A layer$-2$ device transmits the message bits $100100$ and it is protected from errors using the Cyclic redundancy check $($CRC$)$ polynomial x$3+$ x$2+1.$

$($a$)$ Use binary long division to illustrate the CRC bits that are transmitted to detect errors. $[2$ M$]$

$($b$)$ Suppose the fourth bit and the ninth from left of the codeword $($message $+$ CRC bits$)$ is inverted due to noise in the transmission link. What is the result of the receiver$$s syndrome calculation? How does the receiver know that an error has occurred