- Error-Detection Codes

Binary information may be transmitted through some communication medium, e.g. using wires or wireless media. A corrupted bit will have its value changed from 0 to 1 or vice versa. To be able to detect errors at the receiver end, the sender sends an extra bit (parity bit) with the original binary message. A parity bit is an extra bit included with the n-bit binary message to make the total number of 1’s in this message (including the parity bit) either odd or even. If the parity bit makes the total number of 1’s an odd (even) number, it is called odd (even) parity. The table shows the required odd (even) parity for a 3-bit message

No error is detectable if the transmitted message has 2 bits in error since the total number of 1’s will remain even (or odd) as in the original message. In general, a transmitted message with even number of errors cannot be detected by the parity bit.

- Gray code
The Gray code consist of 16 4-bit code words to represent the decimal Numbers 0 to 15. For Gray code, successive code words differ by only one bit from one to the next