Consider a single error correction (SEC) code that protects 8 bit words with 4 p

Question

Consider a single error correction (SEC) code that protects 8 bit words with 4 parity bits. In this case a parity bit for the entire word (pw) is added in order to provide double error detection (DED). Please assume even parity. a) Let us assume that you need to encode the following byte (the least significant bit is on the left side): Least significant bit 1 0 1 0 1 0 1 1 Use the figure below to show the encoded word. b) Let us assume that the encoded word (shown below) is read. Please determine if there is (are) error(s) in the word. If it is possible to correct, please correct.

Problem Consider a single error correction (SEC) code that protects 8 bit words with 4 parity bits. In this case a parity bit for the entire word (pw) is added in order to provide double error detection (DED). Please assume even parity a) Let us assume that you need to encode the following byte (the least significant bit is on the left side): Least significant bit 3 1 0 1 0 1 0 1 1 Use the figure below to show the encoded word. Bit position 1 2 3 4 5 6 7 8 9 10 11 12 13 Encoded data bits pl p2 p4 d2 d3 d4 p8 d5 d6 d'7 8 pw Encoded data b) Let us assume that the encoded word (shown below) is read. Please determine if there is (are) error(s) in the word. If it is possible to correct, please correct.

Explanation / Answer

1 a) we are using Hamming error detection and correction code

Given

Code word :10101011

given is even parity

we need to calculate parity bits:

p1 = 3,5,7,9,11= xor(1,0,0,1,1) = 1

p2 = 3,6,7,10,11 = xor(1,1,0,0,1) = 1

p4 = 5,6,7,12 = xor(0,1,0,1) = 0

p8 = 9,10,11,12 = xor(1,0,1,1) = 1

P1

1

where PW represents whether we are using even or odd parity

0 ==> even parity

1 ==> odd parity

therefore for the given 8 bit data the encded data is 1110010110110

P1

P2 D1 P4 D2 D3 D4 P8 D5 D6 D7 D8 PW

1

1 1 0 0 1 0 1 1 0 1 1 0

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---