If the Generator Polynomial is 1001, What is the 3-bit CRC for the Message 1100 1001?

What is the 3-bit CRC that will be appended at the end of the message 1100 1001 with a generator polynomial of 1001?

The 3-bit CRC that will be appended at the end of the message 1100 1001 with a generator polynomial of 1001 is 101.

Understanding CRC and Generator Polynomial

CRC (Cyclic Redundancy Check) is an error-detecting code widely used in digital communication systems to identify errors in data transmission. The CRC code is generated based on a generator polynomial and is attached to the message to check for errors during transmission. In this specific case, the message is 1100 1001 and the generator polynomial is 1001. Let's calculate the 3-bit CRC that will be appended to the message: 1. Divide the message by the generator polynomial: 
                    1 0 0 1 ) 1 1 0 0 1 0 0 1 0 0 0
                    1 0 0 1
                    -----
                    1 1 0 0
                    1 0 0 1
                    -----
                        1 1 1 0
                        1 0 0 1
                        -----
                            1 1 1
                            1 0 0 1
                            -----
                                1 0 1
The remainder after dividing is 101, which is the 3-bit CRC that will be appended to the message 1100 1001.
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