Перевести число 4C.5C28F5C28F5 из шестнадцатеричной системы в двоичную

Задача: перевести число 4C.5C28F5C28F5 из шестнадцатеричной в двоичную систему счисления.

Для перевода 4C.5C28F5C28F5 из шестнадцатеричной в двоичную систему счисления, воспользуемся следующим алгоритмом:

1. Переведем число 4C.5C28F5C28F5 из шестнадцатеричной системы в десятичную;
2. Полученное число переведём из десятичной системы в двоичную;

Решение:

1. Для перевода числа 4C.5C28F5C28F5 в десятичную систему воспользуемся формулой:

A_n = a_n-1 ∙ q^n-1 + a_n-2 ∙ q^n-2 + ∙∙∙ + a₀ ∙ q⁰ + a_-1 ∙ q^-1 + ∙∙∙ + a_-m ∙ q^-m

Отсюда:

4C.5C28F5C28F5₁₆=4 ∙ 16¹ + C ∙ 16⁰ + 5 ∙ 16^-1 + C ∙ 16^-2 + 2 ∙ 16^-3 + 8 ∙ 16^-4 + F ∙ 16^-5 + 5 ∙ 16^-6 + C ∙ 16^-7 + 2 ∙ 16^-8 + 8 ∙ 16^-9 + F ∙ 16^-10 + 5 ∙ 16^-11 = 4 ∙ 16 + 12 ∙ 1 + 5 ∙ 0.0625 + 12 ∙ 0.00390625 + 2 ∙ 0.000244140625 + 8 ∙ 1.52587890625E-5 + 15 ∙ 9.5367431640625E-7 + 5 ∙ 5.9604644775391E-8 + 12 ∙ 3.7252902984619E-9 + 2 ∙ 2.3283064365387E-10 + 8 ∙ 1.4551915228367E-11 + 15 ∙ 9.0949470177293E-13 + 5 ∙ 5.6843418860808E-14 = 64 + 12 + 0.3125 + 0.046875 + 0.00048828125 + 0.0001220703125 + 1.4305114746094E-5 + 2.9802322387695E-7 + 4.4703483581543E-8 + 4.6566128730774E-10 + 1.1641532182693E-10 + 1.3642420526594E-11 + 2.8421709430404E-13 = 76.36₁₀

Таким образом:

4C.5C28F5C28F5₁₆ = 76.36₁₀

2. Полученное число 76.36 переведем из десятичной системы счисления в двоичную. Т.к. полученное число содержит дробную часть, нам потребуется перевести вначале целую часть, а затем дробную. Таким образом необходимо:

1. Перевести 76 в двоичную систему;
2. Перевести 0.36 в двоичную систему;

2.1 Для того, чтобы перевести число 76 из десятичной системы счисления в двоичную, необходимо осуществить последовательное деление на 2, до тех пор пока остаток не будет меньше чем 2.

Полученные остатки записываем в обратном порядке, таким образом:

76₁₀=1001100₂

2.2 Для перевода десятичной дроби 0.36 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:

0.36 ∙ 2 = 0.72 (0)
0.72 ∙ 2 = 1.44 (1)
0.44 ∙ 2 = 0.88 (0)
0.88 ∙ 2 = 1.76 (1)
0.76 ∙ 2 = 1.52 (1)
0.52 ∙ 2 = 1.04 (1)
0.04 ∙ 2 = 0.08 (0)
0.08 ∙ 2 = 0.16 (0)
0.16 ∙ 2 = 0.32 (0)
0.32 ∙ 2 = 0.64 (0)
0.64 ∙ 2 = 1.28 (1)

Ответом станет прямая последовательность целых частей произведения. Т.е.

0.36₁₀=0.01011100001₂

2.3. Осталось соединить переведенные части, таким образом:

76.36₁₀=1001100.01011100001₂

Ответ: 4C.5C28F5C28F5₁₆ = 1001100.01011100001₂.

• Смотрите также
• Калькуляторы
• Последние переводы

Полезные материалы

• Системы счисления в информатике
• Что такое шестнадцатеричная система?
• Как шестнадцатеричное число перевести в двоичную систему?

Калькуляторы переводов

• Калькулятор из шестнадцатеричной в двоичную с подробным решением
• Калькулятор из двоичной в десятичную с подробным решением
• Калькулятор из шестнадцатеричной в десятичную с подробным решением
• Калькулятор из двоичной в восьмеричную с подробным решением
• Калькулятор из восьмеричной в шестнадцатеричную с подробным решением
• Калькулятор из одной системы счисления в другую

Последние примеры переводов из 16-ой в 2-ую систему

• Запишите шестнадцатеричное число 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 в двоичной системе
• Какое шестнадцатеричное число соответствует двоичному числу 0000001C?
• Какое шестнадцатеричное число соответствует двоичному коду 6f225619?
• Какое шестнадцатеричное число соответствует двоичному числу 1AF416?
• Как представлено шестнадцатеричное число 6B3 в двоичной системе?
• Какое шестнадцатеричное число соответствует двоичному коду 1872.75?
• Переведите шестнадцатеричное число 2E8 в двоичную систему
• Перевод числа 1011010110 из шестнадцатеричной в двоичную систему счисления
• Переведите шестнадцатеричное число 3571 в двоичную систему
• Представьте шестнадцатеричное число A6E5 в двоичной системе счисления

• Какое число еще хотите перевести?

  * Все поля обязательны
• Введите число: Дробное число вводите через точку
• Основание системы счисления: Введите от 2 до 16
• В какую систему перевести: Введите от 2 до 16
• Перевести

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