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

01000101 00010100
01001010 01001011
11111111 00101100
10101011 01011000
11011100 11101000

Figure 2

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

00100001 01100100 1
01001001 11100001 1
01100101 11000000 1
00111101 10110101 0
01000001 01111111 1
00110001 10001111 0

Figure 3

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

10000011 01100100 0
01010001 00011001 0
01110000 00001111 0
10001010 10010110 1
01110101 01011111 0
01011100 10111011 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:

01000101 00010100 1
01001010 01001011 1
11111111 00101100 1
10101011 01011000 0
11011100 11101000 1
10000111 11000011 0

1. The parity bits for the 16 columns is: 10000111 11000011

2. The parity bits for the 5 rows is: 11101

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

4. The bit that was flipped in figure 2 is (1,2):

00100001 01100100 1
01001001 11100001 1
01100101 11000000 1
00111101 10110101 0
01000001 01111111 1
00110001 10001111 0

For figure 3, the bits that were flipped are (16,4) and (7,2):

10000011 01100100 0
01010001 00011001 0
01110000 00001111 0
10001010 10010110 1
01110101 01011111 0
01011100 10111011 0

5. No, with 2D parity, you can detect the presence of two flipped bits, but you can't know their exact locations in order to correct them.



That's incorrect

That's correct

The answer was: 1000011111000011

Question 1 of 5

The answer was: 11101

Question 2 of 5

The answer was: 0

Question 3 of 5

The answer was: 1,2

Question 4 of 5

The answer was: No

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