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33 votes
33 votes

Consider the circuit given below with initial state $Q_0=1, Q_1=Q_2=0$. The state of the circuit is given by the value $4Q_2+2Q_1+Q_0$

Which one of the following is correct state sequence of the circuit?

  1. $1, 3, 4, 6, 7, 5, 2$
  2. $1, 2, 5, 3, 7, 6, 4$
  3. $1, 2, 7, 3, 5, 6, 4$
  4. $1, 6, 5, 7, 2, 3, 4$
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7 Answers

Best answer
45 votes
45 votes
$$\begin{array}{|c|c|c|} \hline \mathbf{Q_0 = Q_{1prev}\oplus Q_{2prev}}& \mathbf{Q_1 = Q_{0prev}} &\mathbf {Q_2 = Q_{1prev}} \\\hline 1&  0& 0 \\ 0&1&0\\ 1& 0 & 1\\ 1&1 & 0\\ 1 & 1 & 1 \\0&1&1\\ 0&0&1 \\ 1&0&0\\\hline \end{array}$$State $= 4Q_2+ 2Q_1+Q_0$
So, state sequence $= 1, 2, 5, 3, 7, 6, 4$

Correct Answer: $B$
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5 votes
5 votes

The diagram of FF is: 

According to figure, we can write next state as: 

$Q_{0N}=Q_1 \oplus Q_2, Q_{1N}=Q_0,Q_{2N}=Q_1$

Transition table can be given as:

Q2 Q1 Q0 Q2N Q1N Q0N
0 0 0 0 0 0
0 0 1 0 1 0
0 1 0 1 0 1
0 1 1 1 1 1
1 0 0 0 0 1
1 0 1 0 1 1
1 1 0 1 0 0
1 1 1 1 1 0

$4Q_2 + 2Q_1+Q_0$ is simply the decimal equivalent of state. Now, transition diagram can be drawn from above table as:

Correct State Sequence: 1,2,5,3,7,6,4.

Option (B) is correct answer.

Answer:

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