The binary number system (base-2) uses only 0 and 1. Every digital device — from smartphones to supercomputers — processes data as binary.
Conversion
Binary 1011 = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11 in decimal.
Related Bases
- Octal (base-8): Groups of 3 binary digits
- Hexadecimal (base-16): Groups of 4 binary digits, uses 0–9 and A–F
Binary Arithmetic
0+0=0, 0+1=1, 1+0=1, 1+1=10 (carry 1). Same logical rules for multiplication.
Why Computers Use Binary
Digital circuits are built from transistors that are most reliably operated as simple on/off switches — representing exactly two states (0 and 1) is far more robust against electrical noise than trying to distinguish ten distinct voltage levels for base-10. This reliability, not mathematical elegance, is why binary underlies all modern computing.
Bits, Bytes, and Beyond
A single binary digit is a bit. Eight bits make a byte, which can represent 256 distinct values (0–255) — enough for one ASCII character. File sizes scale up from there: kilobyte, megabyte, gigabyte, each roughly 1,000× (or, technically, 1,024×) the previous unit.