Перевести число 322.4587 из десятичной системы в двоичную
Задача: перевести число 322.4587 из десятичной системы счисления в двоичную.
Алгоритм:
Для того, чтобы перевести число 322.4587 из десятичной системы счисления в двоичную, необходимо перевести вначале целую часть, а затем дробную. Таким образом потребуется:>
- Перевести 322 в двоичную систему;
- Перевести 0.4587 в двоичную систему.
Решение:
1. Для того, чтобы перевести число 322 из десятичной системы счисления в двоичную, необходимо осуществить последовательное деление на 2, до тех пор пока остаток не будет меньше чем 2.
— | 322 | 2 | |||||||||||||||
322 | — | 161 | 2 | ||||||||||||||
0 | 160 | — | 80 | 2 | |||||||||||||
1 | 80 | — | 40 | 2 | |||||||||||||
0 | 40 | — | 20 | 2 | |||||||||||||
0 | 20 | — | 10 | 2 | |||||||||||||
0 | 10 | — | 5 | 2 | |||||||||||||
0 | 4 | — | 2 | 2 | |||||||||||||
1 | 2 | 1 | |||||||||||||||
0 |
Полученные остатки записываем в обратном порядке, таким образом:
32210=1010000102
2. Для перевода десятичной дроби 0.4587 в двоичную систему, необходимо выполнить последовательное умножение дроби на 2, до тех пор, пока дробная часть не станет равной 0 или пока не будет достигнута заданная точность вычисления. Получаем:
0.4587 ∙ 2 = 0.9174 (0)
0.9174 ∙ 2 = 1.8348 (1)
0.8348 ∙ 2 = 1.6696 (1)
0.6696 ∙ 2 = 1.3392 (1)
0.3392 ∙ 2 = 0.6784 (0)
0.6784 ∙ 2 = 1.3568 (1)
0.3568 ∙ 2 = 0.7136 (0)
0.7136 ∙ 2 = 1.4272 (1)
0.4272 ∙ 2 = 0.8544 (0)
0.8544 ∙ 2 = 1.7088 (1)
0.7088 ∙ 2 = 1.4176 (1)
Ответом станет прямая последовательность целых частей произведения. Т.е.
0.458710=0.011101010112
3. Осталось соединить переведенные части, таким образом:
Ответ: 322.458710=101000010.011101010112.
Подробнее о том, как переводить числа из десятичной системы в двоичную, смотрите здесь.
Смотрите также:
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