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

01000010 01011100
10111000 01011101
10000100 01010000
00101100 00011111
01011011 11001100

Figure 2

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

11000110 00000100 0
01111111 01110001 1
11000001 10101001 1
00000001 11011101 1
10101110 11110011 1
11010111 11010010 0

Figure 3

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

01101111 10111101 0
00010000 11001101 0
00000111 00100101 1
11100111 00011110 0
10010100 10000000 0
00001011 11011011 1


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:

01000010 01011100 0
10111000 01011101 1
10000100 01010000 0
00101100 00011111 0
01011011 11001100 1
00001001 10000010 0

1. The parity bits for the 16 columns is: 00001001 10000010

2. The parity bits for the 5 rows is: 01001

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

4. The bit that was flipped in figure 2 is (10,0):

11000110 00000100 0
01111111 01110001 1
11000001 10101001 1
00000001 11011101 1
10101110 11110011 1
11010111 11010010 0

For figure 3, the bit that was flipped is (11,2):

01101111 10111101 0
00010000 11001101 0
00000111 00100101 1
11100111 00011110 0
10010100 10000000 0
00001011 11011011 1

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



That's incorrect

That's correct

The answer was: 0000100110000010

Question 1 of 5

The answer was: 01001

Question 2 of 5

The answer was: 0

Question 3 of 5

The answer was: 10,0

Question 4 of 5

The answer was: Yes

Question 5 of 5

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