Перевести число 0.01001100110011001 из двоичной системы в десятичную

Задача: перевести число 0.01001100110011001 из двоичной в 10-ую систему счисления.

Решение:

Для перевода числа 0.01001100110011001 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:

0.01001100110011001₂=0 ∙ 2⁰ + 0 ∙ 2^-1 + 1 ∙ 2^-2 + 0 ∙ 2^-3 + 0 ∙ 2^-4 + 1 ∙ 2^-5 + 1 ∙ 2^-6 + 0 ∙ 2^-7 + 0 ∙ 2^-8 + 1 ∙ 2^-9 + 1 ∙ 2^-10 + 0 ∙ 2^-11 + 0 ∙ 2^-12 + 1 ∙ 2^-13 + 1 ∙ 2^-14 + 0 ∙ 2^-15 + 0 ∙ 2^-16 + 1 ∙ 2^-17 = 0 ∙ 1 + 0 ∙ 0.5 + 1 ∙ 0.25 + 0 ∙ 0.125 + 0 ∙ 0.0625 + 1 ∙ 0.03125 + 1 ∙ 0.015625 + 0 ∙ 0.0078125 + 0 ∙ 0.00390625 + 1 ∙ 0.001953125 + 1 ∙ 0.0009765625 + 0 ∙ 0.00048828125 + 0 ∙ 0.000244140625 + 1 ∙ 0.0001220703125 + 1 ∙ 6.103515625E-5 + 0 ∙ 3.0517578125E-5 + 0 ∙ 1.52587890625E-5 + 1 ∙ 7.62939453125E-6 = 0 + 0 + 0.25 + 0 + 0 + 0.03125 + 0.015625 + 0 + 0 + 0.001953125 + 0.0009765625 + 0 + 0 + 0.0001220703125 + 6.103515625E-5 + 0 + 0 + 7.62939453125E-6 = 0.29999542236328₁₀

Ответ: 0.01001100110011001₂ = 0.29999542236328₁₀.

Подробнее о том, как переводить числа из двоичной системы в десятичную, смотрите здесь.

• Смотрите также
• Калькуляторы
• Последние переводы

Полезные материалы

• Что такое системы счисления в информатике?
• Двоичная система счисления
• Правила перевода двоичных чисел в десятичную систему счисления

Калькуляторы переводов

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

Последние примеры переводов из 2-ой в 10-ую систему

• Переведите 1001001110010001 из двоичной в десятичную систему
• Представьте двоичное число 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в десятичной системе
• Перевести 11000111.11100110011 из двоичной в десятичную систему счисления
• Переведите двоичное число 100100101.1011 в десятичную систему
• Переведите 111000.001 из двоичной в десятичную систему счисления
• Какое двоичное число соответствует десятичному коду 10001000110000?
• Перевод 101011010101101111 из двоичной в десятичную систему
• Как выглядит двоичное число 0101110000110000 в десятичной системе счисления?
• Как будет записано двоичное число 100010001000 в десятичной системе счисления?
• Перевод 1110110001111 из двоичной в десятичную 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

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