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GATE 2017 EC (EC2) – Question 55

Digital Circuits · Combinatorial Circuits · 2 marks · Multiple choice

A programmable logic array is shown. The Boolean function F implemented is

Diagram for GATE 2017 EC (EC2) question 55
  1. $\bar P\bar QR+\bar PQR+P\bar Q\bar R$
  2. $(\bar P+\bar Q+R)(\bar P+Q+R)(P+\bar Q+\bar R)$
  3. $\bar P\bar QR+\bar PQR+P\bar QR$
  4. $(\bar P+\bar Q+R)(\bar P+Q+R)(P+\bar Q+R)$

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Correct answer: (C) $\bar P\bar QR+\bar PQR+P\bar QR$

Explanation

Each marked intersection connects one literal to an AND-product row. Reading the rows from top to bottom gives $\bar P\bar QR$, $\bar PQR$ and $P\bar QR$.

The three AND outputs feed an OR gate, so the product terms are added:
$$F=\bar P\bar QR+\bar PQR+P\bar QR.$$
This is **C**. The product-of-sums options use the wrong gate structure, while A complements R incorrectly in the third term.

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