Q4. (72, 64) SEC/DED Hamming code is a modified SEC Hamming code which can corre
ID: 3730323 • Letter: Q
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Q4. (72, 64) SEC/DED Hamming code is a modified SEC Hamming code which can correct all single bit errors and detect double bit errors in the data. It is usually used in a memory system with 64-bit data word and 8 parity bits. Compared to that, what is the error correction and detection capabilities of a single-parity-per-byte code with the same number of data and parity bit? List the types of multiple errors that are detectable by the single-parity-per-byte code. (Hint: In single-parity-per-byte code, the 64-bit data is separated into 8 groups of 8-bit data word and one parity bit is added for each group of 8- bit data word.)Explanation / Answer
Single parity per byte code detect errors with a parity bit. The parity bit is computed as the exclusive-OR (even parity) or exclusive-NOR (odd parity) of all of the other bits in the word. Thus, the resulting word with a parity bit will always have an even (for even parity) or odd (for odd parity) number of 1 bits in it.
Types of Error detected:
We can't tell which bit was corrupted, double errors go undetected, triple errors get detected, quadruple errors don't, etc. Random garbage has a 50% probability of being accepted as valid.
To design a code that can detect d single bit errors, the minimum Hamming distance for the set of codewords must be d + 1 (or more). That way, no set of d errors in a single bit could turn one valid codeword into some other valid codeword.
To design a code that can correct d single bit errors, a minimum distance of 2d + 1 is required. That puts the valid codewords so far apart that even after bit errors in d of the bits, it is still less than half the distance to another valid codeword, so the receiver will be able to determine what the correct starting codeword was.
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