

Transmitted message = 10001100 Received message = 11101100  VVVVVVVV Error polynomial = 01100000 
Error = ReceivedMsg XOR TransmittedMsg 

Error = ReceivedMsg XOR TransmittedMsg Therefore: Error % GP = (ReceivedMsg XOR TransmittedMsg) % GP (GP = Gen Poly) = (ReceivedMsg % GP) XOR (TransmittedMsg % GP) // TransmittedMsg % GP = 0 !!! = (ReceivedMsg % GP) XOR 0 = ReceivedMsg % GP 


ReceivedMsg % GenPolynome = Error % GenPolynome !!! 
Therefore:
if ( Error % GenPolynome ≠ 0000...0000 )
then: bit errors has been detected

In other words:

Generator polynomial: 1101 (Math. notation: 1×x^{3} + 1×x^{2} + 0×x^{1} + + 1×x^{0}) N = 4 (Generator polynomial has 4 terms, or bits in "1001") 