Suppose you want to transmit the message $1011001001001011$ and protect it from

errors using the CRC$-8$ polynomial i$.$e$.$

x

$8+$ x$2+$ x$1+1$

i$)$ Use polynomial long division to determine the message that should be

transmitted.

ii$)$ Suppose the leftmost bit of the message is inverted due to noise on the

transmission link. What is the result of the receiver$$s CRC calculation? How

does the receiver know that an error has occurred?