Parity Check

A Basic Error Detection Method

Parity checking detects transmission errors by constraining the total number of '1's in each data block. It does not correct errors. It gives the receiver a basic way to determine whether a data block was corrupted during transmission. The core idea is to add one extra bit, the parity bit, to each block of data.

This method adds only a small amount of redundancy to achieve a basic level of integrity checking.

How Parity Check Works

The sender and receiver must first agree on which type of parity to use. There are two options: even parity or odd parity.

Even Parity Example

1. Sender's side: Consider the 7-bit ASCII code for the letter 'K', which is $1001011$.
   • Count the '1's in $1001011$: There are four '1's.
   • Since four is an even number, the sender sets the parity bit to 0.
   • The transmitted 8-bit block is $1001011$ followed by $0$.
2. Receiver's side: The receiver gets the 8-bit block $10010110$.
   • It counts the total number of '1's: There are four '1's.
   • Since four is an even number, it matches the agreed-upon even parity. The parity check accepts the block as valid.

Limits of a Parity Check

A single parity check cannot detect an even number of bit errors. The following example uses data $1001011$, an even parity bit $0$, and the transmitted block $10010110$.

With one parity bit, the parity check detects any odd number of errors (1, 3, 5, etc.). It does not detect an even number of errors (2, 4, 6, etc.).