## Error Detection Codes

**Error Detection Codes:**

** **Binary information transmitted through some form of communication medium is subject to external noise that could change bits from one to zero and vice versa. In most practical systems, there is always a finite probability of the occurrence of a single error. Two types of codes that are used for single error detection and correction are Error detection codes and Error correction codes. An Error detection code is a binary code that detects digital errors during transmission detected errors cannot be corrected but their presence is indicated.

Parity bit: The most common error detection code is Parity bit. It is used to detect the errors, the messages will be sent with an extra bit called Parity bit. A parity bit is an extra bit included with a binary message to make the total number of one’s either odd or even. A message of three bits and two possible parity bits [P (Odd) and P (Even)] are shown below.

Message
XYZ |
P(Odd) | P(Even) |

000 | 1 | 0 |

001 | 0 | 1 |

010 | 0 | 1 |

011 | 1 | 0 |

100 | 0 | 1 |

101 | 1 | 0 |

110 | 1 | 0 |

111 | 0 | 1 |

- P(Odd) bit is chosen in such a way as to make the sum of one’s odd
- P(Even) bit is chosen to make the sum of all one’s even.
- In either case, the sum is taken over the message and the P bit
- The even parity scheme has the disadvantage of having a bit combination of all zeros while tin the odd parity there is always one bit that is one
- P(Odd) is the complement of P(Even)

Parity generator: During transfer of information from one location to another, the parity bit is handled as follows

- At the sending end, the message is applied to a parity generator, where the required parity bit is generated.
- The message, including the parity bit, is transmitted to its destination.

Parity checker: At the receiving end, all the incoming bits are applied to a parity checker that checks the proper parity adopted.

An error is detected if the checked parity does not conform to the adopted parity. The parity method detects the presence of odd number of errors. An even number of errors is not detected.

Parity generator and checker networks are logic circuits constructed with exclusive OR functions. Exclusive OR function of three or more variables is by definition an odd function. An odd function is a logic function whose value is binary 1 if and only if an odd number of variables are equal to 1. According to this definition the P(Even) function is the exclusive OR of x, y, and z because it is equal to one when either one or all three of the variables are equal to 1. The P(Odd) is the complement of the P(Even) function.

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