Number Systems

A number system is a way of representing numbers. Computers use binary (base-2) internally.

Common Number Systems

  • Decimal (base-10): Digits 0–9. Used in everyday life.
  • Binary (base-2): Digits 0 and 1. Used inside computers.
  • Octal (base-8): Digits 0–7. Used as a shorthand for binary.
  • Hexadecimal (base-16): Digits 0–9 and A–F. Common in memory addressing.

Conversions

To convert decimal 45 to binary: 45 ÷ 2 = 22 R1 → 22 ÷ 2 = 11 R0 → 11 ÷ 2 = 5 R1 → 5 ÷ 2 = 2 R1 → 2 ÷ 2 = 1 R0 → 1 ÷ 2 = 0 R1. Reading remainders bottom-up: 101101.