# Digital-Grand Test -Q12

+1 vote

A finite state machine (FSM) has the following sequence of states at the outputs of its D-type state registers, and if the state registers are initialised to state 0 0 0 , or if the state registers are initialised to state 1 1 1 .

Using the principles of synchronous design, we implement a counter having the state sequence  specified as above. Assume that D-type FlipFlops are to be used and that unused states do not occur.

are outputs of flip flops , respectively. State of the counter is written as

Which of the following is a correct set of minterms for the input of the flip flops?

(A).

(B).

(C).

(D). asked Jun 10 in Digital
reshown Jun 12

There is no need to solve this question a long way. The simple thing we can observe for a D-FF is that

So,  Just look at the column of Q(next) and find where it is 1. The corresponding value of  will be the minterm for D.

For   :

Just look at the column of  and find where it is 1. The corresponding value of  will be the minterm for  is 1 for  = 011 ; 101 ; 110 ; 111

So, minterms for  = (3,5,6,7)

For   :

Just look at the column of  and find where it is 1. The corresponding value of  will be the minterm for  is 1 for  = 001 ; 010 ; 101 ; 111

So, minterms for   = (1,2,5,7)

For   :

Just look at the column of  and find where it is 1. The corresponding value of  will be the minterm for  is 1 for  = 000 ; 010 ; 101 ; 110

So, minterms for   = (0,2,5,6) answered Jun 26 by (112,760 points)