Number Base Converter
Convert numbers between binary, decimal, octal, and hexadecimal
Binary (Base 2):
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Octal (Base 8):
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Decimal (Base 10):
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Hexadecimal (Base 16):
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About Number Bases
A numeral system (or number base) is a writing system for expressing numbers using digits or other symbols in a consistent manner.
Common Number Bases
Binary (Base 2)
Uses only two digits: 0 and 1. Fundamental to computer systems.
Example: 1010₂ = 10₁₀
Octal (Base 8)
Uses digits 0-7. Sometimes used in computing as a shorthand for binary.
Example: 12₈ = 10₁₀
Decimal (Base 10)
Uses digits 0-9. The standard system for everyday use.
Example: 10₁₀ = 10
Hexadecimal (Base 16)
Uses digits 0-9 and letters A-F. Widely used in computing.
Example: A₁₆ = 10₁₀
How to Use This Tool
- Enter the number you want to convert
- Select the base of the input number
- Choose which bases you want to convert to
- Click the convert button
- View your results in the result section
Conversion Examples
Decimal to Binary:
13₁₀ = 1101₂
13 ÷ 2 = 6 remainder 1
6 ÷ 2 = 3 remainder 0
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
Binary to Decimal:
1101₂ = 13₁₀
1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 8 + 4 + 0 + 1 = 13
Decimal to Hexadecimal:
255₁₀ = FF₁₆
255 ÷ 16 = 15 remainder 15 (F)
15 ÷ 16 = 0 remainder 15 (F)
Applications of Different Number Bases
- Binary: Computer processors, digital circuits, data storage
- Octal: Unix file permissions, digital displays
- Decimal: Everyday counting, financial calculations, measurements
- Hexadecimal: Memory addresses, color codes, assembly language