Q$.$ Design a BIST architecture for CUT shown in Fig. $1$ as per the following specifications;

$($a$)$ Use cellular automata as TPG whose cells follow Rule $150$

and $90$ as shown in Fig. $2$ and seed is $1110.$

$($b$)$ Use MISR with characteristic polynomial $x^4+x^3+x+1$ and determine the signature, if $fl$ is connected at input of first flipflop and $f2$ at second, using both tabular and division method.