Exercise $3.$ The following string of $7$ data bits is transmitted $($from left to right$)"1110111".$ A CRC is

attached at the end of the string during transmission. The CRC is computed using the generator polynomial

$g(D)=D^4+D^2+D+1.$

A$)$ Compute $c(D),$ defined as the remainder when $D^{4}s(D)$ is divided by $g(D),$ using modulo $2$ arithmetic,

where $s(D)$ is the polynomial representing the string of data bits. Write down the sequence of bits as they

are transmitted inclusive of CRC$,$ starting left with the first bit to be transmitted $[$pt$.10].$

B$)$ Assume that at the receiver the sequence of bits is affected by an error, described by $e(D)=D^{10}+D^3.$

Compute $r(D),$ defined as the remainder when $D^{3}s(D)+c(D)+e(D)$ is divided by $g(D),$ using modulo

$2$ arithmetic. Is the error detected by the receiver, and if so$,$ why $[$pt$.10]?$