GATE CSE 2011 | Question: 50

Question

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?

• A. $000$
• B. $001$
• C. $010$
• D. $011$

Answer 1

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 $=4.$

Comments

Here $D_3$ is wrongly written.

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I think there is an error at $D_3$ at $CLOCK =1$.

Given, $P,Q$ and $R$ have a value $0, 1$ and $0$ respectively.

$D_{1}= R = 0$

$D_{2}=$$\overline{(P+R)} = 1$

$D_{3} = Q$$\overline{R} = 1$

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This question has 2 sub parts and in both the subparts the 2^nd subpart has been answered. There is no answer provided for the 1^st question (which should have been over here)

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@vaibhavkedia968 you can see other answers also if you didn’t understood this one

and in best answer also the question is answered correctly

Answer 2

D_P = Q_R

D_Q = ( Q_P + Q_R )’

D_R = Q_Q (Q_R)’

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.

Answer 3

As simple as possible

Comments

is there any video link of this question??

Answer 4

option d) 011