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GATE 2022 IN – Question 23

Digital Electronics · Number systems and combinational logic · 1 mark · Multiple select

The output $F$ of the digital circuit shown can be written in the form(s) ______.

Diagram for GATE 2022 IN question 23
  1. $\overline{AB}$
  2. $\bar A+\bar B$
  3. $\overline{A+B}$
  4. $\bar A\bar B$

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Show answer and explanation

Correct answer: (A) $\overline{AB}$; (B) $\bar A+\bar B$

Explanation

The first multiplexer selects 1 for B=0 and 0 for B=1, yielding Bbar. The second outputs 1 for A=0 and Bbar for A=1: F=Abar+ABbar=Abar+Bbar=NOT(AB).

Thus **A,B** are equivalent expressions.