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GATE 2016 EE – Question 21

Analog and Digital Electronics · VCOs and timers, combinatorial and sequential logic circuits, multiplexers, demultiplexers · 1 mark · Multiple choice

Consider the following circuit which uses a 2-to-1 multiplexer as shown in the figure below. The Boolean expression for output F in terms of A and B is

A 2-to-1 multiplexer with select input B. Data input 0 is connected to $\bar{A}$ (A passed through an inverter), and data input 1 is connected to A. The output is F.
  1. $A \oplus B$
  2. $\overline{A + B}$
  3. $A + B$
  4. $\overline{A \oplus B}$

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Correct answer: (D) $\overline{A \oplus B}$

Explanation

The multiplexer outputs input 0 when $B = 0$ and input 1 when $B = 1$. So $F = \bar{B}\bar{A} + BA$. This is 1 when $A$ and $B$ are equal, which is the complement of the exclusive-OR, $\overline{A \oplus B}$.