Andrew S. Tanenbaum Edition 5th Exercise 3 Question 17 (Page No. 253)

Question

A bit stream 10011101 is transmitted using the standard CRC method described in the
text. The generator polynomial is x 3 + 1. Show the actual bit string transmitted. Suppose
that the third bit from the left is inverted during transmission. Show that this
error is detected at the receiver’s end. Give an example of bit errors in the bit string
transmitted that will not be detected by the receiver.

Answer 1

Generator polynomial=$x^3+1=1*x^3+0*x^2+0*x^1+1*x^0$=1001

So we've to append three 0s at the end of message

Message transmitted=10011101100

The 3rd bit from left gets inverted. So receiver receives 10111101100

[both sender and receiver agrees on generating polynomial]

non-zero remainder indicates error