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

How to Use the Number Base Converter

Convert numbers between binary, decimal, hexadecimal, and octal for programming and computer science

Step-by-Step Instructions

Enter Number

Input the number you want to convert in any supported base

Select Source Base

Choose from Binary (2), Octal (8), Decimal (10), or Hexadecimal (16)

Choose Target Base

Select the number base you want to convert to

View All Bases

See instant conversion to all supported number bases

Copy Results

Copy converted numbers to use in programming or calculations

Verify Results

Cross-check with step-by-step conversion breakdown

Pro Tips

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Programming Use: Binary for bit operations, Hex for memory addresses, Decimal for calculations

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Number Formats: Binary (0-1), Octal (0-7), Decimal (0-9), Hex (0-9, A-F)

⚡

Common Patterns: Powers of 2 are simple in binary, RGB colors use hex values

🎯

Memory & Storage: Computer memory addresses and file sizes often use hexadecimal

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Debugging: Convert between bases to understand how data is stored and represented

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.

What are the letter values in hexadecimal?

In hexadecimal: A=10, B=11, C=12, D=13, E=14, F=15. This extends to higher bases using the alphabet in order.

How do I validate if a number is valid in a specific base?

A number is valid in a base if all its digits are less than the base value. For example, "89" is invalid in base 8 because 8 and 9 don't exist in base 8 (which only uses digits 0-7).