The GATE Grind

GATE 2024 IN – Question 16

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

The simplified form of the Boolean function $F=(A+\bar A B)+\bar A(A+\bar B)C$ is

  1. $A+B+C$
  2. $ABC$
  3. $B+\bar A C$
  4. $\bar A+BC$

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Show answer and explanation

Correct answer: (A) $A+B+C$

Explanation

Use $A+\bar A B=A+B$ and $\bar A(A+\bar B)C=\bar A\bar B C$.

Hence $F=A+B+\bar A\bar B C$. With $X=A+B$, this is $X+\bar X C=X+C=A+B+C$.

Answer: **A**.