Перевести число 11100101.1 из двоичной системы в шестнадцатеричную
Задача: перевести число 11100101.1 из двоичной в шестнадцатеричную систему счисления.
Для перевода 11100101.1 из двоичной в шестнадцатеричную систему счисления, воспользуемся следующим алгоритмом:
- Переведем число 11100101.1 из двоичной системы в десятичную;
- Полученное число переведём из десятичной системы в шестнадцатеричную;
Решение:
1. Для перевода числа 11100101.1 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:
11100101.12=1 ∙ 27 + 1 ∙ 26 + 1 ∙ 25 + 0 ∙ 24 + 0 ∙ 23 + 1 ∙ 22 + 0 ∙ 21 + 1 ∙ 20 + 1 ∙ 2-1 = 1 ∙ 128 + 1 ∙ 64 + 1 ∙ 32 + 0 ∙ 16 + 0 ∙ 8 + 1 ∙ 4 + 0 ∙ 2 + 1 ∙ 1 + 1 ∙ 0.5 = 128 + 64 + 32 + 0 + 0 + 4 + 0 + 1 + 0.5 = 229.510
Таким образом:
11100101.12 = 229.510
2. Полученное число 229.5 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 229 в шестнадцатеричную систему;
- Перевести 0.5 в шестнадцатеричную систему;
2.1 Для того, чтобы перевести число 229 из десятичной системы счисления в шестнадцатеричную, необходимо осуществить последовательное деление на 16, до тех пор пока остаток не будет меньше чем 16.
— | 229 | 16 | |
224 | 14 | ||
5 |
Полученные остатки записываем в обратном порядке, таким образом:
22910=14516
2.2 Для перевода десятичной дроби 0.5 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:
0.5 ∙ 16 = 8 (8)
Ответом станет прямая последовательность целых частей произведения. Т.е.
0.510=0.816
2.3. Осталось соединить переведенные части, таким образом:
229.510=145.816
Ответ: 11100101.12 = 145.816.
Смотрите также:
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в шестнадцатеричной системе
- Переведите 01101000011001010111001001100101 из двоичной в шестнадцатеричную систему счисления
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- Представьте двоичное число 1001100110111011.00111011 в шестнадцатеричной системе счисления
- Переведите двоичное число 11100.001 в шестнадцатеричную систему
- Представить двоичное число 1010101110 в шестнадцатеричной системе счисления
- Как перевести 11001010101010110100101010010111101001.10100100010100111 из двоичной в шестнадцатеричную систему?
- Как перевести 11011110.0110011001100110 из двоичной в шестнадцатеричную систему счисления?