GATE CSE 2011 | Question: 51

Question

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?

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Comments

Refer - https://gateoverflow.in/2157/gate2011-50

---

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)???

Answer 1

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: $B$

Comments

how 000->010 ? i understood that R+(Next State of R) = Q(present State) * R'(previous State complement) but Q = 1 and R = 0

---

Q is not that in present state, that is last value at Q.

---

ok thank you...

---

does distinct number of states means distinct state present in loop?  what about state on 110 ->>001 this is also distinct state , including this would give answer as 5

Answer 2

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