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

00101110 00101100
11111101 11001011
10010110 10110111
11101100 11110110
01100101 00010000

Figure 2

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

11111101 11001110 0
10011010 01111000 0
10100111 01111001 0
01101111 11100101 0
01100100 10001011 1
11001011 10101001 1

Figure 3

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

10001011 11110100 1
11110000 01010001 0
01001101 01001000 0
01001110 01010101 0
11010110 00101010 0
10101110 10010010 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:

00101110 00101100 1
11111101 11001011 0
10010110 10110111 0
11101100 11110110 1
01100101 00010000 1
11001100 10110110 1

1. The parity bits for the 16 columns is: 11001100 10110110

2. The parity bits for the 5 rows is: 10011

3. The parity bit for the parity row is: 1

4. The bit that was flipped in figure 2 is (12,3):

11111101 11001110 0
10011010 01111000 0
10100111 01111001 0
01101111 11100101 0
01100100 10001011 1
11001011 10101001 1

For figure 3, the bit that was flipped is (16,1):

10001011 11110100 1
11110000 01010001 0
01001101 01001000 0
01001110 01010101 0
11010110 00101010 0
10101110 10010010 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: 1100110010110110

Question 1 of 5

The answer was: 10011

Question 2 of 5

The answer was: 1

Question 3 of 5

The answer was: 12,3

Question 4 of 5

The answer was: Yes

Question 5 of 5

Try Another Problem

We’d appreciate your leave us feedback on this networking tutor.

We gratefully acknowledge the programming and problem design work of John Broderick (UMass '21), which has really helped to substantially improve this site. The networking tutor was designed and implemented by Hashim Zia and Shayan Ahmad from New York University Abu Dhabi.

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