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(Redirected from Odd parity)

7 bits of data	byte with parity bit
	even	odd
0000000	'0'0000000	'1'0000000
1010001	'1'1010001	'0'1010001
1101001	'0'1101001	'1'1101001
1111111	'1'1111111	'0'1111111

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.
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.

Contents

Error detection

Usage

Parity block

External links

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.
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

★
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★ TRANSMISSION ERROR
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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

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★ TRANSMISSION ERROR
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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:
A computes even parity: 0^0^1^0 = 1
A sends: 10010

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★
★ TRANSMISSION ERROR
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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.
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 B3
C1 Cp C2 C3
Dp D1 D2 D3
Note: Data blocks are in the format A#, parity blocks Ap.

External links

★ Quick way to get the odd parity of an integer

★ Different methods of generating the parity bit, among other bit operations