Problem $3(20$ points$)$

Consider the data sequence $1-0010-1010,$ and the generator $($divisor$)$ polynomial $P(x)=x^4+x^2+$

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

$Tt(x).$

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 $E(x)=x^6+1.$ Is this pattern detectable? Why

or why not?