For the 8 bit word 00111001,the check bits stored with it would we 0111.…
2015
For the 8 bit word 00111001,the check bits stored with it would we 0111. Suppose when the word is read from memory, the check bits are calculated to be 1101. What is the data word that was read from memory?
- A.
10011001
- B.
00011001
- C.
00111000
- D.
11000110
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Correct answer: B
Step 1: Compute the syndrome by XORing the stored check bits with the recalculated check bits.
Stored check bits: 0111; recalculated check bits: 1101; syndrome = 0111 XOR 1101 = 1010 (binary) = 10 (decimal).
Step 2: Map the syndrome to the codeword bit that is in error in a Hamming(12,8) code.
Parity bit positions: 1, 2, 4, 8.
Data bit positions: 3, 5, 6, 7, 9, 10, 11, 12 (these hold the 8 data bits).
Syndrome 10 points to codeword position 10, which is the 6th data bit when data bits are counted from the least-significant (rightmost) data bit.
Step 3: Flip that data bit in the original data word 00111001.
Interpret the 8-bit word with the least-significant bit as the rightmost bit. Flipping the 6th data bit (counting from the right) changes 00111001 into 00011001.
Answer: the data word read from memory is 00011001.