For the diagram immediately following write equation for the

For the diagram immediately following, write equation for the following: Write an equation for A(t + 1), i.e, . A at the next state. Write an equation foe B (t + 1), B at the next state. Complete the truth table far A and B at the next state in the table.

Solution

Basic Data to Solve :

Truth Table for Exclusive Or Gate :

A

B

Result

0

0

1

0

1

0

1

0

0

1

1

1

Truth Table D-Flip Flop

Q(t)

Q(t+1)

0

0

1

1

Truth Table D-Flip Flop

JK latch truth table

J

K

Q_next

Comment

0

0

Q

No change

0

1

0

Reset

1

0

1

Set

1

1

Q

Toggle

Explanation :

Question1 :

We are assuming clock pulse are applying at a time to all flipflops in ckt,now D flip lop produce same input as ouput and JK flip flop produce if input is 0 0 no change in output, if input is 0 1 then output is 0, if input is 1 0 out put is 1, if input is 1 1 then output is toggled.

Ex: if A=0,B=0,X=0 then D flipflop output (Anext state) is value of B and JK flipflop output (B next state) is produced with two inputs values exclusive –or function(Not B,A=>1,0) à 0 ,X(0).

D flipflop output 0,Jk flipflop output 0.

The process is continued for all input variable s below table obtained

A

B

X

Anext

Bnext

0

0

0

0

0

0

0

1

0

0

0

1

0

1

1

0

1

1

1

0

1

0

0

0

1

1

0

1

0

1

1

1

0

1

1

1

1

0

1

0

Finally Anext(A,B,X) =F(B) & Bnext (A,B,X)= A^ B X^ +A B^ X^ + A B^ X+A B X^

A	B	Result
0	0	1
0	1	0
1	0	0
1	1	1