GATE | GATE CS 2021 | Set 1 | Question 39

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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