Перевести число 1C34 из шестнадцатеричной системы в двоичную
Задача: перевести число 1C34 из шестнадцатеричной в двоичную систему счисления.
Для перевода 1C34 из шестнадцатеричной в двоичную систему счисления, воспользуемся следующим алгоритмом:
- Переведем число 1C34 из шестнадцатеричной системы в десятичную;
- Полученное число переведём из десятичной системы в двоичную;
Решение:
1. Для перевода числа 1C34 в десятичную систему воспользуемся формулой:
An = an-1 ∙ qn-1 + an-2 ∙ qn-2 + ∙∙∙ + a0 ∙ q0
Отсюда:
1C3416=1 ∙ 163 + C ∙ 162 + 3 ∙ 161 + 4 ∙ 160 = 1 ∙ 4096 + 12 ∙ 256 + 3 ∙ 16 + 4 ∙ 1 = 4096 + 3072 + 48 + 4 = 722010
Таким образом:
1C3416 = 722010
2. Полученное число 7220 переведем из десятичной системы счисления в двоичную. Для этого, осуществим последовательное деление на 2, до тех пор пока остаток не будет меньше чем 2.
— | 7220 | 2 | |||||||||||||||||||||||
7220 | — | 3610 | 2 | ||||||||||||||||||||||
0 | 3610 | — | 1805 | 2 | |||||||||||||||||||||
0 | 1804 | — | 902 | 2 | |||||||||||||||||||||
1 | 902 | — | 451 | 2 | |||||||||||||||||||||
0 | 450 | — | 225 | 2 | |||||||||||||||||||||
1 | 224 | — | 112 | 2 | |||||||||||||||||||||
1 | 112 | — | 56 | 2 | |||||||||||||||||||||
0 | 56 | — | 28 | 2 | |||||||||||||||||||||
0 | 28 | — | 14 | 2 | |||||||||||||||||||||
0 | 14 | — | 7 | 2 | |||||||||||||||||||||
0 | 6 | — | 3 | 2 | |||||||||||||||||||||
1 | 2 | 1 | |||||||||||||||||||||||
1 |
Полученные остатки записываем в обратном порядке, таким образом:
722010=11100001101002
Ответ: 1C3416 = 11100001101002.
Смотрите также:
Полезные материалы
Калькуляторы переводов
Последние примеры переводов из 16-ой в 2-ую систему
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