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GATE 2019 EE – Question 45

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

The output expression for the Karnaugh map shown below is

Diagram for GATE 2019 EE question 45
  1. $Q\bar R+S$
  2. $Q\bar R+\bar S$
  3. $QR+S$
  4. $Q\bar R+\bar S$

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Show answer and explanation

Correct answer: (A) $Q\bar R+S$

Explanation

The rows $RS=01$ and $RS=11$ are all ones, which gives the term $S$. In the row $RS=00$ the ones are in the columns $PQ=01$ and $11$, i.e. $Q=1$, and there $R=0$, which gives $Q\bar R$. The row $RS=10$ is all zeros. So $F=S+Q\bar R$.