$15$ Points$)$ Consider the following state table.

Present Next State Output

State X $=0$ X $=1$ Z

A B F $1$

B D E $0$

C B D $1$

D F A $0$

E F A $1$

F D C $0$

$($a$)$ Reduce the state table to a minimum number of states using implication

charts.

$($b$)$ Realize the table using D Flip$-$flops $($please assign binary numbers to the

states in the order of the alphabet, i$.$e$.$ reduced states: A$,$C$,$D$,$E$,$ then A$=00,$

C$=01,$ D$=10,$ E$=11).$

$($c$)$ Realize the table using JK Flip$-$flops $($please assign binary numbers to the

states in the order of the alphabet, i$.$e$.$ reduced states: A$,$C$,$D$,$E$,$ then A$=00,$

C$=01,$ D$=10,$ E$=11)$