Binary (base 2)

How binary works

Binary is the base-2 number system, which writes every number with just two digits, 0 and 1. Each position is worth twice the one to its right: 1, 2, 4, 8, 16, 32 and so on. The binary number 1010 is 8 + 2 = 10.

Each binary digit is called a bit, and eight bits make a byte, which can hold values from 0 (00000000) to 255 (11111111). In programming, binary literals are often written with a 0b prefix, as in 0b1010.

Each position is worth 2 times the position to its right: 1, 2, 4, 8, 16 and so on. So 11111111 means 1 × 2⁷ + 1 × 2⁶ + 1 × 2⁵ + 1 × 2⁴ + 1 × 2³ + 1 × 2² + 1 × 2¹ + 1 × 2⁰ = 255.

Where binary is used

• All digital computers and electronics store and process data in binary.
• Network masks and IP addresses (255.255.255.0 is 24 ones followed by 8 zeros).
• File permissions, flags and bit masks in programming.
• Digital logic design and computer science education.

History

Gottfried Wilhelm Leibniz described modern binary arithmetic in 1703, noting its similarity to the hexagrams of the Chinese I Ching. George Boole's algebra of logic (1854) and Claude Shannon's 1937 thesis linking it to electrical switches made binary the language of modern computers.