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GATE 2021 CS – Question 39

Computer Networks · Data Link Layer: Error Detection, Medium Access Control, Flow Control · 2 marks · Multiple choice

Assume that a 12-bit Hamming codeword consisting of 8-bit data and 4 check bits is $d_8d_7d_6d_5c_8d_4d_3d_2c_4d_1c_2c_1$, where the data bits and the check bits are given in the following tables:
Data bits: $d_8=1, d_7=1, d_6=0, d_5=x, d_4=0, d_3=1, d_2=0, d_1=1$
Check bits: $c_8=y, c_4=0, c_2=1, c_1=0$
Which one of the following choices gives the correct values of $x$ and $y$?

  1. $x$ is 0 and $y$ is 0.
  2. $x$ is 0 and $y$ is 1.
  3. $x$ is 1 and $y$ is 0.
  4. $x$ is 1 and $y$ is 1.

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Show answer and explanation

Correct answer: (A) $x$ is 0 and $y$ is 0.

Explanation

Positions: c1=1, c2=2, d1=3, c4=4, d2=5, d3=6, d4=7, c8=8, d5=9... Even-parity checks with c1=0 and c2=1 force x=0, and c8's check then gives y=0.