Number Base Converter

Convert numbers between different bases including binary, decimal, hexadecimal, octal, and custom bases (2-36).

Number Conversion

Enter a number and select its base to convert to other number systems

Input Number

Input Base

How Number Bases Work

Positional Notation: Each digit's value depends on its position

Base Value: Determines how many digits are available (0 to base-1)

Powers: Each position represents a power of the base

Example: 123₁₀ = 1×10² + 2×10¹ + 3×10⁰

Programming Applications

Binary: Computer memory, digital logic, bit operations

Hexadecimal: Memory addresses, color codes, debugging

Octal: Unix file permissions, legacy systems

Base64: Data encoding, email attachments, web APIs

Quick Examples

Click any example to load it for conversion

Number Base Reference

Common number bases and their uses

Binary (Base 2)

Base 2

Base-2 system used in computers

Digits: 01

Example: 1010

Octal (Base 8)

Base 8

Base-8 system, common in Unix permissions

Digits: 01234567

Example: 755

Decimal (Base 10)

Base 10

Base-10 system, everyday numbers

Digits: 0123456789

Example: 42

Hexadecimal (Base 16)

Base 16

Base-16 system, used in programming

Digits: 0123456789ABCDEF

Example: A1B2

Base32 (Base 32)

Base 32

Base-32 encoding, used in URLs

Digits: 0123456789ABCDEFGHIJKLMNOPQRSTUV

Example: MFRGG

Base36 (Base 36)

Base 36

Base-36 system, uses all alphanumeric

Digits: 0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ

Example: ZZ

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Frequently Asked Questions

Why do computers use binary?

Computers use binary because digital circuits can easily represent two states: on (1) and off (0). This corresponds to electrical signals being present or absent, making binary the natural choice for digital systems.

What's the highest base I can use?

This calculator supports bases from 2 to 36. Base 36 uses digits 0-9 and letters A-Z, which exhausts the standard alphanumeric characters. Higher bases would require additional symbols.

How do I convert fractions between bases?

This calculator currently handles whole numbers only. Converting fractional parts requires a different algorithm involving multiplying the fractional part by the target base repeatedly.