Hamming & SECDED Code (a) For data, using 3 Hamming code parity bits determine the maximum...

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Hamming & SECDED Code (a) For data, using 3 Hamming code parity bits determine the maximum...

Hamming & SECDED Code

(a) For data, using 3 Hamming code parity bits determine the maximum number of data bits that can be protected.

(b) A SECDED encoded character has been retrieved, with the hexadecimal value of 409(base16). You may assume that the SECDED parity is even.

1. Was there an error in transmission? Explain your answer.

2. If there was an error, either correct it (reporting the corrected ASCII character) or explain why it could not be corrected (Show your Hamming/SECDED table).

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Answer 1

Answer #1

(a) For data, using 3 Hamming code parity bits determine the maximum number of data bits that can be protected.

A byte of data: 10011010
Create the data word, leaving spaces for the parity bits: _ _ 1 _ 0 0 1 _ 1 0 1 0
Calculate the parity for each parity bit (a ? represents the bit position being set):

Position 1 checks bits 1,3,5,7,9,11:
? _ 1 _ 0 0 1 _ 1 0 1 0. Even parity so set position 1 to a 0: 0 _ 1 _ 0 0 1 _ 1 0 1 0
Position 2 checks bits 2,3,6,7,10,11:
0 ? 1 _ 0 0 1 _ 1 0 1 0. Odd parity so set position 2 to a 1: 0 1 1 _ 0 0 1 _ 1 0 1 0
Position 4 checks bits 4,5,6,7,12:
0 1 1 ? 0 0 1 _ 1 0 1 0. Odd parity so set position 4 to a 1: 0 1 1 1 0 0 1 _ 1 0 1 0
Position 8 checks bits 8,9,10,11,12:
0 1 1 1 0 0 1 ? 1 0 1 0. Even parity so set position 8 to a 0: 0 1 1 1 0 0 1 0 1 0 1 0
Code word: 011100101010.

(b) A SECDED encoded character has been retrieved, with the hexadecimal value of 409(base16). You may assume that the SECDED parity is even.

Length of Data Sequence	Number of Parity Bits	Length of CodeWord
12	5	17

Parity Scheme

P₀ = D₀ + D₁ + D₃ + D₄ + D₆ + D₈ + D₁₀ + D₁₁
P₁ = D₀ + D₂ + D₃ + D₅ + D₆ + D₉ + D₁₀
P₂ = D₁ + D₂ + D₃ + D₇ + D₈ + D₉ + D₁₀
P₃ = D₄ + D₅ + D₆ + D₇ + D₈ + D₉ + D₁₀
P₄ = D₁₁

Syndrome Matrix

D₁₁	D₁₀	D₉	D₈	D₇	D₆	D₅	D₄	D₃	D₂	D₁	D₀	P₄	P₃	P₂	P₁	P₀
1	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0
0	1	1	1	1	1	1	1	0	0	0	0	0	1	0	0	0
0	1	1	1	1	0	0	0	1	1	1	0	0	0	1	0	0
0	1	1	0	0	1	1	0	1	1	0	1	0	0	0	1	0
1	1	0	1	0	1	0	1	1	0	1	1	0	0	0	0	1

1)The checksum matrix shows that the received codeword contains no errors.

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