Перевести число 0000100110011001100110011001100110010000000000010001000000010 из двоичной системы в шестнадцатеричную
Задача: перевести число 0000100110011001100110011001100110010000000000010001000000010 из двоичной в шестнадцатеричную систему счисления.
Для перевода 0000100110011001100110011001100110010000000000010001000000010 из двоичной в шестнадцатеричную систему счисления, воспользуемся следующим алгоритмом:
- Переведем число 0000100110011001100110011001100110010000000000010001000000010 из двоичной системы в десятичную;
- Полученное число переведём из десятичной системы в шестнадцатеричную;
Решение:
1. Для перевода числа 0000100110011001100110011001100110010000000000010001000000010 в десятичную систему воспользуемся формулой:
An = an-1 ∙ qn-1 + an-2 ∙ qn-2 + ∙∙∙ + a0 ∙ q0
Отсюда:
00001001100110011001100110011001100100000000000100010000000102=0 ∙ 260 + 0 ∙ 259 + 0 ∙ 258 + 0 ∙ 257 + 1 ∙ 256 + 0 ∙ 255 + 0 ∙ 254 + 1 ∙ 253 + 1 ∙ 252 + 0 ∙ 251 + 0 ∙ 250 + 1 ∙ 249 + 1 ∙ 248 + 0 ∙ 247 + 0 ∙ 246 + 1 ∙ 245 + 1 ∙ 244 + 0 ∙ 243 + 0 ∙ 242 + 1 ∙ 241 + 1 ∙ 240 + 0 ∙ 239 + 0 ∙ 238 + 1 ∙ 237 + 1 ∙ 236 + 0 ∙ 235 + 0 ∙ 234 + 1 ∙ 233 + 1 ∙ 232 + 0 ∙ 231 + 0 ∙ 230 + 1 ∙ 229 + 1 ∙ 228 + 0 ∙ 227 + 0 ∙ 226 + 1 ∙ 225 + 0 ∙ 224 + 0 ∙ 223 + 0 ∙ 222 + 0 ∙ 221 + 0 ∙ 220 + 0 ∙ 219 + 0 ∙ 218 + 0 ∙ 217 + 0 ∙ 216 + 0 ∙ 215 + 0 ∙ 214 + 1 ∙ 213 + 0 ∙ 212 + 0 ∙ 211 + 0 ∙ 210 + 1 ∙ 29 + 0 ∙ 28 + 0 ∙ 27 + 0 ∙ 26 + 0 ∙ 25 + 0 ∙ 24 + 0 ∙ 23 + 0 ∙ 22 + 1 ∙ 21 + 0 ∙ 20 = 0 ∙ 1152921504606846976 + 0 ∙ 576460752303423488 + 0 ∙ 288230376151711744 + 0 ∙ 144115188075855872 + 1 ∙ 72057594037927936 + 0 ∙ 36028797018963968 + 0 ∙ 18014398509481984 + 1 ∙ 9007199254740992 + 1 ∙ 4503599627370496 + 0 ∙ 2251799813685248 + 0 ∙ 1125899906842624 + 1 ∙ 562949953421312 + 1 ∙ 281474976710656 + 0 ∙ 140737488355328 + 0 ∙ 70368744177664 + 1 ∙ 35184372088832 + 1 ∙ 17592186044416 + 0 ∙ 8796093022208 + 0 ∙ 4398046511104 + 1 ∙ 2199023255552 + 1 ∙ 1099511627776 + 0 ∙ 549755813888 + 0 ∙ 274877906944 + 1 ∙ 137438953472 + 1 ∙ 68719476736 + 0 ∙ 34359738368 + 0 ∙ 17179869184 + 1 ∙ 8589934592 + 1 ∙ 4294967296 + 0 ∙ 2147483648 + 0 ∙ 1073741824 + 1 ∙ 536870912 + 1 ∙ 268435456 + 0 ∙ 134217728 + 0 ∙ 67108864 + 1 ∙ 33554432 + 0 ∙ 16777216 + 0 ∙ 8388608 + 0 ∙ 4194304 + 0 ∙ 2097152 + 0 ∙ 1048576 + 0 ∙ 524288 + 0 ∙ 262144 + 0 ∙ 131072 + 0 ∙ 65536 + 0 ∙ 32768 + 0 ∙ 16384 + 1 ∙ 8192 + 0 ∙ 4096 + 0 ∙ 2048 + 0 ∙ 1024 + 1 ∙ 512 + 0 ∙ 256 + 0 ∙ 128 + 0 ∙ 64 + 0 ∙ 32 + 0 ∙ 16 + 0 ∙ 8 + 0 ∙ 4 + 1 ∙ 2 + 0 ∙ 1 = 0 + 0 + 0 + 0 + 72057594037927936 + 0 + 0 + 9007199254740992 + 4503599627370496 + 0 + 0 + 562949953421312 + 281474976710656 + 0 + 0 + 35184372088832 + 17592186044416 + 0 + 0 + 2199023255552 + 1099511627776 + 0 + 0 + 137438953472 + 68719476736 + 0 + 0 + 8589934592 + 4294967296 + 0 + 0 + 536870912 + 268435456 + 0 + 0 + 33554432 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 8192 + 0 + 0 + 0 + 512 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 2 + 0 = 8646911282538957010
Таким образом:
00001001100110011001100110011001100100000000000100010000000102 = 8646911282538957010
2. Полученное число 86469112825389570 переведем из десятичной системы счисления в шестнадцатеричную. Для этого, осуществим последовательное деление на 16, до тех пор пока остаток не будет меньше чем 16.
— | 86469112825389570 | 16 | |||||||||||||||||||||||||||
8.646911282539E+16 | — | 5.4043195515868E+15 | 16 | ||||||||||||||||||||||||||
0 | 5.4043195515868E+15 | — | 3.3776997197418E+14 | 16 | |||||||||||||||||||||||||
0 | 3.3776997197418E+14 | — | 21110623248386 | 16 | |||||||||||||||||||||||||
2 | 21110623248384 | — | 1319413953024 | 16 | |||||||||||||||||||||||||
2 | 1319413953024 | — | 82463372064 | 16 | |||||||||||||||||||||||||
0 | 82463372064 | — | 5153960754 | 16 | |||||||||||||||||||||||||
0 | 5153960752 | — | 322122547 | 16 | |||||||||||||||||||||||||
2 | 322122544 | — | 20132659 | 16 | |||||||||||||||||||||||||
3 | 20132656 | — | 1258291 | 16 | |||||||||||||||||||||||||
3 | 1258288 | — | 78643 | 16 | |||||||||||||||||||||||||
3 | 78640 | — | 4915 | 16 | |||||||||||||||||||||||||
3 | 4912 | — | 307 | 16 | |||||||||||||||||||||||||
3 | 304 | — | 19 | 16 | |||||||||||||||||||||||||
3 | 16 | 1 | |||||||||||||||||||||||||||
3 |
Полученные остатки записываем в обратном порядке, таким образом:
8646911282538957010=13333333200220016
Ответ: 00001001100110011001100110011001100100000000000100010000000102 = 13333333200220016.
Смотрите также:
Полезные материалы
Калькуляторы переводов
- Онлайн калькулятор из двоичной в шестнадцатеричную систему с решением
- Онлайн калькулятор из десятичной в восьмеричную систему с решением
- Онлайн калькулятор из десятичной в шестнадцатеричную систему с решением
- Онлайн калькулятор из шестнадцатеричной в десятичную систему с решением
- Онлайн калькулятор из двоичной в восьмеричную систему с решением
- Онлайн калькулятор из восьмеричной в двоичную систему с решением
Последние примеры переводов из 2-ой в 16-ую систему
- Перевести число 100100110101.0011100001 из двоичной в шестнадцатеричную систему
- Как представлено двоичное число 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в шестнадцатеричной системе счисления?
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- Представить двоичное число 000110100101 в шестнадцатеричной системе счисления