Question

Problem 3: Single Parity bit [10 Points]

[11000101] is an 8-bit data codeword before appending a parity bit. Please append a parity bit to this codeword such that:

1. The resulting encoded codeword has even parity
2. The resulting encoded codeword has odd parity
3. Would all possible errors be detected when using even parity? Provide an example to support your answer.
4. Would all possible errors be detected when using odd parity? Provide an example to support your answer.

Answer 1

Answer a) 110001010  the parity bit is 0 so that the total number of 1's in the code is 4

Answer b)110001011 the parity bit is 1 so that the total number of 1's in the code is 5

Answer c) Single bit error can be detected using one bit even parity. If we want to detect more than one bit error then we have to append more even parity bits.

detecting 1 bit error : in the above given example 110001010 (after adding parity bit), if there is any change in any one of the bit then total number of 1's in the code will be change, so the receiver can detect one bit error by counting number of 1's in the code.

if there is change more than 1 bits then the receiver can not detect all possible errors . We have to append more even parity to detect more than one bit error.

Answer d) Similary( as in c)Single bit error can be detected using one bit odd parity. If we want to detect more than one bit error then we have to append more odd parity bits.

detecting 1 bit error : in the above given example 110001011 (after adding parity bit), if there is any change in any one of the bit then total number of 1's in the code will be change, so the receiver can detect one bit error by counting number of 1's in the code.

if there is change in more than 1 bits then the receiver can not detect all possible errors . We have to append more odd parity to detect more than one bit error.