Information Theory

Question 1 [UGC NET June 2015 Paper III]

For the 8-bit word 00111001, the check bits stored with it would be 0111. Suppose when the word is read from memory, the check bits are calculated to be 1101.What is the data word that was read from memory?
(A) 10011001               (B) 00011001
(C) 00111000               (D) 11000110
Answer: B
            00111001 is Data bits &
            0111 is Parity bit.
The Hamming Word initially calculated was:
bit number:
12
11
10
9
8
7
6
5
4
3
2
1
0
0
1
1
0
1
0
0
1
1
1
1


0 0 1 1 0 1 0 0 1 1 1 1 Doing an exclusive-OR
              0111 
              1101
==========
XOR     1010

Here 1010 indicating an error in position bit number 10th of the Hamming Word. Thus, the data word read from memory was 00011001.

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