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, $\dpi{100} Q_A , Q_B$ and $\dpi{100} Q_C :$

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 $\dpi{100} (D_A,D_B,D_C)$ are to be used and that unused states do not occur.

$\dpi{100} Q_A,Q_B,Q_C$ are outputs of flip flops $\dpi{100} D_A, D_B,D_C$, respectively. State of the counter is written as $\dpi{100} (Q_A,Q_B,Q_C).$

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

(A). $\dpi{100} D_A = \{ 3,5,6,7 \} , D_B = \{ 1,2,6,7 \} , D_C = \{ 0,2,5,6 \}$

(B). $\dpi{100} D_A = \{ 0,2,5,6 \} , D_B = \{ 1,2,5,7 \} , D_C = \{ 3,5,6,7 \}$

(C). $\dpi{100} D_A = \{ 3,5,6,7 \} , D_B = \{ 1,2,5,7 \} , D_C = \{ 0,2,5,6 \}$

(D). $\dpi{100} D_A = \{ 3,5,6,7 \} , D_B = \{ 1,2,5,7 \} , D_C = \{ 0,3,5,6 \}$

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

$D = Q_{next}$

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

For $D_A$  :

Just look at the column of $Q_{ANext}$ and find where it is 1. The corresponding value of $Q_AQ_BQ_C$ will be the minterm for $D_A$$Q_{ANext}$ is 1 for $Q_AQ_BQ_C$ = 011 ; 101 ; 110 ; 111

So, minterms for $D_A$ = (3,5,6,7)

For $D_B$  :

Just look at the column of $Q_{BNext}$ and find where it is 1. The corresponding value of $Q_AQ_BQ_C$ will be the minterm for $D_B$$Q_{BNext}$ is 1 for $Q_AQ_BQ_C$ = 001 ; 010 ; 101 ; 111

So, minterms for  $D_B$ = (1,2,5,7)

For $D_C$  :

Just look at the column of $Q_{CNext}$ and find where it is 1. The corresponding value of $Q_AQ_BQ_C$ will be the minterm for $D_C$$Q_{CNext}$ is 1 for $Q_AQ_BQ_C$ = 000 ; 010 ; 101 ; 110

So, minterms for  $D_C$ = (0,2,5,6)

answered Jun 26 by (112,760 points)