Перевести число 0101011010100 из двоичной системы в шестнадцатеричную
Задача: перевести число 0101011010100 из двоичной в шестнадцатеричную систему счисления.
Для перевода 0101011010100 из двоичной в шестнадцатеричную систему счисления, воспользуемся следующим алгоритмом:
- Переведем число 0101011010100 из двоичной системы в десятичную;
- Полученное число переведём из десятичной системы в шестнадцатеричную;
Решение:
1. Для перевода числа 0101011010100 в десятичную систему воспользуемся формулой:
An = an-1 ∙ qn-1 + an-2 ∙ qn-2 + ∙∙∙ + a0 ∙ q0
Отсюда:
01010110101002=0 ∙ 212 + 1 ∙ 211 + 0 ∙ 210 + 1 ∙ 29 + 0 ∙ 28 + 1 ∙ 27 + 1 ∙ 26 + 0 ∙ 25 + 1 ∙ 24 + 0 ∙ 23 + 1 ∙ 22 + 0 ∙ 21 + 0 ∙ 20 = 0 ∙ 4096 + 1 ∙ 2048 + 0 ∙ 1024 + 1 ∙ 512 + 0 ∙ 256 + 1 ∙ 128 + 1 ∙ 64 + 0 ∙ 32 + 1 ∙ 16 + 0 ∙ 8 + 1 ∙ 4 + 0 ∙ 2 + 0 ∙ 1 = 0 + 2048 + 0 + 512 + 0 + 128 + 64 + 0 + 16 + 0 + 4 + 0 + 0 = 277210
Таким образом:
01010110101002 = 277210
2. Полученное число 2772 переведем из десятичной системы счисления в шестнадцатеричную. Для этого, осуществим последовательное деление на 16, до тех пор пока остаток не будет меньше чем 16.
— | 2772 | 16 | |||
2768 | — | 173 | 16 | ||
4 | 160 | 10 | |||
D |
Полученные остатки записываем в обратном порядке, таким образом:
277210=10D416
Ответ: 01010110101002 = 10D416.
Смотрите также:
Полезные материалы
Калькуляторы переводов
- Онлайн переводы из двоичной в шестнадцатеричную с подробным решением
- Онлайн переводы из десятичной в восьмеричную с подробным решением
- Онлайн переводы из двоичной в десятичную с подробным решением
- Онлайн переводы из шестнадцатеричной в десятичную с подробным решением
- Онлайн переводы из восьмеричной в шестнадцатеричную с подробным решением
- Онлайн переводы из шестнадцатеричной в восьмеричную с подробным решением
Последние примеры переводов из 2-ой в 16-ую систему
- Переведите двоичное число 110011001101 в шестнадцатеричную систему
- Запишите двоичное число 1110001.1101111010 в шестнадцатеричной системе
- Запиши двоичное число 101011011010 в шестнадцатеричной системе счисления
- Перевести число 101011000000000 из двоичной в шестнадцатеричную систему
- Как будет записано двоичное число 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