Decimal to Binary Converter

About this calculator

Computers store and process every value in binary (base 2) — using only the digits 0 and 1 — because a transistor's two stable electrical states map naturally onto two symbols, so converting a familiar base-10 (decimal) number into binary is the fundamental translation between how humans count and how hardware actually represents numbers. The conversion works by repeatedly dividing the decimal number by 2 and reading the remainders in reverse order, or equivalently by finding which powers of 2 sum to the target number.

Hexadecimal (base 16) and octal (base 8) are shown alongside binary because both are compact shorthand for binary that programmers use constantly — each hex digit represents exactly 4 binary bits and each octal digit represents exactly 3, making them far easier to read and write than long strings of 0s and 1s, which is why memory addresses, color codes, and file permissions are conventionally written in hex or octal rather than binary.

This calculator takes a decimal number and returns its binary, hexadecimal, and octal representations.