Перевести число 10101001101011110 из двоичной системы в шестнадцатеричную
Задача: перевести число 10101001101011110 из двоичной в шестнадцатеричную систему счисления.
Для перевода 10101001101011110 из двоичной в шестнадцатеричную систему счисления, воспользуемся следующим алгоритмом:
- Переведем число 10101001101011110 из двоичной системы в десятичную;
- Полученное число переведём из десятичной системы в шестнадцатеричную;
Решение:
1. Для перевода числа 10101001101011110 в десятичную систему воспользуемся формулой:
An = an-1 ∙ qn-1 + an-2 ∙ qn-2 + ∙∙∙ + a0 ∙ q0
Отсюда:
101010011010111102=1 ∙ 216 + 0 ∙ 215 + 1 ∙ 214 + 0 ∙ 213 + 1 ∙ 212 + 0 ∙ 211 + 0 ∙ 210 + 1 ∙ 29 + 1 ∙ 28 + 0 ∙ 27 + 1 ∙ 26 + 0 ∙ 25 + 1 ∙ 24 + 1 ∙ 23 + 1 ∙ 22 + 1 ∙ 21 + 0 ∙ 20 = 1 ∙ 65536 + 0 ∙ 32768 + 1 ∙ 16384 + 0 ∙ 8192 + 1 ∙ 4096 + 0 ∙ 2048 + 0 ∙ 1024 + 1 ∙ 512 + 1 ∙ 256 + 0 ∙ 128 + 1 ∙ 64 + 0 ∙ 32 + 1 ∙ 16 + 1 ∙ 8 + 1 ∙ 4 + 1 ∙ 2 + 0 ∙ 1 = 65536 + 0 + 16384 + 0 + 4096 + 0 + 0 + 512 + 256 + 0 + 64 + 0 + 16 + 8 + 4 + 2 + 0 = 8687810
Таким образом:
101010011010111102 = 8687810
2. Полученное число 86878 переведем из десятичной системы счисления в шестнадцатеричную. Для этого, осуществим последовательное деление на 16, до тех пор пока остаток не будет меньше чем 16.
— | 86878 | 16 | |||||||
86864 | — | 5429 | 16 | ||||||
E | 5424 | — | 339 | 16 | |||||
5 | 336 | — | 21 | 16 | |||||
3 | 16 | 1 | |||||||
5 |
Полученные остатки записываем в обратном порядке, таким образом:
8687810=1535E16
Ответ: 101010011010111102 = 1535E16.
Смотрите также:
Полезные материалы
Калькуляторы переводов
- Калькулятор переводов из двоичной в шестнадцатеричную систему с решением
- Калькулятор переводов из десятичной в восьмеричную систему с решением
- Калькулятор переводов из десятичной в шестнадцатеричную систему с решением
- Калькулятор переводов из двоичной в восьмеричную систему с решением
- Калькулятор переводов из восьмеричной в двоичную систему с решением
- Калькулятор переводов из восьмеричной в шестнадцатеричную систему с решением
Последние примеры переводов из 2-ой в 16-ую систему
- Переведите 000000000001000 из двоичной в шестнадцатеричную систему счисления
- Запишите двоичное число 110000110101001100110 в шестнадцатеричной системе счисления
- Запиши двоичное число 1010101010111100 в шестнадцатеричной системе счисления
- Запишите двоичное число 1101110101001 в шестнадцатеричной системе
- Запишите двоичное число 100101000010010111001 в шестнадцатеричной системе счисления
- Перевести 1110011.10100011 из двоичной в шестнадцатеричную систему счисления
- Запишите двоичное число 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в шестнадцатеричной системе
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