Let us consider a CRC generator polynomial is given below:

$x^{32}+x^{26}+x^{23}+x^{22}+x^{16}+x^{12}+x^{11}+x^{10}+x^8+x^7+x^5+x^4+x^{\text{'}}$

Answer the following questions.

$($a$)$ How many single$-$bit errors can be detected by this generator polynomial? Please justify your answer.

$($b$)$ How many out of ${10}^{12}$ burst errors of size $33$ are left undetected. Provide the calculation.

$($c$)$ How many out of ${10}^{12}$ burst errors of size $56$ are left undetected. Provide the calculation.

$($d$)$ Is it capable of detecting a burst error of size $17?$ Justify your response.