Base Number System Guide
Understanding the four main number systems used in computing and mathematics.
Binary (Base-2)
Computers, digital electronics
Digits: 0, 1
Prefix: 0b
Octal (Base-8)
Unix permissions, legacy computing
Digits: 0-7
Prefix: 0o
Decimal (Base-10)
Everyday human counting
Digits: 0-9
Prefix: None
Hexadecimal (Base-16)
Colors, memory addresses, programming
Digits: 0-9, A-F
Prefix: 0x
Comparison: The number 255
Binary
11111111
Octal
377
Decimal
255
Hex
FF
Why Different Bases?
Different number bases serve different purposes. Binary is the native language of digital circuits. Hexadecimal provides a compact representation of binary (every 4 bits = 1 hex digit). Octal groups binary into 3-bit chunks. Decimal is what humans naturally understand. Being able to convert between them is essential for programming, networking, and digital electronics.