059],{"id":8060,"d":4474},"MJX-68-TEX-N-39",[555,8062,8063],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,8064,8065],{"dataMmlNode":562},[555,8066,8067,8120,8151],{"dataMmlNode":7013},[555,8068,8069],{"dataMmlNode":7016,"transform":7017},[555,8070,8071,8076],{"dataMmlNode":7020},[555,8072,8073],{"dataMmlNode":616},[567,8074],{"dataC":637,"xLinkHref":8075},"#MJX-68-TEX-N-2B",[555,8077,8078,8099],{"dataMmlNode":7013,"transform":2133},[555,8079,8080],{"dataMmlNode":7016,"transform":7358},[555,8081,8082],{"dataMmlNode":7020},[555,8083,8084],{"dataMmlNode":3010,"dataMjxTexclass":3011},[555,8085,8086,8089,8092,8095,8097],{"dataMmlNode":906},[567,8087],{"dataC":930,"xLinkHref":8088},"#MJX-68-TEX-N-31",[567,8090],{"dataC":913,"xLinkHref":8091,"transform":915},"#MJX-68-TEX-N-30",[567,8093],{"dataC":909,"xLinkHref":8094,"transform":918},"#MJX-68-TEX-N-35",[567,8096],{"dataC":930,"xLinkHref":8088,"transform":1134},[567,8098],{"dataC":930,"xLinkHref":8088,"transform":1320},[555,8100,8101],{"dataMmlNode":7016,"transform":7379},[555,8102,8103],{"dataMmlNode":7020},[555,8104,8105],{"dataMmlNode":3010,"dataMjxTexclass":3011},[555,8106,8107,8109,8112,8115,8117],{"dataMmlNode":906},[567,8108],{"dataC":930,"xLinkHref":8088},[567,8110],{"dataC":1357,"xLinkHref":8111,"transform":915},"#MJX-68-TEX-N-32",[567,8113],{"dataC":1114,"xLinkHref":8114,"transform":918},"#MJX-68-TEX-N-37",[567,8116],{"dataC":930,"xLinkHref":8088,"transform":1134},[567,8118],{"dataC":1082,"xLinkHref":8119,"transform":1320},"#MJX-68-TEX-N-34",[555,8121,8122],{"dataMmlNode":7016,"transform":7394},[555,8123,8124],{"dataMmlNode":7020,"transform":2133},[555,8125,8126],{"dataMmlNode":7013},[555,8127,8128],{"dataMmlNode":7016},[555,8129,8130,8134,8139,8146],{"dataMmlNode":7020},[555,8131,8132],{"dataMmlNode":906},[567,8133],{"dataC":930,"xLinkHref":8088},[555,8135,8136],{"dataMmlNode":906,"transform":915},[567,8137],{"dataC":1984,"xLinkHref":8138},"#MJX-68-TEX-N-36",[555,8140,8141,8143],{"dataMmlNode":906,"transform":918},[567,8142],{"dataC":930,"xLinkHref":8088},[567,8144],{"dataC":1100,"xLinkHref":8145,"transform":915},"#MJX-68-TEX-N-33",[555,8147,8148],{"dataMmlNode":906,"transform":1320},[567,8149],{"dataC":4566,"xLinkHref":8150},"#MJX-68-TEX-N-39",[7141,8152],{"dataLine":7143,"className":8153,"x1":558,"y1":7734,"x2":8154,"y2":7734},[7145],"3278",[406,8156,8157,8158,8161,8162,8164,8165,8167],{},"11 + 14 = 1 * 16 + 9 (9) ",[8159,8160],"br",{},"\n5 + 7 + 1 = 13 (D) ",[8159,8163],{},"\n10 + 12 = 1*16 + 6 (6) ",[8159,8166],{},"\n0 + 0 + 1 = 1 (1)",[406,8169,8170],{},[409,8171,8172],{},"Ответ: 16D9",[1136,8174,8176],{"id":8175},"вычитание-в-шестнадцатеричной-системе","Вычитание в шестнадцатеричной системе",[406,8178,8179],{},"☑️Вычесть C5B - A7E",[406,8181,8182],{},[506,8183,8185],{"className":8184,"jax":510},[509],[512,8186,8187,8213],{"style":7629,"xmlns":515,"width":8027,"height":7631,"role":518,"focusable":519,"viewBox":8028,"xmlnsXLink":521},[523,8188,8189,8192,8195,8198,8201,8204,8207,8210],{},[526,8190],{"id":8191,"d":703},"MJX-69-TEX-N-2212",[526,8193],{"id":8194,"d":883},"MJX-69-TEX-N-31",[526,8196],{"id":8197,"d":1339},"MJX-69-TEX-N-32",[526,8199],{"id":8200,"d":872},"MJX-69-TEX-N-35",[526,8202],{"id":8203,"d":876},"MJX-69-TEX-N-30",[526,8205],{"id":8206,"d":1064},"MJX-69-TEX-N-37",[526,8208],{"id":8209,"d":1050},"MJX-69-TEX-N-34",[526,8211],{"id":8212,"d":1060},"MJX-69-TEX-N-33",[555,8214,8215],{"stroke":557,"fill":557,"stroke-width":558,"transform":559},[555,8216,8217],{"dataMmlNode":562},[555,8218,8219,8280,8307],{"dataMmlNode":7013},[555,8220,8221],{"dataMmlNode":7016,"transform":7017},[555,8222,8223,8228],{"dataMmlNode":7020},[555,8224,8225],{"dataMmlNode":616},[567,8226],{"dataC":750,"xLinkHref":8227},"#MJX-69-TEX-N-2212",[555,8229,8230,8255],{"dataMmlNode":7013,"transform":2133},[555,8231,8232],{"dataMmlNode":7016,"transform":7358},[555,8233,8234],{"dataMmlNode":7020},[555,8235,8236,8244,8249],{"dataMmlNode":3010,"dataMjxTexclass":3011},[555,8237,8238,8241],{"dataMmlNode":906},[567,8239],{"dataC":930,"xLinkHref":8240},"#MJX-69-TEX-N-31",[567,8242],{"dataC":1357,"xLinkHref":8243,"transform":915},"#MJX-69-TEX-N-32",[555,8245,8246],{"dataMmlNode":906,"transform":918},[567,8247],{"dataC":909,"xLinkHref":8248},"#MJX-69-TEX-N-35",[555,8250,8251,8253],{"dataMmlNode":906,"transform":1134},[567,8252],{"dataC":930,"xLinkHref":8240},[567,8254],{"dataC":930,"xLinkHref":8240,"transform":915},[555,8256,8257],{"dataMmlNode":7016,"transform":7379},[555,8258,8259],{"dataMmlNode":7020},[555,8260,8261,8268,8273],{"dataMmlNode":3010,"dataMjxTexclass":3011},[555,8262,8263,8265],{"dataMmlNode":906},[567,8264],{"dataC":930,"xLinkHref":8240},[567,8266],{"dataC":913,"xLinkHref":8267,"transform":915},"#MJX-69-TEX-N-30",[555,8269,8270],{"dataMmlNode":906,"transform":918},[567,8271],{"dataC":1114,"xLinkHref":8272},"#MJX-69-TEX-N-37",[555,8274,8275,8277],{"dataMmlNode":906,"transform":1134},[567,8276],{"dataC":930,"xLinkHref":8240},[567,8278],{"dataC":1082,"xLinkHref":8279,"transform":915},"#MJX-69-TEX-N-34",[555,8281,8282],{"dataMmlNode":7016,"transform":7394},[555,8283,8284],{"dataMmlNode":7020,"transform":2133},[555,8285,8286],{"dataMmlNode":7013},[555,8287,8288],{"dataMmlNode":7016},[555,8289,8290,8294,8301],{"dataMmlNode":7020},[555,8291,8292],{"dataMmlNode":906},[567,8293],{"dataC":930,"xLinkHref":8240},[555,8295,8296,8298],{"dataMmlNode":906,"transform":915},[567,8297],{"dataC":930,"xLinkHref":8240},[567,8299],{"dataC":1100,"xLinkHref":8300,"transform":915},"#MJX-69-TEX-N-33",[555,8302,8303,8305],{"dataMmlNode":906,"transform":1134},[567,8304],{"dataC":930,"xLinkHref":8240},[567,8306],{"dataC":1100,"xLinkHref":8300,"transform":915},[7141,8308],{"dataLine":7143,"className":8309,"x1":558,"y1":7734,"x2":8154,"y2":7734},[7145],[406,8311,8312,8313,8315,8316,8318,8319,8321],{},"(11+16) - 14 = 13 (D) ",[8159,8314],{},"\n(5 - 1 + 16) - 7 = 13 (D) ",[8159,8317],{},"\n(12 - 1) - 10 = 1 (1) ",[8159,8320],{},"\n1 13 13",[406,8323,8324],{},[409,8325,8326],{},"Ответ: 1DD",[406,8328,8329],{},[1249,8330,8331],{},"Каждый полубайт(4 бита) или тетрада отлично \"упаковывается\" в одну шестнадцатеричную цифру и поэтому шестнадцатеричная система удобна для представления ячеек памяти компьютера.\nТакже числа от 0 до 255 отлично \"упаковываются\" в две шестнадцатеричные цифры (00...FF) для кодирования оттенков палитры цвета RGB(красный зелёный синий).\nЭто удобно при записи и представлении цвета пикселя на изображении.",[5242,8333,8334],{},[406,8335,8336,8337,8340,8341],{},"Для упрощения расчётов и исключения возможных ошибок при выполнении арифметических операций в недесятичных системах счисления рекомендуется вначале перевести все числа-операнды в десятичную систему счисления, выполнить расчёты в ней, а затем выполнить перевод результата в искомую систему счисления.\n",[1249,8338,8339],{},"Незначащими"," в записи числа являются только нули, стоящие слева от числа(которые не влияют на числовое значение и могут быть отброшены). Все остальные нули и единицы в записи числа являются ",[1249,8342,8343],{},"значащими!",[8345,8346,8347],"style",{},"\nmjx-container[jax=\"SVG\"] {\n  direction: ltr;\n}\n\nmjx-container[jax=\"SVG\"] > svg {\n  overflow: visible;\n  min-height: 1px;\n  min-width: 1px;\n}\n\nmjx-container[jax=\"SVG\"] > svg a {\n  fill: blue;\n  stroke: blue;\n}\n\nmjx-container[jax=\"SVG\"][display=\"true\"] {\n  display: block;\n  text-align: center;\n  margin: 1em 0;\n}\n\nmjx-container[jax=\"SVG\"][display=\"true\"][width=\"full\"] {\n  display: flex;\n}\n\nmjx-container[jax=\"SVG\"][justify=\"left\"] {\n  text-align: left;\n}\n\nmjx-container[jax=\"SVG\"][justify=\"right\"] {\n  text-align: right;\n}\n\ng[data-mml-node=\"merror\"] > g {\n  fill: red;\n  stroke: red;\n}\n\ng[data-mml-node=\"merror\"] > rect[data-background] {\n  fill: yellow;\n  stroke: none;\n}\n\ng[data-mml-node=\"mtable\"] > line[data-line], svg[data-table] > g > line[data-line] {\n  stroke-width: 70px;\n  fill: none;\n}\n\ng[data-mml-node=\"mtable\"] > rect[data-frame], svg[data-table] > g > rect[data-frame] {\n  stroke-width: 70px;\n  fill: none;\n}\n\ng[data-mml-node=\"mtable\"] > .mjx-dashed, svg[data-table] > g > .mjx-dashed {\n  stroke-dasharray: 140;\n}\n\ng[data-mml-node=\"mtable\"] > .mjx-dotted, svg[data-table] > g > .mjx-dotted {\n  stroke-linecap: round;\n  stroke-dasharray: 0,140;\n}\n\ng[data-mml-node=\"mtable\"] > g > svg {\n  overflow: visible;\n}\n\n[jax=\"SVG\"] mjx-tool {\n  display: inline-block;\n  position: relative;\n  width: 0;\n  height: 0;\n}\n\n[jax=\"SVG\"] mjx-tool > mjx-tip {\n  position: absolute;\n  top: 0;\n  left: 0;\n}\n\nmjx-tool > mjx-tip {\n  display: inline-block;\n  padding: .2em;\n  border: 1px solid #888;\n  font-size: 70%;\n  background-color: #F8F8F8;\n  color: black;\n  box-shadow: 2px 2px 5px #AAAAAA;\n}\n\ng[data-mml-node=\"maction\"][data-toggle] {\n  cursor: pointer;\n}\n\nmjx-status {\n  display: block;\n  position: fixed;\n  left: 1em;\n  bottom: 1em;\n  min-width: 25%;\n  padding: .2em .4em;\n  border: 1px solid #888;\n  font-size: 90%;\n  background-color: #F8F8F8;\n  color: black;\n}\n\nforeignObject[data-mjx-xml] {\n  font-family: initial;\n  line-height: normal;\n  overflow: visible;\n}\n\nmjx-container[jax=\"SVG\"] path[data-c], mjx-container[jax=\"SVG\"] use[data-c] {\n  stroke-width: 3;\n}\n",{"title":6986,"searchDepth":8349,"depth":8350,"links":8351},2,5,[8352],{"id":399,"depth":8353,"text":400,"children":8354},3,[8355,8390,8395],{"id":404,"depth":8356,"text":367,"children":8357},4,[8358,8359,8360,8361,8362,8363,8364,8365,8366,8373,8374,8381,8384,8387],{"id":1138,"depth":8350,"text":1139},{"id":1148,"depth":8350,"text":1149},{"id":1226,"depth":8350,"text":1227},{"id":3505,"depth":8350,"text":3506},{"id":4590,"depth":8350,"text":4591},{"id":4719,"depth":8350,"text":4720},{"id":5249,"depth":8350,"text":5250},{"id":5561,"depth":8350,"text":5562},{"id":5576,"depth":8350,"text":5577,"children":8367},[8368,8370,8371,8372],{"id":5584,"depth":8369,"text":5585},6,{"id":5760,"depth":8369,"text":5761},{"id":5898,"depth":8369,"text":5899},{"id":6112,"depth":8369,"text":6113},{"id":6257,"depth":8350,"text":6258},{"id":6942,"depth":8350,"text":8375,"children":8376},"Арифметика в недесятичных системах счисления (на примере двоичной арифметики)",[8377,8378,8379,8380],{"id":6952,"depth":8369,"text":6953},{"id":6961,"depth":8369,"text":6962},{"id":6970,"depth":8369,"text":6971},{"id":6979,"depth":8369,"text":6980},{"id":6986,"depth":8350,"text":6986,"children":8382},[8383],{"id":7170,"depth":8369,"text":7171},{"id":7177,"depth":8350,"text":6986,"children":8385},[8386],{"id":7291,"depth":8369,"text":7292},{"id":7309,"depth":8350,"text":6986,"children":8388},[8389],{"id":7547,"depth":8369,"text":7548},{"id":7601,"depth":8356,"text":7602,"children":8391},[8392,8393,8394],{"id":7614,"depth":8350,"text":7615},{"id":7741,"depth":8350,"text":7742},{"id":7856,"depth":8350,"text":7857},{"id":8008,"depth":8356,"text":8009,"children":8396},[8397,8398],{"id":8015,"depth":8350,"text":8016},{"id":8175,"depth":8350,"text":8176},"2026-01-19","Двоичная, троичная, восьмеричная, шестнадцатеричная системы счисления. Арифметика в системах счисления","md","images\u002Fblog\u002Ftoi\u002Fst5\u002Fimg.png",{},30,true,{"title":367,"description":8400},"c5m_e-KtckpYesFTbQ_zdZAo4PD-CvdzEvC0DQL6058",[8409,8411],{"title":363,"path":364,"stem":365,"description":8410,"children":-1},"Вероятностный и алфавитный подход к измерению информации",{"title":371,"path":372,"stem":373,"description":8412,"children":-1},"Диаграммы Эйлера — Венна в информатике при решении задач",1780737506504]