Перевести число 11001111.111 из двоичной системы в шестнадцатеричную

Задача: перевести число 11001111.111 из двоичной в шестнадцатеричную систему счисления.

Для перевода 11001111.111 из двоичной в шестнадцатеричную систему счисления, воспользуемся следующим алгоритмом:

1. Переведем число 11001111.111 из двоичной системы в десятичную;
2. Полученное число переведём из десятичной системы в шестнадцатеричную;

Решение:

1. Для перевода числа 11001111.111 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:

11001111.111₂=1 ∙ 2⁷ + 1 ∙ 2⁶ + 0 ∙ 2⁵ + 0 ∙ 2⁴ + 1 ∙ 2³ + 1 ∙ 2² + 1 ∙ 2¹ + 1 ∙ 2⁰ + 1 ∙ 2^-1 + 1 ∙ 2^-2 + 1 ∙ 2^-3 = 1 ∙ 128 + 1 ∙ 64 + 0 ∙ 32 + 0 ∙ 16 + 1 ∙ 8 + 1 ∙ 4 + 1 ∙ 2 + 1 ∙ 1 + 1 ∙ 0.5 + 1 ∙ 0.25 + 1 ∙ 0.125 = 128 + 64 + 0 + 0 + 8 + 4 + 2 + 1 + 0.5 + 0.25 + 0.125 = 207.875₁₀

Таким образом:

11001111.111₂ = 207.875₁₀

2. Полученное число 207.875 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:

1. Перевести 207 в шестнадцатеричную систему;
2. Перевести 0.875 в шестнадцатеричную систему;

2.1 Для того, чтобы перевести число 207 из десятичной системы счисления в шестнадцатеричную, необходимо осуществить последовательное деление на 16, до тех пор пока остаток не будет меньше чем 16.

Полученные остатки записываем в обратном порядке, таким образом:

207₁₀=12F₁₆

2.2 Для перевода десятичной дроби 0.875 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:

0.875 ∙ 16 = 14 (E)

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

0.875₁₀=0.E₁₆

2.3. Осталось соединить переведенные части, таким образом:

207.875₁₀=12F.E₁₆

Ответ: 11001111.111₂ = 12F.E₁₆.

• Смотрите также
• Калькуляторы
• Последние переводы

Полезные материалы

• Системы счисления в информатике
• Двоичная система счисления
• Как переводить из двоичной в шестнадцатеричную систему?

Калькуляторы переводов

• Калькулятор из двоичной в шестнадцатеричную 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 шестнадцатеричной в десятичную с подробным решением
• Калькулятор из восьмеричной в двоичную с подробным решением

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

• Переведите двоичное число 011000110 в шестнадцатеричную систему
• Представить двоичное число 1101110.0001 в шестнадцатеричной системе
• Представить двоичное число 10000111101010 в шестнадцатеричной системе
• Запиши двоичное число 1011011110.0100111 в шестнадцатеричной системе счисления
• Запиши двоичное число 11111100010 в шестнадцатеричной системе
• Запишите двоичное число 011110101 в шестнадцатеричной системе
• Как перевести число 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из двоичной в шестнадцатеричную систему?
• Переведите двоичное число 10011001001.1001 в шестнадцатеричную систему счисления
• Перевести 1000011110 из двоичной в шестнадцатеричную систему счисления
• Перевести число 10.0101111 из двоичной в шестнадцатеричную систему 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

Оцените материал:

(пока оценок нет)

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