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, Q_A , Q_B and Q_C :

image

if the state registers are initialised to state 0 0 0 , or

image

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 (D_A,D_B,D_C) are to be used and that unused states do not occur.

Q_A,Q_B,Q_C are outputs of flip flops D_A, D_B,D_C, respectively. State of the counter is written as (Q_A,Q_B,Q_C).

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

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

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

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

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

asked Jun 10 in Digital by gbeditor (44,560 points)
reshown Jun 12 by gbeditor

1 Answer

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Best answer

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_AQ_{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_BQ_{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_CQ_{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 deepak-gatebook (112,760 points)
Answer:
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