Error Detection And Correction Codes (Digital Logic)

Basic approach used for error detection is the use of redundancy, where additional bits are added to facilitate detection and correction of errors. 

Popular technique are: 

  • Simply Parity Check
  • Two-dimension parity check
  • Checksum
  • Cyclic redundancy check

Parity method for Error Detection

Table: Message with even parity and odd parity




Even Parity 

Definition: In even parity the number of bits set to 1 in a data item, including the parity bit itself is always even. If the number of 1s in the data is odd, the parity bit is set to 1 to make the total number of 1s even.


Odd Parity

Definition: In odd parity the number of bits set to 1 in the data item including the parity bit is always odd. If the number of 1s in the data is even the parity bit is set to 1 to make the total number of 1s odd.

Notes:

- Parity method is only for the error detection not for the error correction.

This method provide for the detection of single bit error (or any odd number of errors, which is very unlikely) but cannot check for two errors in one group.  


 Here we have the parity checking schema : -












Solving some problems related parity bit:


Example : 1

Assign the proper even parity bit to the following code groups.

(a) 1010

(b) 101101

(c) 1110000

Solution: 

Make the parity bit either 1 or 0 as necessary to make the total number of 1s even. The parity bit will be left-most bit.

For (a)  01010

For (b) 0101101

For (c) 11110000


Example : 2

Add an even parity bit to the 7-bit ASCII code for the letter K. An odd parity system receives the following code groups: 10110, 11010, 110011, 110101110100 and 1100010101010. Determine which groups, if any are in error.

Solution:

Since odd parity is required, any group with an even number of 1s is incorrect. The following groups are in error: 11011 and 1100010101010. 


Practice Question :

1. Determine which of the following even parity codes are in error:

(a) 100110010
(b) 011101010
(c) 10111111010001010

2. Attach the proper even parity bit to each of the following bytes of data:

(a) 10100100
(b) 00001001
(c) 11111110

Comment your answer !

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