Binary Converter

Type a number in any field and the other three update instantly. Hex input accepts letters A-F (case insensitive). Binary only accepts 0 and 1. Fractional and negative numbers are not supported.

Decimal (base 10) is the system humans settled on, almost certainly because we have 10 fingers. Each position is a power of 10.

Binary (base 2) is the language of computers. Transistors have two states: on (1) and off (0). Every number, character, image, and instruction on any computer is ultimately represented as a sequence of 1s and 0s. Groups of 8 bits form a byte, which can represent 256 values (0-255).

Hexadecimal (base 16) uses digits 0-9 then A-F for values 10-15. It became the standard shorthand for binary in computing because one hex digit maps exactly to 4 bits, so a byte is always two hex characters (e.g. 255 = FF). This is why colours in CSS are written as #RRGGBB, memory addresses appear as 0x7FFDA3, and file signatures are shown in hex dumps.

Octal (base 8) uses digits 0-7 and maps one digit to exactly 3 bits. It was widely used in early computing (PDP and Unix systems) because early machines often worked with 12-, 24-, or 36-bit word sizes that divided neatly into 3-bit groups. Its main surviving use today is Unix file permissions: chmod 755 sets owner read/write/execute (7), group read/execute (5), others read/execute (5).

All four systems use positional notation: the value of each digit depends on its position. Reading right to left, each position is a successive power of the base.