$4$b$)$ A $6-$bit CRC is used in the original DS$1$ signal. The $6-$bit CRC allows the detection of any burst error of $6$ bits

or less in length. It detects large random errors with a probability of $1-2^{-6}.$

The ITU standard CRC$-6$ generator polynomial is $x^6+x+1,$ corresponding to the bit sequence $1000011.$

Determine the check sequence for the input $10110001$