Please do the diagrams using pen or pencil $($a$)$ Design a sequential circuit and state transition diagram with two $D$ flip$-$flops A and $B,$ and one input $06$

$x.$ When $x=0,$ the state of the circuit remains the same. When $x=1,$ the circuit goes through the state

transitions as $(00$:$10),(01$:$11),(10$:$01),(11$:$00),$ and repeats with output $y=\{1,0,1,1\}.[$CO$3]$

$($b$)$ Implement the function, $F={\displaystyle \underset{?}{\overset{?}{}}}(0,1,4,6,9,11,13,15)$ using $($i$)161$ MUX only $($ii$)81$ MUX only. $04$