A parity bit is a binary digit that indicates whether the number of bits with value of one in a given set of bits is even or odd. Parity bits are used as the simplest error detecting code. This article is about the unit of information, see Bit (disambiguation) for other meanings. ... This article is about the number one. ... In mathematics, any integer (whole number) is either even or odd. ... In mathematics, any integer (whole number) is either even or odd. ... It has been suggested that this article or section be merged with SEC-DED. (Discuss) In mathematics, computer science, telecommunication, and information theory, error detection and correction has great practical importance in maintaining data (information) integrity across noisy channels and less-than-reliable storage media. ...

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 a given set of bits is odd (making the total number of ones even). An odd parity bit is set to 1 if the number of ones in a given set of bits is even (making the total 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. A cyclic redundancy check (CRC) is a type of function that takes as input a data stream of any length and produces as output a value of a certain fixed size. ... In mathematics, a polynomial is an expression that is constructed from one variable or more variables and constants, using only the operations of addition, subtraction, multiplication, and constant positive whole number exponents. ...

Additionally, parity bits can be referred to as mark parity, where the parity bit is always 1, and space parity, where the bit is always 0.

Error detection

If an odd number of bits (including the parity bit) are 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 an example of an error-correcting code. In telecommunications, transmission is the act of transmitting electrical messages (and the associated phenomena of radiant energy that passes through media). ... This article is about XOR in the sense of an electronic logic gate (e. ... In telecommunication, a Hamming code is a linear error-correcting code named after its inventor, Richard Hamming. ...

For example, our parity bit can be computed as follows assuming we are sending a simple 4-bit value 1001 (the parity bit is the leftmost bit of the sent/received values):

 A computes even parity: 1^0^0^1 = 0 A sends: 01001 B receives: 01001 B validates even parity: 1^0^0^1 = 0 

 A computes odd parity: ~(1^0^0^1) = 1 A sends: 11001 B receives: 11001 B validates odd parity: ~(1^0^0^1) = 1 

This mechanism enables the detection of single bit errors, because if one bit gets flipped due to line noise, there will be an incorrect number of ones in the received data. In the two examples above, B's calculated parity value matches the parity bit in its received value, indicating there are no single bit errors. Consider the following example assuming even parity when sending 4-bit value 0010 (the parity bit is the leftmost bit of the sent/received values):

 A computes even parity: 0^0^1^0 = 1 A sends: 10010 *** TRANSMISSION ERROR *** B receives: 11010 B validates even parity: 1^0^1^0 = 0 

B's calculated parity value (0) does not match the parity bit (1) in its received value, indicating the bit error. Here's the same example (even parity, value 0010) but now the parity bit itself gets corrupted:

 A computes even parity: 0^0^1^0 = 1 A sends: 10010 *** TRANSMISSION ERROR *** B receives: 00010 B validates even parity: 0^0^1^0 = 1 

Once again, B's calculated parity value (1) does not match the parity bit (0) in its received value, indicating the bit error.

There is a limitation to parity schemes. A parity bit is only guaranteed to detect an odd number of bit errors. If an even number of bits have errors, the parity bit records the correct number of ones, even though the data is corrupt. (See also error detection and correction.) Consider the same example as before (even parity, value 0010) with an even number of corrupted bits: It has been suggested that this article or section be merged with SEC-DED. (Discuss) In mathematics, computer science, telecommunication, and information theory, error detection and correction has great practical importance in maintaining data (information) integrity across noisy channels and less-than-reliable storage media. ...

 A computes even parity: 0^0^1^0 = 1 A sends: 10010 *** TRANSMISSION ERROR *** B receives: 11011 B validates even parity: 1^0^1^1 = 1 

B's calculated parity value (1) matches the parity bit (1) in its received value, thereby failing to catch the two bit errors.

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. Computer hardware is the physical part of a computer, including the digital circuitry, as distinguished from the computer software that executes within the hardware. ... Scuzzy redirects here. ... A microprocessor is a programmable digital electronic component that incorporates the functions of a central processing unit (CPU) on a single semiconducting integrated circuit (IC). ... For other uses, see cache (disambiguation). ... Primary storage is a category of computer storage, often called main memory. ...

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 telecommunications and computer science, serial communications is the process of sending data one bit at one time, sequentially, over a communications channel or computer bus. ... Data transmission is the conveyance of any kind of information from one space to another. ... Asynchronous start-stop describes an asynchronous transmission protocol in which a start signal is sent prior to each code symbol and a stop signal is sent after each code symbol. ... Image:ASCII fullsvg There are 95 printable ASCII characters, numbered 32 to 126. ...

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 hardware 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). A UART or universal asynchronous receiver-transmitter is a piece of computer hardware that translates between parallel bits of data and serial bits. ... An operating system (OS) is the software that manages the sharing of the resources of a computer and provides programmers with an interface used to access those resources. ... In computing, a hardware register is a storage area for Digital electronics and particularly Computer hardware including the Central processing unit (CPU) and input/output (I/O) of different kinds. ...

History

A "parity track" was present on the first magnetic tape data storage in 1951. Magnetic tape has been used for data storage for over 50 years. ...

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. For other uses, see Raid. ...

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 B3 C1 Cp C2 C3 Dp D1 D2 D3 

 Note: Data blocks are in the format A#, parity blocks Ap. 

Fast, cheap, good: choose two” In computing, a redundant array of independent disks (more commonly known as a RAID) is a system of using multiple hard drives for sharing or replicating data among the drives. ...

External links

• Quick way to get the odd parity of an integer
• Different methods of generating the parity bit, among other bit operations