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Assume that a 12-bit Hamming codeword consisting of 8-bit data and 4 check bits is d8d7d6d5c8d4d3d2c4d1c2c1, where the data bits and the check bits are given in the following tables:

Data bits

d8

d7

d6

d5

d4

d3

d2

d1

1

1

0

x

0

1

0

1

 

c8

c4

c2

c1

Y

0

1

0


Which one of the following choices gives the correct values of x and y?
1. x is 1 and y is 0.
2. x is 1 and y is 1.
3. x is 0 and y is 1.
4. x is 0 and y is 0.

1 Answer

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Best answer
Correct Answer - Option 4 : x is 0 and y is 0.

Answer: Option 4

Data

Data bits

d8

d7

d6

d5

d4

d3

d2

d1

1

1

0

x

0

1

0

1

 

c8

c4

c2

c1

y

0

1

0

Codeword =  d8d7d6d5c8d4d3d2c4d1c2c1

Codeword = 

1

1

0

x

y

0

1

0

0

1

1

0

B12

B11

B10

B9

B8

B7

B6

B5

B4

B3

B2

B1

 

C1=B1 ⊕ B3 ⊕ B5 ⊕ B7 ⊕ B9 ⊕ B11 = 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ x ⊕ 1; for even parity x=0

C2 = B2 ⊕ B3 ⊕ B6 ⊕ B7 ⊕ B10 ⊕ B11 = 1 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 1;

C4 = B4 ⊕ B5 ⊕ B6 ⊕ B7 ⊕ B12 = 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 1; 

C8 = y ⊕ 0⊕ 0 ⊕ 1⊕  ⊕ 1; for even parity y = 0 (putting x = 0) 

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