Number systems

Computers work in binary (base 2) because circuits have two reliable states: on and off. Programmers also use hexadecimal (base 16) as a compact way to write binary.

• Decimal (base 10) uses digits 0–9; binary (base 2) uses only 0 and 1; hexadecimal (base 16) uses 0–9 and A–F.
• Converting binary → decimal: add the place values (128, 64, 32, 16, 8, 4, 2, 1) where a 1 appears.
• Converting decimal → binary: repeatedly subtract the largest power of two (or divide by 2 and track remainders).
• One hex digit represents exactly four binary bits, so hex is a shorthand for binary.
• Example: 1101₂ = 8+4+1 = 13₁₀ = D₁₆.

• Bit — a single binary digit (0 or 1).
• Byte — 8 bits; the basic unit of storage.