Solution
The correct answer is option 1.
Key Points
Arrange one below the other the XOR operations
For correcting, the d-bit error hamming distance should be 2d+1.
So,2d+1=5
d=2
It means the hamming distance between the codeword 0000000111 and gives option should be 2-bits. Only Option 1 matches.
Option verify:
|
(xor) 0000000111
0000011111
-----------------------------
0000011000
(2-bit error)
|
(xor) 0000000111
0000000000
---------------------------
00000001110
(3-bit error)
|
(xor 0000000111
1111100000
------------------------
1111100111
(8-bit error)
|
(xor) 0000000111
1111111111
---------------------
1111111000
(7-bit error)
|
0000011111 is minimum with the 2-bit error.
∴ Hence the correct answer is 0000011111.