Parity Bit Calculator (Even & Odd)

Formula

How this is calculated

A parity bit is a single extra bit appended to a data word so a receiver can detect single-bit transmission errors. The calculator first reads your data word: in binary mode it must contain only 0s and 1s, and in decimal mode it converts a non-negative integer to its binary representation. It then counts the number of 1 bits (the population count, or popcount).

Even parity chooses the extra bit so the total number of 1s in the word plus parity bit is even, which means the parity bit simply equals popcount mod 2. Odd parity does the opposite: it makes the total number of 1s odd, so the odd parity bit is 1 minus the even parity bit. The result panel shows the count of 1s and 0s, both parity bits, and the original word with each parity bit appended at the end.

Parity detects any odd number of flipped bits but cannot detect an even number of errors, nor can it locate or correct the error — for that you need stronger codes such as CRC or Hamming codes. Inputs must be whole, non-negative values; empty input, decimals, or non-binary characters return no result.