Data transmitted on a link uses the following 2D parity scheme for error detection:
Each sequence of 28 bits is arranged in a 4×7 matrix (rows r
0 through r
3, and columns d
7 through d
1) and is padded with a column d
0 and row r
4 of parity bits computed using the Even parity scheme. Each bit of column d
0 (respectively, row r
4) gives the parity of the corresponding row (respectively, column). These 40 bits are transmitted over the data link.
The table shows data received by a receiver and has n corrupted bits. What is the minimum possible value of n?
(A) 1
(B) 2
(C) 3
(D) 4
Answer:(C)Explanation: In the given 2D parity matrix, all rows except
have even parity. Therefore there must be atleast 1 bit error in this row.
Also, there are three columns with odd parities (odd parity indicates errors),
,
and
.
So there must be a minimum of 3 bit errors.
All three errors could have occurred in
or two of these errors could have occurred in any other row. Since
has an odd parity, there is at least one bit-error in this row.
Therefore option (C) is correct.
This explanation is provided by
Chirag Manwani.
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