Mathematik

Base Conversion Calculator

Number Base Converter

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Was ist 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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Formel

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

Variablenbeschreibung

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Symbol	Name	Einheit	Beschreibung
n	Number base (2-36)	—	—
d	Digit value	—	—
p	Digit position (rightmost = 0)	—	—

Anleitung 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

Gelöste Beispiele

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Beispiel 1

Gegeben:Decimal 42 to binary

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

Praktische Anwendungen

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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

Häufig gestellte Fragen

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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.

Referenzen

›Number bases — Khan Academy

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Reviewed October 2026

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