Перевести число 1001110101 из двоичной системы в восьмеричную
Задача: перевести число 1001110101 из двоичной в восьмеричную систему счисления.
Для перевода 1001110101 из двоичной в восьмеричную систему счисления, воспользуемся следующим алгоритмом:
- Переведем число 1001110101 из двоичной системы в десятичную;
- Полученное число переведём из десятичной системы в восьмеричную;
Решение:
1. Для перевода числа 1001110101 в десятичную систему воспользуемся формулой:
An = an-1 ∙ qn-1 + an-2 ∙ qn-2 + ∙∙∙ + a0 ∙ q0
Отсюда:
10011101012=1 ∙ 29 + 0 ∙ 28 + 0 ∙ 27 + 1 ∙ 26 + 1 ∙ 25 + 1 ∙ 24 + 0 ∙ 23 + 1 ∙ 22 + 0 ∙ 21 + 1 ∙ 20 = 1 ∙ 512 + 0 ∙ 256 + 0 ∙ 128 + 1 ∙ 64 + 1 ∙ 32 + 1 ∙ 16 + 0 ∙ 8 + 1 ∙ 4 + 0 ∙ 2 + 1 ∙ 1 = 512 + 0 + 0 + 64 + 32 + 16 + 0 + 4 + 0 + 1 = 62910
Таким образом:
10011101012 = 62910
2. Полученное число 629 переведем из десятичной системы счисления в восьмеричную. Для этого, осуществим последовательное деление на 8, до тех пор пока остаток не будет меньше чем 8.
— | 629 | 8 | |||||
624 | — | 78 | 8 | ||||
5 | 72 | — | 9 | 8 | |||
6 | 8 | 1 | |||||
1 |
Полученные остатки записываем в обратном порядке, таким образом:
62910=11658
Ответ: 10011101012 = 11658.
Смотрите также:
Полезные материалы
Калькуляторы переводов
- Онлайн переводы из двоичной в восьмеричную с подробным решением
- Онлайн переводы из десятичной в восьмеричную с подробным решением
- Онлайн переводы из десятичной в шестнадцатеричную с подробным решением
- Онлайн переводы из двоичной в шестнадцатеричную с подробным решением
- Онлайн переводы из восьмеричной в шестнадцатеричную с подробным решением
- Онлайн переводы из одной системы счисления в другую
Последние примеры переводов из 2-ой в 8-ую систему
- Запишите двоичное число 100101.011 в восьмеричной системе счисления
- Представить двоичное число 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в восьмеричной системе
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