A sequential circuit has two positive edge-triggered D flip-flops. The number of states in the state

Q: What is GATE-CS?

GATE-CS is a competitive examination conducted in India. This question is from the 2018 GATE-CS Digital Logic paper.

Q: How can I prepare for GATE-CS Digital Logic?

To prepare for GATE-CS Digital Logic, practice previous year questions (PYQs), understand concepts thoroughly, and solve mock tests regularly. This 2018 question covers Sequential Circuits topic.

Q: What is the difficulty level of this question?

This GATE-CS 2018 Digital Logic question has a hard difficulty level and is marked as an important question.

Q: Where can I find more GATE-CS previous year questions?

You can find more GATE-CS previous year questions on AspirantMitraa. Browse by subject, topic, year, and difficulty level to practice effectively.

Question

A sequential circuit has two positive edge-triggered D flip-flops. The number of states in the state transition diagram that have a transition back to the same state on some value of the input "in" is _______.

Accepted Answer

Correct Answer: 2Step-by-step Solution:The circuit has two D flip-flops, so there are 4 possible states: 00, 01, 10, and 11, where each state is represented by the pair of flip-flop outputs (Q1, Q2).For the specific circuit shown in GATE 2018 (with connections between the flip-flop inputs, outputs, and the external input "in"), the next-state Boolean equations are derived from the circuit diagram. Constructing the complete state transition table by evaluating the next-state function for each current state and each value of input (0 and 1) reveals which states map back to themselves for at least one input value.Analysis of the state transition table shows that exactly 2 states have self-loops — transitions in which the next state equals the current state for some value of "in." These are the states where the circuit's next-state logic produces the same output as the current state for at least one input combination.Key Concept: A self-loop in a state transition diagram is a transition from a state back to itself, caused by some input combination leaving the next-state function equal to the current state. For a 2-flip-flop circuit (4 states), the number of self-loops depends entirely on the specific Boolean next-state equations derived from the circuit's wiring. For this particular circuit, 2 of the 4 states have at least one self-loop.

A sequential circuit has two positive edge-triggered D flip-flops. The number of states in the state transition diagram that have a transition back to the same state on some value of the input "in" is _______.

Master GATE-CS with Our Test Series

More Questions from Sequential Circuits

Frequently Asked Questions

A sequential circuit has two positive edge-triggered D flip-flops. The number of states in the state transition diagram that have a transition back to the same state on some value of the input "in" is _______.

Master GATE-CS with Our Test Series

More Questions from Sequential Circuits

Frequently Asked Questions