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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. $011$
edited | 2.6k views

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 $=4.$

edited

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.

edited by

As simple as possible  option d) 011

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