Error correction data communication1 assignment 1.error detection techniques 2.polynomials

The answers are correct. And the further explanation is being given in explanation section.

Explanation:

1. In the first part, Checksum is being used. You should know one thing that the previous methods like checksum were able to detect the error only, and they were not able to correct the code. The error correction code and the first of them were being given by Hamming, and that was one bit. His work was given even better shape by greats like Shannon.

2. CRC is better than checksum, and in the second question, the CRC method is being used. Through the given polynomial we find the divisor by converting the polynomial to binomial representation. And since the CRC is of three bits, we add the three 0 to the right of the given binary number. And then we divide the resultant binary value by the divisor. The remainder is the CRC, and this is much like Checksum. And this remainder is added to the original binary value given to us. The final value plus the divisor is then sent to the destination. The receiver divides the data codeword by divisor, and if he gets the answer 000, then the receiver can believe that the code word he received is the correct one.

3. In the third question, the binomial value is to be converted to the polynomial. And for this, we check the power at which value is 1. And that power of x is added in the polynomial. Thus, we get the polynomial as can be seen.

And these are error detection codes. We have the error correction code as well.