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+18 votes
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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. $1, 6, 5, 7, 2, 3, 4$
asked in Digital Logic by Veteran (52k points)
edited by | 2.5k views

3 Answers

+32 votes
Best answer
$$\begin{array}{|c|c|c|} \hline \mathbf{Q_0 = Q_{1prev}\oplus Q_{2prev}}& \mathbf{Q_1 = Q_{0prev}} &\mathbf {Q_2 = Q_{1prev}} \\\hline 1&  0& 0 \\ 0&1&0\\ 1& 0 & 1\\ 1&1 & 0\\ 1 & 1 & 1 \\0&1&1\\ 0&0&1 \\ 1&0&0\\\hline \end{array}$$

State $= 4Q_2+ 2Q_1+Q_0$
So, state sequence $= 1, 2, 5, 3, 7, 6, 4$

Correct Answer: $B$
answered by Veteran (408k points)
edited by
0
How to get this table ??
0
Table is from the figure. I have now added the formula for each column.
0
Thnx .
0
what is the significance of state eq. ?? in this question ??
0
what does state equation represent ?
0

I got the table, but didn't get this 4Q2 + 2Q1+Q0.

0
it is decimal equivalent of binary state.
+1

sir i didnt understand how u apply 4Q2 + 2Q1+Q0 to column please explain .....till the table i understood .....

+11
$Q_0Q_1Q_2 = 100,\;\; \text{state =}\;4\times 0+2\times 0+ 1 = 1$
0
It represents the initial state...I think
+1
4Q2 + 2Q1+Q0 WHT IS THE USE OF THIS
+1
it represents the lsb as q0 and msb as q2 , no other significance
0
Use of equation is to distinguish between LSB and MSB.
0
4Q2 + 2Q1+Q0 is just to tell us which is MSB and which is LSB.

I hope it helps.
0
@everyone from which topic this question belongs too.

I have no clue about this.

Please help me with the prerequisites needed for this topic.
+1
Jeet,  it is counter in digital logic, in prerequisites, you must know Flip-flops, behavior, characteristic equations and excitation table.
0
Thanks a lot, Sir.
+8 votes

answer - B

Q0n = Q1n-1 exor Q2n-1

Q1n = Q0n-1

Q2n = Q1n-1

answered by Loyal (8.7k points)
+1 vote

option (B)

answered by Junior (851 points)
0
How did u get that present states of q0,q1,q2
0
3 bits maximum 8 possible values (2^3) and initially I started with the given condition in question.
Answer:

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