digital logic

Question

An AB flip flop is constructed from a JK flip flop as shown in the figure. The expression for the next state Q_{n + 1} is

Comments

Q_n+1 = JQ' + K'Q

= (A'+B')Q' + B'Q

= A'Q' + B'

Answer 1

A	B	J	K	Q(n+1)
0	0	1	1	1
0	1	1	Qn	Qn'
1	0	1	1	1
1	1	0	0	0

Q(n+1) = A'B' + AB' + A'BQn'

              = B' + A'BQn'

              = B' + A'Qn'   -------(Answer)

Answer 2

For J-K flip flop, Q next is

Qn +1 = JQ' + K'Q

 

Where J = A' + B'

              K = B

Qn + 1 =(A' + B')Q' + B'Q

            = A'Q' + B'Q' +B'Q

           =  A'Q' + B'