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A computer network uses polynomial over GF(2) for error checking with 8 bits as information bits and uses x3 + x + 1 as the generator polynomial to generate the check bits.
In this network, the message 01011011 is transmitted as
In this network, the message 01011011 is transmitted as
- a)01011011010
- b)01011011011
- c)01011011101
- d)01011011100
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A computer network uses polynomial over GF(2) for error checking with ...
We add (n-1) 0’s to the LSB of dividend(message) and divided by given GF
The remainder will be CRC, it will be added to the LSB of the original message, that should be transmitted to the receiver. That is: 01011011101.
Most Upvoted Answer
A computer network uses polynomial over GF(2) for error checking with ...
Error Checking with Polynomial over GF(2)
To understand why option 'C' is the correct answer, let's break down the steps involved in error checking using polynomial over GF(2).
Generator Polynomial:
The generator polynomial given is x^3 + x + 1. This means that the check bits will be generated by dividing the information bits with this polynomial.
Message Transmission:
The message that is transmitted is 01011011. To generate the check bits, we need to append enough zeros to the message to accommodate the check bits. In this case, since the generator polynomial is of degree 3, we append 3 zeros to the message.
So the message becomes: 01011011000
Division:
Now we perform polynomial division on the message using the generator polynomial. We divide the message by the generator polynomial, treating all the bits as coefficients of polynomials over GF(2).
The division process involves XOR operations. We start by aligning the most significant bit of the generator polynomial with the most significant bit of the message.
```
0011
------------------
001101101000 | 01011011000
0011
------
011
0011
----
0101
0011
----
0101
0011
----
0110
0011
----
110
0011
----
101
0011
----
10
```
Check Bits:
After the division is complete, the remainder obtained is the check bits. In this case, the remainder obtained is 10.
Final Transmission:
To complete the transmission, we append the check bits to the original message.
So the final transmitted message is: 01011011101
Conclusion:
Based on the steps mentioned above, it is clear that option 'C' (01011011101) is the correct answer as it follows the process of error checking using the given generator polynomial.
To understand why option 'C' is the correct answer, let's break down the steps involved in error checking using polynomial over GF(2).
Generator Polynomial:
The generator polynomial given is x^3 + x + 1. This means that the check bits will be generated by dividing the information bits with this polynomial.
Message Transmission:
The message that is transmitted is 01011011. To generate the check bits, we need to append enough zeros to the message to accommodate the check bits. In this case, since the generator polynomial is of degree 3, we append 3 zeros to the message.
So the message becomes: 01011011000
Division:
Now we perform polynomial division on the message using the generator polynomial. We divide the message by the generator polynomial, treating all the bits as coefficients of polynomials over GF(2).
The division process involves XOR operations. We start by aligning the most significant bit of the generator polynomial with the most significant bit of the message.
```
0011
------------------
001101101000 | 01011011000
0011
------
011
0011
----
0101
0011
----
0101
0011
----
0110
0011
----
110
0011
----
101
0011
----
10
```
Check Bits:
After the division is complete, the remainder obtained is the check bits. In this case, the remainder obtained is 10.
Final Transmission:
To complete the transmission, we append the check bits to the original message.
So the final transmitted message is: 01011011101
Conclusion:
Based on the steps mentioned above, it is clear that option 'C' (01011011101) is the correct answer as it follows the process of error checking using the given generator polynomial.
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A computer network uses polynomial over GF(2) for error checking with 8 bits as information bits and uses x3+ x + 1 as the generator polynomial to generate the check bits.In this network, the message 01011011 is transmitted asa)01011011010b)01011011011c)01011011101d)01011011100Correct answer is option 'C'. Can you explain this answer?
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