Binary Converter

Binary is a base-2 number system that uses only two digits: 0 and 1. Each digit is called a bit. Groups of 8 bits form a byte. Computers use binary because electronic circuits naturally represent two states — off (0) and on (1) — making it the fundamental language of all digital hardware.

Binary (base 2) uses digits 0–1. Octal (base 8) uses digits 0–7. Decimal (base 10) uses digits 0–9 and is the everyday human counting system. Hexadecimal (base 16) uses digits 0–9 plus letters A–F to represent values 10–15. Each system is a positional notation where each position is a power of its base.

Computers use binary because transistors and logic gates have two stable electrical states: high voltage (1) and low voltage (0). Binary arithmetic maps perfectly to these states, making it trivially simple to build reliable, fast hardware. All data — text, images, audio, video — is ultimately stored and processed as sequences of 0s and 1s.

Two's complement is the standard method computers use to represent signed (positive and negative) integers in binary. To negate a number: invert all bits (one's complement) then add 1. For example, +5 in 8-bit binary is 00000101; –5 is 11111011. This scheme makes subtraction identical to addition in hardware, eliminating the need for a separate subtraction circuit.

Binary and its shorthand (hexadecimal) appear throughout programming: file permissions (chmod uses octal, e.g. 755), color codes (#FF5733 in hex), memory addresses, bitmask flags, network masks, character encodings (ASCII/UTF-8), and bitwise operations (&, |, ^, <<, >>). Understanding binary helps you read stack traces, debug low-level code, and work with binary protocols.