Consider the following circuit involving three D-type flip-flops used in a…
2011
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
Attempted by 37 students.
Show answer & explanation
Correct answer: B
Approach: Determine the next-state for PQR on each clock by evaluating the combinational gates shown in the diagram using the current P,Q,R values. Then start from the reset state 000 and step through clock transitions until a previously seen state appears.
State transitions (starting from reset 000):
000 → 001
001 → 011
011 → 010
010 → 000
Conclusion: The circuit cycles through the four distinct states 000, 001, 011 and 010 and then returns to 000. Therefore the total number of distinct outputs represented by PQR produced by this counter is 4.
Tip for verification:
Make a two-column next-state table listing each current PQR and the resulting next PQR, obtaining the mapping for all eight combinations.
Starting from 000, follow the mapping until a repeat state is reached; the number of distinct states seen before repetition is the cycle length.
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