Odd parity

A parity bit, or check bit, is a bit added to a string of binary code to ensure that the total number of 1-bits in the string is even or odd. Parity bits are used as the simplest form of error detecting code.

There are two variants of parity bits: even parity bit and odd parity bit.

In the case of even parity, for a given set of bits, the occurrences of bits whose value is 1 is counted. If that count is odd, the parity bit value is set to 1, making the total count of occurrences of 1s in the whole set (including the parity bit) an even number. If the count of 1s in a given set of bits is already even, the parity bit's value is 0.

In the case of odd parity, the coding is reversed. For a given set of bits, if the count of bits with a value of 1 is even, the parity bit value is set to 1 making the total count of 1s in the whole set (including the parity bit) an odd number. If the count of bits with a value of 1 is odd, the count is already odd so the parity bit's value is 0.

Even parity is a special case of a cyclic redundancy check (CRC), where the 1-bit CRC is generated by the polynomial x+1.

If a bit is present at a point otherwise dedicated to a parity bit, but is not used for parity, it may be referred to as a mark parity bit if the parity bit is always 1, or a space parity bit if the bit is always 0. In such cases where the value of the bit is constant, it may be called a stick parity bit even though its function has nothing to do with parity. The function of such bits varies with the system design, but examples of functions for such bits include timing management, or identification of a packet as being of data or address significance. If its actual bit value is irrelevant to its function, the bit amounts to a Don't-care term.

Parity bits are generally applied to the smallest units of a communication protocol, typically 8-bit octets (bytes), although they can also be applied separately to an entire message string of bits.

The decimal math equivalent to the parity bit is the Check digit.

In mathematics, parity refers to the evenness or oddness of an integer, which for a binary number is determined only by the least significant bit. In telecommunications and computing, parity refers to the evenness or oddness of the number of bits with value one within a given set of bits, and is thus determined by the value of all the bits. It can be calculated via an XOR sum of the bits, yielding 0 for even parity and 1 for odd parity. This property of being dependent upon all the bits and changing value if any one bit changes allows for its use in error detection schemes.

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