Gourt Home::Gourt :: Parity bit
| 7 bits of data | byte with parity bit | |
| even | odd | |
| 0000000 | 00000000 | 00000001 |
| 1010001 | 10100011 | 10100010 |
| 1101001 | 11010010 | 11010011 |
| 1111111 | 11111111 | 11111110 |
There are two types of parity bits: even parity bit and odd parity bit. An even parity bit is set to 1 if the number of ones in given set of bits is odd (making the number of ones even). An odd parity bit is set to 1 if the number of ones in given set of bits is even (making the number of ones odd). Even parity is actually a special case of a cyclic redundancy check (CRC), where the 1-bit CRC is generated by the polynomial x+1.
Error detection
If an odd number of bits (including the parity bit) is changed in transmission of a set of bits then parity bit will be incorrect and will thus indicate that an error in transition has occurred. Therefore, parity bit is an error detecting code, but is not an error correcting code as there is no way to determine which particular bit is corrupted. The data must be discarded entirely, and re-transmitted from scratch. On a noisy transmission medium a successful transmission could take a long time, or even never occur. Parity does have the advantage, however, that it is about the best possible code that uses only a single bit of space and it requires only a number of XOR gates to generate. See Hamming code for other error-correction codes.
Usage
Because of its simplicity, parity is used in many hardware applications where an operation can be repeated in case of difficulty, or where simply detecting the error is helpful. For example, the SCSI bus uses parity to detect transmission errors, and many microprocessor instruction caches include parity protection. Because the I-cache data is just a copy of main memory, it can be thrown away and re-fetched if it is found to be corrupted.
In serial data transmission, a common format is 7 data bits, an even parity bit, and one or two stop bits. This format neatly accommodates all the 7-bit ASCII characters in a convenient 8-bit byte. Other formats are possible; 8 bits of data plus a parity bit can convey all 8-bit byte values.
In serial communication contexts, parity is usually generated and checked by interface hardware (e.g., a UART) and, on reception, the result made available to the CPU (and so to, for instance, the operating system) via a status bit in a register in the interface hardware. Recovery from the error is usually done by retransmitting the data, the details of which are usually handled by software (e.g., the operating system I/O routines).
Parity block
A parity block is used by certain RAID levels, redundancy is achieved by the use of parity blocks. If a single drive in the array fails, data blocks and a parity block from the working drives can be combined to reconstruct the missing data.Given the diagram below, where each column is a disk, assume A1 = 00000111, A2 = 00000101, and A3 = 0000000. Ap, generated by XORing A1, A2, and A3, will then equal 00000010. If the second drive fails, A2 will no longer be accessible, but can be reconstructed by XORing A1, A3, and Ap:
A1 XOR A3 XOR Ap = 00000101
RAID Array A1 A2 A3 Ap B1 B2 Bp C1 C2 C3 C4 Cp
Note: Data blocks are in the format A#, parity blocks Ap.
Telecommunications | Error detection and correction
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"Parity bit"