Number Base Converter
Convert numbers between decimal, binary, hexadecimal, and octal systems.
Number Base Conversion
Computers think in binary (base 2), programmers often work in hexadecimal (base 16), and humans prefer decimal (base 10). This tool converts between all of them, plus octal (base 8).
Hex is compact - one hex digit represents 4 binary digits. That's why memory addresses and color codes use hex. Reading raw binary is tedious; hex makes it manageable.
Quick Conversions
- 255 (decimal) = FF (hex) = 11111111 (binary)
- 16 (decimal) = 10 (hex) = 10000 (binary)
- Hex A-F represent 10-15
Understanding Number Systems
Number systems are ways of representing quantities using a specific set of symbols. The base (or radix) determines how many unique symbols are used. Decimal uses 10 symbols (0-9), binary uses 2 (0-1), octal uses 8 (0-7), and hexadecimal uses 16 (0-9 plus A-F).
Computers fundamentally operate in binary because transistors have two states: on (1) and off (0). Hexadecimal is popular in programming because it compactly represents binary data'each hex digit equals exactly 4 binary digits (bits), making it easier to read memory addresses, color codes, and byte values.
Common Conversions
- Binary 1010 = Decimal 10: (1×8) + (0×4) + (1×2) + (0×1)
- Hex FF = Decimal 255: (15×16) + (15×1)
- Octal 777 = Decimal 511:Common in Unix file permissions
Frequently Asked Questions
Why is hexadecimal used for colors?
Colors in web design use RGB values from 0-255 for each channel (red, green, blue). Hexadecimal represents 0-255 with just two digits (00-FF), making color codes compact: #FF0000 (red), #00FF00 (green), #0000FF (blue), #FFFFFF (white).
When would I use octal?
Octal is primarily used for Unix/Linux file permissions. Permission mode 755 means owner has read/write/execute (7), while group and others have read/execute (5). Each digit represents 3 binary bits: read(4) + write(2) + execute(1).
Why do programmers need binary?
Binary is essential for bitwise operations, understanding memory layout, working with flags and permissions, network protocols, and debugging at the hardware level. Bit manipulation is often faster than arithmetic operations and is used extensively in systems programming.