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

If all the flip-flops were reset to $0$ at power on, what is the total number of distinct outputs (states) represented by $PQR$ generated by the counter?

  1. $3$
  2. $4$
  3. $5$
  4. $6$
in Digital Logic by Veteran (105k points)
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Is Number of distinct states means number of state present in the loop I.e 0-2-3-4-0?????but what about 001(output)???

2 Answers

+25 votes
Best answer
Characteristic equation of D FF is , $Q(t+1)=D$

So, $P^+ = R, \;\;Q^+=\overline{P+R},\;\;\text{and}\;R^+=Q.R'$

Sequence of states will be as:

${\begin{array}{|c|c|}\hline
\textbf{Clock Pulse}&    \textbf{PQR} \\\hline
\text{Initially}&000 \\\hline 1&010 \\ \hline    2&011 \\ \hline   3&100 \\ \hline   4&000 \\ \hline   
 \end{array}}$

$4$ is the number of distinct states.

Correct Answer: $B$
by Veteran (57k points)
edited by
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how 000->010 ? i understood that R+(Next State of R) = Q(present State) * R'(previous State complement) but Q = 1 and R = 0
+1
Q is not that in present state, that is last value at Q.
0
ok thank you...
+3 votes
Initial State Final State
Qp Qq Qr Qpn Qqn Qrn
0 0 0  0 1 0
0 0 1 1 0 0
0 1 0 0 1 1
0 1 1 1 0 0
1 0 0  0 0 0 
1 0 1  1 0 0
1 1 0 0 0 1
1 1 1 1 0 0

if we draw the state diagram from this we'll get 

0 --> 2 --> 3 --> 4 --> 0

which represents a mod 4 counter, hence the total number of distinct output states = 4

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