Перевести число 111111000001111101010 из двоичной системы в шестнадцатеричную
Задача: перевести число 111111000001111101010 из двоичной в шестнадцатеричную систему счисления.
Для перевода 111111000001111101010 из двоичной в шестнадцатеричную систему счисления, воспользуемся следующим алгоритмом:
- Переведем число 111111000001111101010 из двоичной системы в десятичную;
- Полученное число переведём из десятичной системы в шестнадцатеричную;
Решение:
1. Для перевода числа 111111000001111101010 в десятичную систему воспользуемся формулой:
An = an-1 ∙ qn-1 + an-2 ∙ qn-2 + ∙∙∙ + a0 ∙ q0
Отсюда:
1111110000011111010102=1 ∙ 220 + 1 ∙ 219 + 1 ∙ 218 + 1 ∙ 217 + 1 ∙ 216 + 1 ∙ 215 + 0 ∙ 214 + 0 ∙ 213 + 0 ∙ 212 + 0 ∙ 211 + 0 ∙ 210 + 1 ∙ 29 + 1 ∙ 28 + 1 ∙ 27 + 1 ∙ 26 + 1 ∙ 25 + 0 ∙ 24 + 1 ∙ 23 + 0 ∙ 22 + 1 ∙ 21 + 0 ∙ 20 = 1 ∙ 1048576 + 1 ∙ 524288 + 1 ∙ 262144 + 1 ∙ 131072 + 1 ∙ 65536 + 1 ∙ 32768 + 0 ∙ 16384 + 0 ∙ 8192 + 0 ∙ 4096 + 0 ∙ 2048 + 0 ∙ 1024 + 1 ∙ 512 + 1 ∙ 256 + 1 ∙ 128 + 1 ∙ 64 + 1 ∙ 32 + 0 ∙ 16 + 1 ∙ 8 + 0 ∙ 4 + 1 ∙ 2 + 0 ∙ 1 = 1048576 + 524288 + 262144 + 131072 + 65536 + 32768 + 0 + 0 + 0 + 0 + 0 + 512 + 256 + 128 + 64 + 32 + 0 + 8 + 0 + 2 + 0 = 206538610
Таким образом:
1111110000011111010102 = 206538610
2. Полученное число 2065386 переведем из десятичной системы счисления в шестнадцатеричную. Для этого, осуществим последовательное деление на 16, до тех пор пока остаток не будет меньше чем 16.
— | 2065386 | 16 | |||||||||
2065376 | — | 129086 | 16 | ||||||||
A | 129072 | — | 8067 | 16 | |||||||
E | 8064 | — | 504 | 16 | |||||||
3 | 496 | — | 31 | 16 | |||||||
8 | 16 | 1 | |||||||||
F |
Полученные остатки записываем в обратном порядке, таким образом:
206538610=1F83EA16
Ответ: 1111110000011111010102 = 1F83EA16.
Смотрите также:
Полезные материалы
Калькуляторы переводов
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