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GATE 2017 EE – Question 23

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

The Boolean expression $AB + A\bar{C} + BC$ simplifies to

  1. $BC + A\bar{C}$
  2. $AB + A\bar{C} + B$
  3. $AB + A\bar{C}$
  4. $AB + BC$

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Show answer and explanation

Correct answer: (A) $BC + A\bar{C}$

Explanation

By the consensus theorem, $AB$ is the consensus of $BC$ and $A\bar{C}$, so it is redundant. Check with minterms: $AB + A\bar{C} + BC$ is true for 100, 110, 111 and 011, and $BC + A\bar{C}$ is true for exactly the same four cases. So the expression simplifies to $BC + A\bar{C}$.