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

11110001 11100011
10100111 00101000
00001000 10110001
10101010 10000111
10101100 01001110

Figure 2

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

00001011 11001111 1
01001011 01111001 1
11110110 10000101 0
11000100 01101111 1
11000101 10001100 1
00110111 11010000 0

Figure 3

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

00111111 11011001 0
10000110 10101101 0
11101000 00111111 0
11100001 00001001 0
10111001 10011011 0
00101001 11011001 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:

11110001 11100011 0
10100111 00101000 1
00001000 10110001 1
10101010 10000111 0
10101100 01001110 0
01011000 10110011 0

1. The parity bits for the 16 columns is: 01011000 10110011

2. The parity bits for the 5 rows is: 01100

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

4. The bit that was flipped in figure 2 is (0,2):

00001011 11001111 1
01001011 01111001 1
11110110 10000101 0
11000100 01101111 1
11000101 10001100 1
00110111 11010000 0

For figure 3, the bit that was flipped is (2,0):

00111111 11011001 0
10000110 10101101 0
11101000 00111111 0
11100001 00001001 0
10111001 10011011 0
00101001 11011001 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: 0101100010110011

Question 1 of 5

The answer was: 01100

Question 2 of 5

The answer was: 0

Question 3 of 5

The answer was: 0,2

Question 4 of 5

The answer was: Yes

Question 5 of 5

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