Calculate the parity of a byte with the value 29 ten and show the pattern stored
ID: 3873081 • Letter: C
Question
Calculate the parity of a byte with the value 29ten 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 there’s 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 “X”s 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 “X”s are in the way. So we’ve 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 that’s 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: ___________ ___________
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:
Explanation / Answer
1) 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.??
A: For even parity the number of 1's in the string must be even . The number of 1's=5
so Yes it indicates an error
2)
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 there’s an error? _____ Yes _____ No.
Can you generalize when this parity scheme will fail to identify a corrupted string?
A. a)The parity bit calculated for data 0000 0001 was 1 so it means even parity is to be maintained.
The corrupted string received is 1001 0111 1
For even parity the number of 1's in the string must be even . The number of 1's=6
so NO it indicates an error
b) in general if even number of bits are flipped ,parity scheme fails to identify error
3)
A This is hamming code.The the boxes are not greyed out in the question you posted but i know what to do exactly.
Calculate the even parity of each row and place a 1 or 0 as needed in the parity bit coverage cell
bit position: 1 2 3 4 5 6 7 8 9 10 11 12
input: 0 1 1 0 1 0 1 1 1 0 1 0
encoded: p1 p2 d1 p4 d2 d3 d4 p8 d5 d6 d7 d8
pariy bit
p1=1 0 1 1 1 1 1
p2 =0 1 1 0 1 0 1
p4= 0 0 1 0 1 0
p8=1 1 1 0 1 0
p8 p4 p2 p1
total: 1 0 0 1= 9 in binary
so the 9th bit is in error so flip it
Corrected 12-bit string
0110 1011 0010
(shown as 3 groups of 4 bits for clarity)
Corrected 8-bit data: extracting all the data bits from the 12 bit string
1 101 0010
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