GATE CSE 2021 Set 1 Q39: Missing data and check bits in a 12-bit Hamming codeword

Computer Networks
2 marks
MCQ
−2/3 if wrong

Assume that a 12-bit Hamming codeword consisting of 8-bit data and 4 check bits is $d_8 d_7 d_6 d_5 c_8 d_4 d_3 d_2 c_4 d_1 c_2 c_1$ , where the data bits and the check bits are given in the following tables:

Which one of the following choices gives the correct values of $x$ and $y$ ?

Data bits
$d_8$	$d_7$	$d_6$	$d_5$	$d_4$	$d_3$	$d_2$	$d_1$
1	1	0	$x$	0	1	0	1

Check bits
$c_8$	$c_4$	$c_2$	$c_1$
$y$	0	1	0

Try it: multiple choice: exactly one correct option

Wrong answer costs 2/3 mark in GATE.

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Answer: A (official GATE 2021 final answer key)

Concept used: In a Hamming code the check bit at position $2^k$ makes the parity even over all positions whose binary index has bit $k$ set.

First step: Number the positions 12 down to 1; $c_1$ covers positions 1, 3, 5, 7, 9, 11, which include $d_5 = x$ at position 9.

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Source: official GATE 2021 Set 1 CS question paper and final answer key, organised by IIT Bombay. Question paper · Answer key

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GATE CSE 2021 Set 1 Q39: Missing data and check bits in a 12-bit Hamming codeword

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