paritycheck

Paritycheck is a basic error-detection mechanism used in data transmission and storage to verify the integrity of a bit string. It works by appending a parity bit to the data so that the total number of 1s has a defined parity, either even or odd.

In even parity, the parity bit is chosen so that the total number of 1s in the transmitted word is even; in odd parity, the total is odd. At the receiving end, the parity is recomputed and compared with the transmitted parity. If they do not match, an error is detected.

Parity checks are simple and lightweight but have limitations. A single parity bit can detect any odd number of bit flips within the word, but it cannot detect even numbers of errors, nor can it identify which bit changed. If two or more bits flip in a way that preserves the parity, the error may go undetected, and the method cannot correct errors.

In coding theory and practical systems, parity checks are extended through more sophisticated schemes. Parity-check matrices (H) define parity constraints for linear block codes, with the syndrome s = rH^T used to detect and sometimes locate errors. More powerful techniques—such as cyclic redundancy checks (CRC) and error-correcting codes (ECC), including Hamming codes—provide stronger detection and correction capabilities.

Applications of parity checks span simple data buses, memory modules, and RAID-like storage systems that use parity blocks to enable data recovery after failures. While inexpensive, parity checks are typically used in combination with more robust methods to achieve higher reliability.