Consider the data sequence $1-0010-1010,$ and the generator $($divisor$)$ polynomial $()=$

$4+$

$2+$

$1.$

a$)(8$ points$)$ Use long division to compute the corresponding CRC and specify the transmitted frame

$().$

b$)(4$ points$)$ Construct the corresponding shift register for the given generator $($divisor$)$ pattern P$.$

c$)(4$ points$)$ Are ALL single bit errors detectable? Why or why not?

d$)(4$ points$)$ Assume a $2-$bit error pattern given by $()=$

$6+1.$ Is this pattern detectable? Why

or why not?