GATE 2026 EC – Question 63
The average bit error rate at the input of a (7, 4, 1) Hamming decoder is 0.10. The probability that the decoder will fail to decode a received word correctly is ________. (rounded off to two decimal places)
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Correct answer: 0.14 to 0.16
Explanation
A (7,4) Hamming code corrects only single errors, so decoding fails for 2 or more errors in 7 bits. $P=1-(0.9)^7-7(0.1)(0.9)^6=1-0.4783-0.3720\approx0.15$.