Consider using CRC with the degree$-5$ binary polynomial $1$ to encode a $10-$bit

information pattern $1000001101$ where the leftmost bit represents the binary coefficient of the

highest$-$degree term of the data polynomial.

a$.(2$ points$)$ Find the corresponding data polynomial, and the encoded CRC polynomial and

codeword.

b$.(2$ points$)$ If the CRC codeword in a$.$ is contaminated with an error pattern expressed as $$

$,$ can the above CRC coding scheme detect the erroneous data? Justify your answer.

c$.(2$ points$)$ Repeat b with an error pattern expressed as $.$