Parity bit

• A parity bit, or check bit, is a bit added to a string of binary code that indicates whether the 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.

Even parity bit

• In even parity bit, sending data consist must be even number of 1-bit count. In these case it will add parity bit zero other wise one.

7 bits of data	(count of 1-bits)	8 bits including parity
0000000	0	00000000
1010001	3	10100011
1101001	4	11010010
1111111	7	11111111

Odd parity bit

• In Odd parity bit, sending data consist must be odd number of 1-bit count. In these case it will add parity bit zero other wise one.

7 bits of data	(count of 1-bits)	8 bits including parity
0000000	0	00000001
1010001	3	10100010
1101001	4	11010011
1111111	7	11111110

Error detection

• The below table shows the successful transmission while sending data from A to B.

Type of bit parity	Successful transmission scenario
Even parity	A wants to transmit data: 1001 A computes parity bit value: 1+0+0+1 (mod 2) = 0 A adds parity bit and sends data: 10010 B receives data: 10010 B computes parity: 1+0+0+1+0 (mod 2) = 0 B reports correct transmission after observing expected even result.
Odd parity	A wants to transmit data: 1001 Acomputes parity bit value: 1+0+0+1 + 1 (mod 2) = 1 A adds parity bit and sends data: 10011 B receives data: 10011 B computes overall parity: 1+0+0+1+1 (mod 2) = 1 B reports correct transmission after observing expected odd result.

• The below table shows the failed transmission scenario while sending data from A to B.

Type of bit parity error	Failed transmission scenario
Even parity Error in the second bit	A wants to transmit data: 1001 A computes parity bit value: 1+0+0+1 = 0 A adds parity bit and sends data: 10010 ...TRANSMISSION ERROR... B receives data: 11010 B computes overall parity: 1+1+0+1+0 = 1 B reports incorrect transmission after observing unexpected odd result.
Even parity Error in the parity bit	A wants to transmit data: 1001 A computes even parity value: 1+0+0+1 = 0 A sends data: 10010 ...TRANSMISSION ERROR... B receives data: 10011 Bcomputes overall parity: 1+0+0+1+1 = 1 B reports incorrect transmission after observing unexpected odd result.

History

• A "parity track" was present on the first magnetic tape data storage in 1951.
• Parity in this form, applied across multiple parallel signals, is known as a transverse redundancy check.
• This can be combined with parity computed over multiple bits sent on a single signal, a longitudinal redundancy check.