Перевести число 10110000110001101011 из двоичной системы в восьмеричную
Задача: перевести число 10110000110001101011 из двоичной в восьмеричную систему счисления.
Для перевода 10110000110001101011 из двоичной в восьмеричную систему счисления, воспользуемся следующим алгоритмом:
- Переведем число 10110000110001101011 из двоичной системы в десятичную;
- Полученное число переведём из десятичной системы в восьмеричную;
Решение:
1. Для перевода числа 10110000110001101011 в десятичную систему воспользуемся формулой:
An = an-1 ∙ qn-1 + an-2 ∙ qn-2 + ∙∙∙ + a0 ∙ q0
Отсюда:
101100001100011010112=1 ∙ 219 + 0 ∙ 218 + 1 ∙ 217 + 1 ∙ 216 + 0 ∙ 215 + 0 ∙ 214 + 0 ∙ 213 + 0 ∙ 212 + 1 ∙ 211 + 1 ∙ 210 + 0 ∙ 29 + 0 ∙ 28 + 0 ∙ 27 + 1 ∙ 26 + 1 ∙ 25 + 0 ∙ 24 + 1 ∙ 23 + 0 ∙ 22 + 1 ∙ 21 + 1 ∙ 20 = 1 ∙ 524288 + 0 ∙ 262144 + 1 ∙ 131072 + 1 ∙ 65536 + 0 ∙ 32768 + 0 ∙ 16384 + 0 ∙ 8192 + 0 ∙ 4096 + 1 ∙ 2048 + 1 ∙ 1024 + 0 ∙ 512 + 0 ∙ 256 + 0 ∙ 128 + 1 ∙ 64 + 1 ∙ 32 + 0 ∙ 16 + 1 ∙ 8 + 0 ∙ 4 + 1 ∙ 2 + 1 ∙ 1 = 524288 + 0 + 131072 + 65536 + 0 + 0 + 0 + 0 + 2048 + 1024 + 0 + 0 + 0 + 64 + 32 + 0 + 8 + 0 + 2 + 1 = 72407510
Таким образом:
101100001100011010112 = 72407510
2. Полученное число 724075 переведем из десятичной системы счисления в восьмеричную. Для этого, осуществим последовательное деление на 8, до тех пор пока остаток не будет меньше чем 8.
— | 724075 | 8 | |||||||||||
724072 | — | 90509 | 8 | ||||||||||
3 | 90504 | — | 11313 | 8 | |||||||||
5 | 11312 | — | 1414 | 8 | |||||||||
1 | 1408 | — | 176 | 8 | |||||||||
6 | 176 | — | 22 | 8 | |||||||||
0 | 16 | 2 | |||||||||||
6 |
Полученные остатки записываем в обратном порядке, таким образом:
72407510=26061538
Ответ: 101100001100011010112 = 26061538.
Смотрите также:
Полезные материалы
Калькуляторы переводов
- Калькулятор переводов из двоичной в восьмеричную систему
- Калькулятор переводов из десятичной в двоичную систему
- Калькулятор переводов из двоичной в десятичную систему
- Калькулятор переводов из восьмеричной в десятичную систему
- Калькулятор переводов из шестнадцатеричной в десятичную систему
- Калькулятор переводов из одной системы счисления в другую
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- Перевести число 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из двоичной в восьмеричную систему
- Перевести двоичное число 1010101100011001 в восьмеричную систему
- Переведите двоичное число 001100101101110 в восьмеричную систему