Перевести число 001011100000101100001111111111111110100100001001101100000001 из двоичной системы в шестнадцатеричную
Задача: перевести число 001011100000101100001111111111111110100100001001101100000001 из двоичной в шестнадцатеричную систему счисления.
Для перевода 001011100000101100001111111111111110100100001001101100000001 из двоичной в шестнадцатеричную систему счисления, воспользуемся следующим алгоритмом:
- Переведем число 001011100000101100001111111111111110100100001001101100000001 из двоичной системы в десятичную;
- Полученное число переведём из десятичной системы в шестнадцатеричную;
Решение:
1. Для перевода числа 001011100000101100001111111111111110100100001001101100000001 в десятичную систему воспользуемся формулой:
An = an-1 ∙ qn-1 + an-2 ∙ qn-2 + ∙∙∙ + a0 ∙ q0
Отсюда:
0010111000001011000011111111111111101001000010011011000000012=0 ∙ 259 + 0 ∙ 258 + 1 ∙ 257 + 0 ∙ 256 + 1 ∙ 255 + 1 ∙ 254 + 1 ∙ 253 + 0 ∙ 252 + 0 ∙ 251 + 0 ∙ 250 + 0 ∙ 249 + 0 ∙ 248 + 1 ∙ 247 + 0 ∙ 246 + 1 ∙ 245 + 1 ∙ 244 + 0 ∙ 243 + 0 ∙ 242 + 0 ∙ 241 + 0 ∙ 240 + 1 ∙ 239 + 1 ∙ 238 + 1 ∙ 237 + 1 ∙ 236 + 1 ∙ 235 + 1 ∙ 234 + 1 ∙ 233 + 1 ∙ 232 + 1 ∙ 231 + 1 ∙ 230 + 1 ∙ 229 + 1 ∙ 228 + 1 ∙ 227 + 1 ∙ 226 + 1 ∙ 225 + 0 ∙ 224 + 1 ∙ 223 + 0 ∙ 222 + 0 ∙ 221 + 1 ∙ 220 + 0 ∙ 219 + 0 ∙ 218 + 0 ∙ 217 + 0 ∙ 216 + 1 ∙ 215 + 0 ∙ 214 + 0 ∙ 213 + 1 ∙ 212 + 1 ∙ 211 + 0 ∙ 210 + 1 ∙ 29 + 1 ∙ 28 + 0 ∙ 27 + 0 ∙ 26 + 0 ∙ 25 + 0 ∙ 24 + 0 ∙ 23 + 0 ∙ 22 + 0 ∙ 21 + 1 ∙ 20 = 0 ∙ 576460752303423488 + 0 ∙ 288230376151711744 + 1 ∙ 144115188075855872 + 0 ∙ 72057594037927936 + 1 ∙ 36028797018963968 + 1 ∙ 18014398509481984 + 1 ∙ 9007199254740992 + 0 ∙ 4503599627370496 + 0 ∙ 2251799813685248 + 0 ∙ 1125899906842624 + 0 ∙ 562949953421312 + 0 ∙ 281474976710656 + 1 ∙ 140737488355328 + 0 ∙ 70368744177664 + 1 ∙ 35184372088832 + 1 ∙ 17592186044416 + 0 ∙ 8796093022208 + 0 ∙ 4398046511104 + 0 ∙ 2199023255552 + 0 ∙ 1099511627776 + 1 ∙ 549755813888 + 1 ∙ 274877906944 + 1 ∙ 137438953472 + 1 ∙ 68719476736 + 1 ∙ 34359738368 + 1 ∙ 17179869184 + 1 ∙ 8589934592 + 1 ∙ 4294967296 + 1 ∙ 2147483648 + 1 ∙ 1073741824 + 1 ∙ 536870912 + 1 ∙ 268435456 + 1 ∙ 134217728 + 1 ∙ 67108864 + 1 ∙ 33554432 + 0 ∙ 16777216 + 1 ∙ 8388608 + 0 ∙ 4194304 + 0 ∙ 2097152 + 1 ∙ 1048576 + 0 ∙ 524288 + 0 ∙ 262144 + 0 ∙ 131072 + 0 ∙ 65536 + 1 ∙ 32768 + 0 ∙ 16384 + 0 ∙ 8192 + 1 ∙ 4096 + 1 ∙ 2048 + 0 ∙ 1024 + 1 ∙ 512 + 1 ∙ 256 + 0 ∙ 128 + 0 ∙ 64 + 0 ∙ 32 + 0 ∙ 16 + 0 ∙ 8 + 0 ∙ 4 + 0 ∙ 2 + 1 ∙ 1 = 0 + 0 + 144115188075855872 + 0 + 36028797018963968 + 18014398509481984 + 9007199254740992 + 0 + 0 + 0 + 0 + 0 + 140737488355328 + 0 + 35184372088832 + 17592186044416 + 0 + 0 + 0 + 0 + 549755813888 + 274877906944 + 137438953472 + 68719476736 + 34359738368 + 17179869184 + 8589934592 + 4294967296 + 2147483648 + 1073741824 + 536870912 + 268435456 + 134217728 + 67108864 + 33554432 + 0 + 8388608 + 0 + 0 + 1048576 + 0 + 0 + 0 + 0 + 32768 + 0 + 0 + 4096 + 2048 + 0 + 512 + 256 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 1 = 20736019639308160110
Таким образом:
0010111000001011000011111111111111101001000010011011000000012 = 20736019639308160110
2. Полученное число 207360196393081601 переведем из десятичной системы счисления в шестнадцатеричную. Для этого, осуществим последовательное деление на 16, до тех пор пока остаток не будет меньше чем 16.
— | 207360196393081601 | 16 | |||||||||||||||||||||||||||
2.0736019639308E+17 | — | 1.2960012274568E+16 | 16 | ||||||||||||||||||||||||||
0 | 1.2960012274568E+16 | — | 8.1000076716048E+14 | 16 | |||||||||||||||||||||||||
0 | 8.1000076716046E+14 | — | 50625047947529 | 16 | |||||||||||||||||||||||||
B | 50625047947520 | — | 3164065496720 | 16 | |||||||||||||||||||||||||
9 | 3164065496720 | — | 197754093545 | 16 | |||||||||||||||||||||||||
0 | 197754093536 | — | 12359630846 | 16 | |||||||||||||||||||||||||
9 | 12359630832 | — | 772476927 | 16 | |||||||||||||||||||||||||
E | 772476912 | — | 48279807 | 16 | |||||||||||||||||||||||||
F | 48279792 | — | 3017487 | 16 | |||||||||||||||||||||||||
F | 3017472 | — | 188592 | 16 | |||||||||||||||||||||||||
F | 188592 | — | 11787 | 16 | |||||||||||||||||||||||||
0 | 11776 | — | 736 | 16 | |||||||||||||||||||||||||
B | 736 | — | 46 | 16 | |||||||||||||||||||||||||
0 | 32 | 2 | |||||||||||||||||||||||||||
E |
Полученные остатки записываем в обратном порядке, таким образом:
20736019639308160110=2E0B0FFFE909B0016
Ответ: 0010111000001011000011111111111111101001000010011011000000012 = 2E0B0FFFE909B0016.
Смотрите также:
Полезные материалы
Калькуляторы переводов
- Калькулятор из двоичной в шестнадцатеричную систему с решением
- Калькулятор из десятичной в восьмеричную систему с решением
- Калькулятор из двоичной в десятичную систему с решением
- Калькулятор из шестнадцатеричной в десятичную систему с решением
- Калькулятор из шестнадцатеричной в восьмеричную систему с решением
- Калькулятор из одной системы счисления в другую
Последние примеры переводов из 2-ой в 16-ую систему
- Запишите двоичное число 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в шестнадцатеричной системе
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