Перевести число 90.75 из десятичной системы в двоичную
Задача: перевести число 90.75 из десятичной системы счисления в двоичную.
Алгоритм:
Для того, чтобы перевести число 90.75 из десятичной системы счисления в двоичную, необходимо перевести вначале целую часть, а затем дробную. Таким образом потребуется:>
- Перевести 90 в двоичную систему;
- Перевести 0.75 в двоичную систему.
Решение:
1. Для того, чтобы перевести число 90 из десятичной системы счисления в двоичную, необходимо осуществить последовательное деление на 2, до тех пор пока остаток не будет меньше чем 2.
| — | 90 | 2 | |||||||||||
| 90 | — | 45 | 2 | ||||||||||
| 0 | 44 | — | 22 | 2 | |||||||||
| 1 | 22 | — | 11 | 2 | |||||||||
| 0 | 10 | — | 5 | 2 | |||||||||
| 1 | 4 | — | 2 | 2 | |||||||||
| 1 | 2 | 1 | |||||||||||
| 0 |
Полученные остатки записываем в обратном порядке, таким образом:
9010=10110102
2. Для перевода десятичной дроби 0.75 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:
0.75 ∙ 2 = 1.5 (1)
0.5 ∙ 2 = 1 (1)
Ответом станет прямая последовательность целых частей произведения. Т.е.
0.7510=0.112
3. Осталось соединить переведенные части, таким образом:
Ответ: 90.7510=1011010.112.
Подробнее о том, как переводить числа из десятичной системы в двоичную, смотрите здесь.
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