$1.$ Non$-$separable Cyclic Code:

$1)$ Design a combinatorial circuit that is capable of encoding four$-$bit information words

into non$-$separable cyclic code words using the generator polynomial

G$($X$)=1+$X$+$X$2$

$+$X$5$

$.$

$2)$ Show the resulting code word for the data word $($d$3$ d$2$ d$1$ d$0)=(1011).$