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Base Conversion Calculator

Number Base Converter

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What is 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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સૂત્ર

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

Variable Legend

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પ્રતીકનામએકમવર્ણન
nNumber base (2-36)——
dDigit value——
pDigit position (rightmost = 0)——

How to Base Conversion Calculator

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

Worked Examples

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Example 1
Given:Decimal 42 to binary
પરિણામ:42÷2=21r0; 21÷2=10r1; 10÷2=5r0; 5÷2=2r1; 2÷2=1r0; 1÷2=0r1 → 101010

Real-World Applications

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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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DecimalBinaryHexOctal
101010A12
16100001020
421010102A52
25511111111FF377

Frequently Asked Questions

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Q

Why do we use bases other than 10?

A

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

Q

What does hexadecimal stand for?

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

Q

How do I convert hex to binary quickly?

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

Mathematically verified
Reviewed October 2026
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