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+14 votes
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Consider the following circuit involving three D-type flip-flops used in a certain type of counter configuration.

 

If at some instance prior to the occurrence of the clock edge, $P, Q$ and $R$ have a value $0$, $1$ and $0$ respectively, what shall be the value of $PQR$ after the clock edge?

  1. $000$
  2. $001$
  3. $010$
  4. $011$
asked in Digital Logic by Veteran (96.1k points)
edited by | 2.6k views

4 Answers

+20 votes
Best answer

Answer - D
As in D-flip-flop , next output is $Q^+=D$

  • $P_{i+1} = R_i$
  • $Q_{i+1} = (P_i + R_i)'$
  • $R_{i+1} = R_i'Q_i$

$$\begin{array}{|c|ccc|ccc|}\hline \textbf{CLOCK} & & \textbf{Inputs} &&&  \textbf{Outputs} \\\hline \text{} & \text{$D_{1}=R$} & \text{$D_{2}= $$\overline{(P+R)}$}& \text{$D_{3} = Q$$\overline{R}$}& \text{P}& \text{Q} & \text{R}\\\hline \text{1} & \text{0} & \text{1}& \text{0}& \text{0}& \text{1} & \text{0}\\\hline \text{2} & \text{0} & \text{1}& \text{1}& \text{0}& \text{1} & \text{1}\\\hline  \text{3} & \text{1} & \text{0}& \text{0}& \text{1}& \text{0} & \text{0}\\\hline   \text{4} & \text{0} & \text{0}& \text{0}& \text{0}& \text{0} & \text{0}\\\hline
5&0&1&0&0&1&0\\\hline
\end{array}$$
So, total number of distinct outputs $=4.$

answered by Loyal (8.7k points)
edited by
+4 votes

DP = QR

DQ = ( QP + QR )’

DR = QQ (QR)’

Characteristic Table:-

Input

Previous State

Next State

DP

DQ

DR

QP

QQ

QR

QPN

QQN

QRN

0

1

0

0

0

0

0

1

0

1

0

0

0

0

1

1

0

0

0

1

1

0

1

0

0

1

1

1

0

0

0

1

1

1

0

0

0

0

0

1

0

0

0

0

0

1

0

0

1

0

1

1

0

0

0

0

1

1

1

0

0

0

1

1

0

0

1

1

1

1

0

0

Thus the value of PQR after 010 is 011. Option D.

answered by (469 points)
edited by
+2 votes

As simple as possible

answered by Junior (667 points)
0 votes

option d) 011

answered by Junior (843 points)
Answer:

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