Перевести число 11001.1 из двоичной системы в шестнадцатеричную

Задача: перевести число 11001.1 из двоичной в шестнадцатеричную систему счисления.

Для перевода 11001.1 из двоичной в шестнадцатеричную систему счисления, воспользуемся следующим алгоритмом:

1. Переведем число 11001.1 из двоичной системы в десятичную;
2. Полученное число переведём из десятичной системы в шестнадцатеричную;

Решение:

1. Для перевода числа 11001.1 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:

11001.1₂=1 ∙ 2⁴ + 1 ∙ 2³ + 0 ∙ 2² + 0 ∙ 2¹ + 1 ∙ 2⁰ + 1 ∙ 2^-1 = 1 ∙ 16 + 1 ∙ 8 + 0 ∙ 4 + 0 ∙ 2 + 1 ∙ 1 + 1 ∙ 0.5 = 16 + 8 + 0 + 0 + 1 + 0.5 = 25.5₁₀

Таким образом:

11001.1₂ = 25.5₁₀

2. Полученное число 25.5 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:

1. Перевести 25 в шестнадцатеричную систему;
2. Перевести 0.5 в шестнадцатеричную систему;

2.1 Для того, чтобы перевести число 25 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:

25₁₀=19₁₆

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:

25.5₁₀=19.8₁₆

Ответ: 11001.1₂ = 19.8₁₆.

• Смотрите также
• Калькуляторы
• Последние переводы

Полезные материалы

• Система счисления в информатике
• Что такое двоичная система?
• Как из двоичной системы счисления переводить числа в шестнадцатеричную?

Калькуляторы переводов

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

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

• Как будет записано двоичное число 0.100101 в шестнадцатеричной системе?
• Запиши двоичное число 11100011101011010 в шестнадцатеричной системе
• Как перевести число 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из двоичной в шестнадцатеричную систему?
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• Какое двоичное число соответствует шестнадцатеричному коду 01100110?
• Какое двоичное число соответствует шестнадцатеричному коду 111.1111?
• Запишите двоичное число 0110100.110001 в шестнадцатеричной системе счисления
• Какое двоичное число соответствует шестнадцатеричному числу 11000110?

• 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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(пока оценок нет)

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