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

$(15$ point$)$

$J_A=x,K_A=B$

$J_B=x,K_B=A^{\text{'}}$

a$)$ Derive the state equations $A_{t+1}$ and $B_{t+1}$ by substituting the input equations for the J and K variables.

b$)$ Draw the state diagram of the circuit.