Calculate the parity of a byte with the value 29_ten and show the pattern stored to memory.

________________ ___

Original 8 bits Parity

Bit

(5 pts) Consider the following 9-bit string: 1001 0110 1 that is one byte followed by an even parity bit. Is an error indicated? _____ Yes _____ No.

(5 pts) What if the original byte the user was trying to transmit was 0000 0001. He calculated the parity as 1, and sent 0000 0001 1. But the data was corrupted, and what we received was very different: 1001 0111 1. Four bits are flipped!

Does our parity think theres an error? _____ Yes _____ No.

Can you generalize when this parity scheme will fail to identify a corrupted string?

We present next a variation on Figure 5.24. In the book, they use Xs to indicate the bits that each parity bit will use in its XOR calculation. We need to insert our data into those fields, so the Xs are in the way. So weve flipped the table to have blanks where we want data, and grey out where do not. We also need a place to write in our calculations for the parity bits, and a place to add up the total!

With those changes, fill in the following table as follows:

First write the 12-bit data into the Input String row. Use the following input:

0110 1011 1010

Copy the bit in each column from the Input String row into every cell in that column thats blank in the bottom half of the table.

Calculate the even parity of each row and place a 1 or 0 as needed in the parity bit coverage cell (on the far left of each row).

Total the parity values and record the result in the Total.

Bit position

1

2

3

4

5

6

7

8

9

10

11

12

Input String

Encoded data bits

p1

p2

d1

p4

d2

d3

d4

p8

d5

d6

d7

d8

Parity bit coverage

p1

p2

p4

p8

Total:

The total indicates which bit if any is in error. Make the needed corrections and report the final output:

Corrected 12-bit string: ___________ ___________ ___________ (shown as 3 groups of 4 bits for clarity)

Corrected 8-bit data: ___________ ___________