Перевести число 1000001011001100111010 из двоичной системы в шестнадцатеричную

Задача: перевести число 1000001011001100111010 из двоичной в шестнадцатеричную систему счисления.

Для перевода 1000001011001100111010 из двоичной в шестнадцатеричную систему счисления, воспользуемся следующим алгоритмом:

1. Переведем число 1000001011001100111010 из двоичной системы в десятичную;
2. Полученное число переведём из десятичной системы в шестнадцатеричную;

Решение:

1. Для перевода числа 1000001011001100111010 в десятичную систему воспользуемся формулой:

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

Отсюда:

1000001011001100111010₂=1 ∙ 2²¹ + 0 ∙ 2²⁰ + 0 ∙ 2¹⁹ + 0 ∙ 2¹⁸ + 0 ∙ 2¹⁷ + 0 ∙ 2¹⁶ + 1 ∙ 2¹⁵ + 0 ∙ 2¹⁴ + 1 ∙ 2¹³ + 1 ∙ 2¹² + 0 ∙ 2¹¹ + 0 ∙ 2¹⁰ + 1 ∙ 2⁹ + 1 ∙ 2⁸ + 0 ∙ 2⁷ + 0 ∙ 2⁶ + 1 ∙ 2⁵ + 1 ∙ 2⁴ + 1 ∙ 2³ + 0 ∙ 2² + 1 ∙ 2¹ + 0 ∙ 2⁰ = 1 ∙ 2097152 + 0 ∙ 1048576 + 0 ∙ 524288 + 0 ∙ 262144 + 0 ∙ 131072 + 0 ∙ 65536 + 1 ∙ 32768 + 0 ∙ 16384 + 1 ∙ 8192 + 1 ∙ 4096 + 0 ∙ 2048 + 0 ∙ 1024 + 1 ∙ 512 + 1 ∙ 256 + 0 ∙ 128 + 0 ∙ 64 + 1 ∙ 32 + 1 ∙ 16 + 1 ∙ 8 + 0 ∙ 4 + 1 ∙ 2 + 0 ∙ 1 = 2097152 + 0 + 0 + 0 + 0 + 0 + 32768 + 0 + 8192 + 4096 + 0 + 0 + 512 + 256 + 0 + 0 + 32 + 16 + 8 + 0 + 2 + 0 = 2143034₁₀

Таким образом:

1000001011001100111010₂ = 2143034₁₀

2. Полученное число 2143034 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:

2143034₁₀=20B33A₁₆

Ответ: 1000001011001100111010₂ = 20B33A₁₆.

• Смотрите также
• Калькуляторы
• Последние переводы

Полезные материалы

• Система счисления в информатике
• Двоичная система счисления
• Как двоичное число перевести в шестнадцатеричную систему счисления?

Калькуляторы переводов

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

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

• Как перевести число 1100000010000100001010010100011100000000000000000000000000000000 из двоичной в шестнадцатеричную систему?
• Переведите 10000001001.0101 из двоичной в шестнадцатеричную систему
• Как представлено двоичное число 11101001.1 в шестнадцатеричной системе?
• Переведите число 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из двоичной в шестнадцатеричную систему счисления
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• Какое число еще хотите перевести?

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

Оцените материал:

(пока оценок нет)

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