Question

A sequential circuit has two JK flip-flops A and B, two inputs r and y, and one output z. The flip-flop input equations and circuit output equation are 

\(\begin{aligned} J_{A} &=A^{\prime} x+B^{\prime} y & K_{A}=B x^{\prime} y^{\prime} \\ J_{B} &=A^{\prime} x y & K_{B}=A^{\prime}+B^{\prime} x \\ z &=A^{\prime} x^{\prime}+B^{\prime} y^{\prime} & \end{aligned}\)

(a) Derive the simplified state equations for A and B. 

(b) Tabulate the state table. 

(c) Draw the state diagram of the çircuit.

Answer 1

(a) Simplified state equations for A and B.

first consider the characteristic equation of any flip-flop:

where Q(t+1) is the next state and Q(t) is current state.

so,

where left hand side A is the next A and right hand side A is current A.

again for B

(b) state table:

A	B	x	y	A	B	J(A)	K(A)	J(B)	K(B)	Z
0	0	0	0	0	0	0	0	0	1	1
0	0	0	1	1	0	1	0	0	1	1
0	0	1	0	1	0	1	0	0	1	1
0	0	1	1	1	1	1	0	1	1	0
0	1	0	0	0	0	0	1	0	1	1
0	1	0	1	0	0	0	0	0	1	1
0	1	1	0	1	0	1	0	0	1	0
0	1	1	1	1	0	1	0	1	1	0
1	0	0	0	1	0	0	0	0	0	1
1	0	0	1	1	0	1	0	0	0	0
1	0	1	0	1	0	1	0	0	1	1
1	0	1	1	1	0	1	0	0	1	0
1	1	0	0	0	1	0	1	0	0	0
1	1	0	1	1	1	0	0	0	0	0
1	1	1	0	1	1	1	0	0	0	0
1	1	1	1	1	1	1	0	0	0	0

(c)

state diagram: