I understand how to do the divisionand according to the teac

I understand how to do the division...and according to the teacher this is correct...what I don\'t understand is, on the equation on the left hand side, where do you get the EXTRA zeros that are not in the original data stream at the end of the stream. There are 24 binary 1s and 0s in the question but 27 in the actual equation..I\'m just referring to the equation that ends with the remainder of 100.

Solution

Message is augmented with n-1 bits where n is the length of the checksum polynomial because after each division steps we are left with n-1 bits (3 in this case) and that is left out from the quotient. To include that information in the quotient in order to check those bits of information too when the message is received, we artificially add n-1 0s (3 0s in this case) so that we are checking if the complete data is received and not neglecting any information.