Математика

Base Conversion Calculator

Number Base Converter

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Что такое Base Conversion Calculator?

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A number base converter converts integers between any base from 2 to 36. Binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16) are the most used in computing.

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Формула

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f(x)Base n to decimal: Σ (digit × n^position); Decimal to base n: repeatedly divide by n, collect remainders

Описание переменных

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Символ	Имя	Единица	Описание
n	Number base (2-36)	—	—
d	Digit value	—	—
p	Digit position (rightmost = 0)	—	—

Как Base Conversion Calculator

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1To convert from base n to decimal: each digit × nᵖᵒˢⁱᵗⁱᵒⁿ, sum all
2Decimal to base n: repeatedly divide by n, collect remainders in reverse
3Digits above 9 use letters: A=10, B=11... Z=35
4Hex ↔ Binary: each hex digit = exactly 4 bits

Решённые примеры

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Пример 1

Дано:Decimal 42 to binary

Результат:42÷2=21r0; 21÷2=10r1; 10÷2=5r0; 5÷2=2r1; 2÷2=1r0; 1÷2=0r1 → 101010

Практическое применение

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Programming and computer architecture

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Memory address display in debugging

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Color codes in web design (#FF00FF)

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Understanding network subnetting

Common Base Conversions

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Decimal	Binary	Hex	Octal
10	1010	A	12
16	10000	10	20
42	101010	2A	52
255	11111111	FF	377

Часто задаваемые вопросы

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Why do we use bases other than 10?

Computers use binary (base 2) and hexadecimal (base 16) for efficiency. Octal (base 8) was historically used in early computing.

What does hexadecimal stand for?

Hexadecimal means 16 (hex- = 6, -decimal = 10). It uses digits 0-9 and letters A-F.

How do I convert hex to binary quickly?

Each hex digit equals exactly 4 binary bits. F = 1111, A = 1010, etc.

Источники

›Number bases — Khan Academy

Mathematically verified

Reviewed October 2026

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