Перевести число 101110010011 из двоичной системы в шестнадцатеричную

Задача: перевести число 101110010011 из двоичной в шестнадцатеричную систему счисления.

Для перевода 101110010011 из двоичной в шестнадцатеричную систему счисления, воспользуемся следующим алгоритмом:

1. Переведем число 101110010011 из двоичной системы в десятичную;
2. Полученное число переведём из десятичной системы в шестнадцатеричную;

Решение:

1. Для перевода числа 101110010011 в десятичную систему воспользуемся формулой:

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

Отсюда:

101110010011₂=1 ∙ 2¹¹ + 0 ∙ 2¹⁰ + 1 ∙ 2⁹ + 1 ∙ 2⁸ + 1 ∙ 2⁷ + 0 ∙ 2⁶ + 0 ∙ 2⁵ + 1 ∙ 2⁴ + 0 ∙ 2³ + 0 ∙ 2² + 1 ∙ 2¹ + 1 ∙ 2⁰ = 1 ∙ 2048 + 0 ∙ 1024 + 1 ∙ 512 + 1 ∙ 256 + 1 ∙ 128 + 0 ∙ 64 + 0 ∙ 32 + 1 ∙ 16 + 0 ∙ 8 + 0 ∙ 4 + 1 ∙ 2 + 1 ∙ 1 = 2048 + 0 + 512 + 256 + 128 + 0 + 0 + 16 + 0 + 0 + 2 + 1 = 2963₁₀

Таким образом:

101110010011₂ = 2963₁₀

2. Полученное число 2963 переведем из десятичной системы счисления в шестнадцатеричную. Для этого, осуществим последовательное деление на 16, до тех пор пока остаток не будет меньше чем 16.

Полученные остатки записываем в обратном порядке, таким образом:

2963₁₀=1193₁₆

Ответ: 101110010011₂ = 1193₁₆.

• Смотрите также
• Калькуляторы
• Последние переводы

Полезные материалы

• Системы счисления в информатике
• Двоичная система счисления
• Перевод двоичных чисел в шестнадцатеричную систему счисления

Калькуляторы переводов

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

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

• Как перевести число 100010010101 из двоичной в шестнадцатеричную систему?
• Запиши двоичное число 110001010110 в шестнадцатеричной системе
• Представить двоичное число 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в шестнадцатеричной системе
• Переведите двоичное число 0011011110100101 в шестнадцатеричную систему
• Переведите число 1010100.11 из двоичной в шестнадцатеричную систему счисления
• Представьте двоичное число 10010111.0111 в шестнадцатеричной системе счисления
• Запишите двоичное число 11101110 в шестнадцатеричной системе
• Представить двоичное число 101101001011 в шестнадцатеричной системе счисления
• Как выглядит двоичное число 1011100000000000 в шестнадцатеричной системе счисления?
• Перевести двоичное число 1000100 в шестнадцатеричную систему

• 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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