Question $2$: $[20$ pts$.]$

a$)$ Analyse the following combinational circuit deriving the truth table and the simplified boolean functions of outputs $F$ and $G$ in terms of input variables.

a$)$ Using $D$ flip$-$flops, construct a $4-$bit ripple counter that counts downward as follows: $(..11,10,9,8,7,6,5,4,3,11,10,9,$dots.