given message is 0111
So here
m1 = 0
m2 = 1
m3 = 1
m4 = 1
a).
Number of parity bits = Total bits - message bits = 7- 4 = 3
b).
1 | 2 | 3 | 4 | 5 | 6 | 7 |
P1 | P2 | m1 | P3 | m2 | m3 | m4 |
P1 | P2 | 0 | P3 | 1 | 1 | 1 |
Now we will calculate the even parity using Exclusive - OR
P1 --> 1,3,5,7 --> P1 0 1 1 --> 0 0 1 1 ----> P1 = 0
P2 --> 2,3,6,7 --> P2 0 1 1 --> 0 0 1 1 ----> P2 = 0
P3 --> 4,5,6,7 --> P3 1 1 1 --> 1 1 1 1 ----> P3 = 1
c).
from the above step we have parity bits P1 = 0, P2 = 0, P3 = 1
So, the final message bits with parity bits is 0001111
d).
To identify that the received message has error calculate decimal value of P3P2 P1 = (100)2 = 4
The 4th bit has error
So, to correct the final message invert the 4th bit
So, now the final message becomes 0000111
e).
Here we are asked to find out error position by injecting(Inverting the 3rd position of initial message )
So, now we have to repeat the steps above again.
Step1:
1 | 2 | 3 | 4 | 5 | 6 | 7 |
P1 | P2 | m1 | P3 | m2 | m3 | m4 |
P1 | P2 | 1 | P3 | 1 | 1 | 1 |
Now we will calculate the even parity using Exclusive - OR
P1 --> 1,3,5,7 --> P1 1 1 1 --> 1 1 1 1 ----> P1 = 1
P2 --> 2,3,6,7 --> P2 1 1 1 --> 1 1 1 1 ----> P2 = 1
P3 --> 4,5,6,7 --> P3 1 1 1 --> 1 1 1 1 ----> P3 = 1
P3P2P1 = 1 1 1 = 7
Therefore the 7th bit has error
Question 2. Using the Hamming code algorithm (7,4), convert a data message (0111) using 7bit. a)...
ASAP Computer Architecture and Organization CSC 264 all questions Question 1. Write a note on general-purpose and special-purpose computers. Briefly explain logic gates and various gates used in digital logic design. Explain how data is represented in a digital computer and state how the signed binary numbers are represented. Using the Hamming code algorithm (7, 4), convert a data message (0110) using 7bit. Find the number of parity bits needed Evaluate the values of parity bits Final message bits with...
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Hamming Code: m = 1010 (4-bit message); odd-parity scheme; Compute Hamming Code on the sender’s side. On the receiver’s side, detect and verify a 7th bit error-position in the transmitted data.
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A Hamming code is a technique where errors can not only be detected but can also be corrected. The simplest example of this kind of code is the (7,4)-Hamming code. In this scheme, a codeword is 7 bits long. We number the positions as follows: 1 2 3 4 5 6 7 The message that is sent is only four bits long, with these four bits occupying positions 3, 5, 6, and 7. Bits 1, 2, and 4 are...
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