GATE 2016 EE (EE2) – Question 36
Analog and Digital Electronics · VCOs and timers, combinatorial and sequential logic circuits, multiplexers, demultiplexers · 2 marks · Multiple choice
The Boolean expression $\overline{(a+\bar b+c+\bar d)+(b+\bar c)}$ simplifies to
- $1$
- $\overline{ab}$
- $ab$
- $0$
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Show answer and explanation
Correct answer: (D) $0$
Explanation
The sum inside the outer complement includes both b and its complement b̄. Therefore its value is one for every input, by b+b̄=1.
It also includes c+c̄=1, providing the same conclusion independently. Complementing that constant one yields **0, D**.
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