What is Binary

Binary is the base-2 number system. It uses only two digits — 0 and 1 — to represent every value. Decimal (the system you use daily) is base-10 with ten digits (0 through 9). Binary works the same way, just with fewer symbols.

How it works

In decimal, each position represents a power of 10. The number 347 means 3 x 100 + 4 x 10 + 7 x 1. In binary, each position represents a power of 2:

Binary:  1 0 1 1
         |  |  |  |
         8  4  2  1  (powers of 2)
         = 8 + 0 + 2 + 1 = 11 in decimal

Counting in binary follows the same carry rules as decimal. After 0 and 1, you carry: 10, 11, 100, 101, 110, 111, 1000. Each additional bit doubles the range of values you can represent.

Arithmetic works identically to decimal arithmetic, just simpler. Addition has only four cases: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (carry the 1). This simplicity is exactly why computers use binary — digital circuits only need to distinguish two voltage levels, making hardware reliable and fast.

Binary is also the native language of boolean logic. A binary 1 maps to true, 0 to false. The AND, OR, and NOT operations that drive every logic gate in a CPU operate directly on binary values.

Why it matters

Binary is how computers see the world. Every number, character, color, and instruction is encoded in binary before a CPU can process it. When you write the decimal number 255 in code, the computer stores it as 11111111 — eight bits, all ones.

Understanding binary makes related concepts accessible. Hexadecimal is a shorthand for binary (each hex digit = 4 bits). Two's complement is how binary represents negative numbers. Floating point is how binary approximates decimals. They all start here.

See How Binary Works for the full lesson on binary arithmetic, conversions, and practical applications.