Question

If a data communication system uses the CRC method, the generator polynomial
G(x) = x^4 + x^3 + 1, and the destination node receives a binary bit sequence of 1101111101
(including the CRC check code). Please answer the following questions.
(1) What is the binary bit sequence corresponding to this generator polynomial?
(2) If the length of the received binary bit sequence is correct, what is the length of the
original binary bit sequence at the sender?
(3) Judging whether an error occurred during transmission? why?

Answer 1

1answer) Cyclic Redundancy Check:

Given Generated polynomial G(x)=x^4x^3+1

It can be written as G(x)=1.x^4 +1.x^3+0.x^2+ 0.x^1+1

The corresponding binary bit sequence of generated polynomial is G=1 1 0 0 1

2answer) Given length of the recieved binary bit is correct then the length of original bit sequence with out cyclic redundancy check codes is

L=length of the bit sequence at reciever side (including CRC Code) -(length of the generated polynomial -1)

L=10-(5-1)=10-4=6

Therefore length of original bit sequence at sender is 6

3) Answer for third question

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