Перевести число 111111100.0001 из двоичной системы в шестнадцатеричную
Задача: перевести число 111111100.0001 из двоичной в шестнадцатеричную систему счисления.
Для перевода 111111100.0001 из двоичной в шестнадцатеричную систему счисления, воспользуемся следующим алгоритмом:
- Переведем число 111111100.0001 из двоичной системы в десятичную;
- Полученное число переведём из десятичной системы в шестнадцатеричную;
Решение:
1. Для перевода числа 111111100.0001 в десятичную систему воспользуемся формулой:
An = an-1 ∙ qn-1 + an-2 ∙ qn-2 + ∙∙∙ + a0 ∙ q0 + a-1 ∙ q-1 + ∙∙∙ + a-m ∙ q-m
Отсюда:
111111100.00012=1 ∙ 28 + 1 ∙ 27 + 1 ∙ 26 + 1 ∙ 25 + 1 ∙ 24 + 1 ∙ 23 + 1 ∙ 22 + 0 ∙ 21 + 0 ∙ 20 + 0 ∙ 2-1 + 0 ∙ 2-2 + 0 ∙ 2-3 + 1 ∙ 2-4 = 1 ∙ 256 + 1 ∙ 128 + 1 ∙ 64 + 1 ∙ 32 + 1 ∙ 16 + 1 ∙ 8 + 1 ∙ 4 + 0 ∙ 2 + 0 ∙ 1 + 0 ∙ 0.5 + 0 ∙ 0.25 + 0 ∙ 0.125 + 1 ∙ 0.0625 = 256 + 128 + 64 + 32 + 16 + 8 + 4 + 0 + 0 + 0 + 0 + 0 + 0.0625 = 508.062510
Таким образом:
111111100.00012 = 508.062510
2. Полученное число 508.0625 переведем из десятичной системы счисления в шестнадцатеричную. Т.к. полученное число содержит дробную часть, нам потребуется перевести вначале целую часть, а затем дробную. Таким образом необходимо:
- Перевести 508 в шестнадцатеричную систему;
- Перевести 0.0625 в шестнадцатеричную систему;
2.1 Для того, чтобы перевести число 508 из десятичной системы счисления в шестнадцатеричную, необходимо осуществить последовательное деление на 16, до тех пор пока остаток не будет меньше чем 16.
— | 508 | 16 | |||
496 | — | 31 | 16 | ||
C | 16 | 1 | |||
F |
Полученные остатки записываем в обратном порядке, таким образом:
50810=1FC16
2.2 Для перевода десятичной дроби 0.0625 в шестнадцатеричную систему, необходимо выполнить последовательное умножение дроби на 16, до тех пор, пока дробная часть не станет равной 0 или пока не будет достигнута заданная точность вычисления. Получаем:
0.0625 ∙ 16 = 1 (1)
Ответом станет прямая последовательность целых частей произведения. Т.е.
0.062510=0.116
2.3. Осталось соединить переведенные части, таким образом:
508.062510=1FC.116
Ответ: 111111100.00012 = 1FC.116.
Смотрите также:
Полезные материалы
Калькуляторы переводов
- Калькулятор из двоичной в шестнадцатеричную с подробным решением
- Калькулятор из десятичной в восьмеричную с подробным решением
- Калькулятор из десятичной в шестнадцатеричную с подробным решением
- Калькулятор из двоичной в десятичную с подробным решением
- Калькулятор из восьмеричной в десятичную с подробным решением
- Калькулятор из восьмеричной в двоичную с подробным решением
Последние примеры переводов из 2-ой в 16-ую систему
- Представьте двоичное число 01110100101001010101010111111101111111 в шестнадцатеричной системе
- Представьте двоичное число 1010110011001 в шестнадцатеричной системе
- Переведите 110110.00101001 из двоичной в шестнадцатеричную систему счисления
- Переведите число 1111101011101011101 из двоичной в шестнадцатеричную систему счисления
- Перевести двоичное число 10110110111 в шестнадцатеричную систему счисления
- Какое двоичное число соответствует шестнадцатеричному числу 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