2.2k views

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. $6$

edited | 2.2k views
0
0
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)???

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
0
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...
 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

by (41 points)