Discussion
If an even parity Hamming code 0110011 is transmitted and that 0100011 is received. The receiver is unaware of what was transmitted ? Determine the bit location where error has occurred using received code.
Answer: C
The error is in the 5th location.
In a 7-bit Hamming code the bit positions are numbered 7 down to 1 from left to right: D7 D6 D5 P4 D3 P2 P1, with parity bits at positions 1, 2 and 4. For the received word 0100011, b7 = 0, b6 = 1, b5 = 0, b4 = 0, b3 = 0, b2 = 1, b1 = 1. With even parity, each check over its group should be 0:
- C1 = b1 ⊕ b3 ⊕ b5 ⊕ b7 = 1 ⊕ 0 ⊕ 0 ⊕ 0 = 1
- C2 = b2 ⊕ b3 ⊕ b6 ⊕ b7 = 1 ⊕ 0 ⊕ 1 ⊕ 0 = 0
- C4 = b4 ⊕ b5 ⊕ b6 ⊕ b7 = 0 ⊕ 0 ⊕ 1 ⊕ 0 = 1
The syndrome C4 C2 C1 = 101 = 5, so bit 5 is wrong. It is the third bit counted from the left, which is the trap in the '3rd location' option.
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