$(10-$point$)$ A sequential circuit has two JK flip$-$flops A and B and one input x $.$ The circuit is described by the following flip$-$flop input equations:

$J_A\frac{?}{b}=ar(A),K_A=B$

$J_B=Ao+x,K_B=B\stackrel{}{x}$

a$)$ Derive state table

b$)$ Derive the state equations $A(t+1)$ and $B(t+1)$ by substituting the input equations for the J and K variables.

c$)$ Design a sequential ckt using JK flipflop

d$)$ Draw the state diagram of the circuit