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GATE 2024 EE Q.25: solution and answer

GATE 2024 · EEQ.25 · 1 mark · MCQ

In the circuit, the present value of is 1. Neglecting the delay in the combinatorial circuit, the values of and , respectively, after the application of the clock will be

GATE 2024 EE question 25: A combinatorial circuit block labelled S = X Y Z has three inputs: Z (top, fed back), X = 1 (middle) and Y = 0 (bottom).Tap to open full size
Figure from the GATE 2024 EE paper. It is part of the question.
Figure description

A combinatorial circuit block labelled S = X Y Z has three inputs: Z (top, fed back), X = 1 (middle) and Y = 0 (bottom). Its output S drives the D input of a D flip-flop, whose clock input is marked 'Clock' with an edge-trigger triangle. The flip-flop's Q output is labelled Z; a feedback wire runs from Q over the top of the diagram back to the Z input of the combinatorial circuit. The Q output is drawn but not connected to anything. Labels under the blocks: 'Combinatorial Circuit' and 'D Flip-flop'.

  1. (A)

  2. (B)

  3. (C)

  4. (D)

Answer and solution

ANSWER

After the clock, becomes and the combinational output becomes . The answer is option (C): .

Official answer: CSource: Official answer key, GATE 2024 EE (IISc Bengaluru)

  1. Before the clock edge, the combinational circuit works from the present state : . So just before the clock.

  2. A D flip-flop's characteristic equation is . On the clock edge it stores , so the next state is .

  3. The combinational circuit has no delay, so updates at once from the new state: .

  4. So after the clock, and , which is option (C). (With , the circuit is a toggle: , where the overline means complement, so flips on every clock edge.)

KEY IDEA

A D flip-flop latches the value at on the clock edge (). Here is computed from the present state . Because the combinational circuit has no delay, is then recomputed straight away from the new . With , (overline = complement), so the circuit toggles .

WATCH OUT FOR

Reporting the value of from before the clock () together with the new , which gives option (A). The question asks for both values after the clock. Once changes to , the delay-free combinational circuit makes immediately.

From the GATE 2024 EE paper. Every question of this paper · Download the full paper · All 30 Sequential questions, with notes

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