Interactive end-of-chapter exercises


Error Detection and Correction: Two Dimensional Parity

Suppose that a packet’s payload consists of 10 eight-bit values (e.g., representing ten ASCII-encoded characters) shown below. (Here, we have arranged the ten eight-bit values as five sixteen-bit values):

Figure 1

01110010 00100111
00100000 11101111
10100001 10101100
00010011 00100000
10000101 01101010

Figure 2

Both the payload and parity bits are shown. One of these bits is flipped.

10101001 01111000 0
10100101 01011110 1
10110001 11110011 0
10101011 10010000 0
01011011 10100110 1
01001101 11100011 1

Figure 3

Both the payload and parity bits are shown; Either one or two of the bits have been flipped.

11110110 01110000 0
00011110 11001100 0
01110111 01111000 0
10110110 00010011 0
11100000 01011101 0
11001001 10101010 0


Question List


1. For figure 1, compute the two-dimensional parity bits for the 16 columns. Combine the bits into one string

2. For figure 1, compute the two-dimensional parity bits for the 5 rows (starting from the top). Combine the bits into one string

3. For figure 1, compute the parity bit for the parity bit row from question 1. Assume that the result should be even.

4. For figure 2, indicate the row and column with the flipped bit (format as: x,y), assuming the top-left bit is 0,0

5. For figure 3, is it possible to detect and correct the bit flips? Yes or No




Solution


The full solution for figure 1 is shown below:

01110010 00100111 0
00100000 11101111 0
10100001 10101100 1
00010011 00100000 0
10000101 01101010 1
01100101 00101110 0

1. The parity bits for the 16 columns is: 01100101 00101110

2. The parity bits for the 5 rows is: 00101

3. The parity bit for the parity row is: 0

4. The bit that was flipped in figure 2 is (16,3):

10101001 01111000 0
10100101 01011110 1
10110001 11110011 0
10101011 10010000 0
01011011 10100110 1
01001101 11100011 1

For figure 3, the bit that was flipped is (10,0):

11110110 01110000 0
00011110 11001100 0
01110111 01111000 0
10110110 00010011 0
11100000 01011101 0
11001001 10101010 0

5. Yes, with 2D parity, you can detect and correct the a single flipped bit



That's incorrect

That's correct

The answer was: 0110010100101110

Question 1 of 5

The answer was: 00101

Question 2 of 5

The answer was: 0

Question 3 of 5

The answer was: 16,3

Question 4 of 5

The answer was: Yes

Question 5 of 5

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We greatly appreciate the work of John Broderick (UMass '21) in helping to develop these interactive problems.

Copyright © 2010-2025 J.F. Kurose, K.W. Ross
Comments welcome and appreciated: kurose@cs.umass.edu