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GATE | GATE CS 2021 | Set 1 | Question 39

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  • Last Updated : 09 Sep, 2021

Assume that a 12-bit Hamming codeword consisting of 8-bit data and 4 check bits is d8d7d6d5c8d4d4d3d2c4d1c2c1, 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?
(A) x is 0 and y is 0
(B) x is 0 and y is 1
(C) x is 1 and y is 0
(D) x is 1 and y is 1


Answer: (A)

Explanation:

A 12-bit Hamming codeword is given: 

d8 d7 d6 d5 c8 d4 d3 d2 c4 d1 c2 c1
1 1 0 x y 0 1 0 0 1 1 0

Check for C1

c1 + d7 + d5 + d4 + d2 + d1 : 0 + 1 + x + 0 + 0 + 1 

x=0 ( for even parity)

Check for C8

c8 + d7 + d6 + d5 : y + 1 + 1 + 0 + 0

y=0 ( for even parity)

So, option (A) is correct.


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