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7 bits of data | byte with parity bit | |

even | odd | |

0000000 | 00000000 | 10000000 |

1010001 | 11010001 | 01010001 |

1101001 | 01101001 | 11101001 |

1111111 | 11111111 | 01111111 |

As for binary digits, there are two variants 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, including the parity bit, 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, including the parity bit, 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.

If the parity bit is present but not used, it may be referred to as mark parity, where the parity bit is always 1, or as space parity, where the bit is always 0.

Parity bit checking is used often for transmission of ASCII characters, since they have 7 bits and the 8th bit can conveniently be used as a parity bit.

For example, our parity bit can be computed as follows assuming we are sending a simple 4-bit value 1001, with the parity bit following on the right, and ^ denoting XOR gate:

Transmission sent using even parity:

A wants to transmit: 1001

A computes parity bit value: 1^0^0^1 = 0

A adds parity bit and sends: 10010

B receives: 10010

B computes overall parity: 1^0^0^1^0 = 0

B reports correct transmission after observing expected even result.

Transmission sent using odd parity:

A wants to transmit: 1001

A computes parity bit value: ~(1^0^0^1) = 1

A adds parity bit and sends: 10011

B receives: 10011

B computes overall parity: 1^0^0^1^1 = 1

B reports correct transmission after observing expected odd result.

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 with a transmission error in the second bit:

Transmission sent using even parity:

A wants to transmit: 1001

A computes parity bit value: 1^0^0^1 = 0

A adds parity bit and sends: 10010

*** TRANSMISSION ERROR ***

`B receives: 11010`

B computes overall parity: 1^1^0^1^0 = 1

B reports incorrect transmission after observing unexpected odd result.

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

A wants to transmit: 1001

A computes even parity value: 1^0^0^1 = 0

A sends: 10010

*** TRANSMISSION ERROR ***

`B receives: 10011`

B computes overall parity: 1^0^0^1^1 = 1

B reports incorrect transmission after observing unexpected odd result.

Once again, B's computes an odd overall parity, 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 with an even number of corrupted bits:

A wants to transmit: 1001

A computes even parity value: 1^0^0^1 = 0

A sends: 10010

*** TRANSMISSION ERROR ***

B receives: 11011

B computes overall parity: 1^1^0^1^1 = 0

B reports correct transmission though actually incorrect.

B observes even parity, as expected, thereby failing to catch the two bit errors.

In serial data transmission, a common format is 7 data bit, 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 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).

Given the diagram below, where each column is a disk, assume A1 = 00000111, A2 = 00000101, and A3 = 00000000. 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

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

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

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Last updated on Sunday October 05, 2008 at 09:05:27 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Sunday October 05, 2008 at 09:05:27 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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