$(5$pt$)$ Circuit Design

A$.$ Make a sequential state assignment for the circuit using $3-$bit codes for the six states using sequential assignment $(1$pt$).$

B$.$ Find the state table $($use $S_2{S}_1{S}_0$ as current states, $x$ as input, $D_2{D}_1{D}_0$ as next states$)(2$pt$).$

C$.$ Write down the sum$-$of$-$minterm for $D_2{D}_1{D}_0,$ as well as don't care condition $d,$ then optimise $D_0$ using K$-$map $(2$pt$).$