Перевести число 000101010010000001100000 из двоичной системы в шестнадцатеричную
Задача: перевести число 000101010010000001100000 из двоичной в шестнадцатеричную систему счисления.
Для перевода 000101010010000001100000 из двоичной в шестнадцатеричную систему счисления, воспользуемся следующим алгоритмом:
- Переведем число 000101010010000001100000 из двоичной системы в десятичную;
- Полученное число переведём из десятичной системы в шестнадцатеричную;
Решение:
1. Для перевода числа 000101010010000001100000 в десятичную систему воспользуемся формулой:
An = an-1 ∙ qn-1 + an-2 ∙ qn-2 + ∙∙∙ + a0 ∙ q0
Отсюда:
0001010100100000011000002=0 ∙ 223 + 0 ∙ 222 + 0 ∙ 221 + 1 ∙ 220 + 0 ∙ 219 + 1 ∙ 218 + 0 ∙ 217 + 1 ∙ 216 + 0 ∙ 215 + 0 ∙ 214 + 1 ∙ 213 + 0 ∙ 212 + 0 ∙ 211 + 0 ∙ 210 + 0 ∙ 29 + 0 ∙ 28 + 0 ∙ 27 + 1 ∙ 26 + 1 ∙ 25 + 0 ∙ 24 + 0 ∙ 23 + 0 ∙ 22 + 0 ∙ 21 + 0 ∙ 20 = 0 ∙ 8388608 + 0 ∙ 4194304 + 0 ∙ 2097152 + 1 ∙ 1048576 + 0 ∙ 524288 + 1 ∙ 262144 + 0 ∙ 131072 + 1 ∙ 65536 + 0 ∙ 32768 + 0 ∙ 16384 + 1 ∙ 8192 + 0 ∙ 4096 + 0 ∙ 2048 + 0 ∙ 1024 + 0 ∙ 512 + 0 ∙ 256 + 0 ∙ 128 + 1 ∙ 64 + 1 ∙ 32 + 0 ∙ 16 + 0 ∙ 8 + 0 ∙ 4 + 0 ∙ 2 + 0 ∙ 1 = 0 + 0 + 0 + 1048576 + 0 + 262144 + 0 + 65536 + 0 + 0 + 8192 + 0 + 0 + 0 + 0 + 0 + 0 + 64 + 32 + 0 + 0 + 0 + 0 + 0 = 138454410
Таким образом:
0001010100100000011000002 = 138454410
2. Полученное число 1384544 переведем из десятичной системы счисления в шестнадцатеричную. Для этого, осуществим последовательное деление на 16, до тех пор пока остаток не будет меньше чем 16.
— | 1384544 | 16 | |||||||||
1384544 | — | 86534 | 16 | ||||||||
0 | 86528 | — | 5408 | 16 | |||||||
6 | 5408 | — | 338 | 16 | |||||||
0 | 336 | — | 21 | 16 | |||||||
2 | 16 | 1 | |||||||||
5 |
Полученные остатки записываем в обратном порядке, таким образом:
138454410=15206016
Ответ: 0001010100100000011000002 = 15206016.
Смотрите также:
Полезные материалы
Калькуляторы переводов
Последние примеры переводов из 2-ой в 16-ую систему
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в шестнадцатеричной системе счисления