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GATE 2021 EE – Question 47

Analog and Digital Electronics · VCOs and timers, combinatorial and sequential logic circuits, multiplexers, demultiplexers · 2 marks · Multiple choice

A counter is constructed with three D flip-flops. The input-output pairs are named $(D_0,Q_0)$, $(D_1,Q_1)$, and $(D_2,Q_2)$, where the subscript 0 denotes the least significant bit. The output sequence is desired to be the Gray-code sequence 000, 001, 011, 010, 110, 111, 101, and 100, repeating periodically. Note that the bits are listed in the $Q_2Q_1Q_0$ format. The combinational logic expression for $D_1$ is

  1. $Q_2Q_1\bar Q_0$
  2. $Q_2Q_0+Q_1\bar Q_0$
  3. $\bar Q_2Q_0+Q_1\bar Q_0$
  4. $Q_2Q_1+\bar Q_2\bar Q_1$

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Show answer and explanation

Correct answer: (C) $\bar Q_2Q_0+Q_1\bar Q_0$

Explanation

$D_1$ must equal the next value of $Q_1$. From the sequence, $Q_1$ becomes 1 after the states 001, 011, 010 and 110, and becomes 0 after 000, 111, 101 and 100. The expression $\bar Q_2Q_0+Q_1\bar Q_0$ is 1 for exactly 001, 011, 010 and 110.