GATE ECE 2018 | Question: 9

Question

A function $F(A, B, C)$ defined by three Boolean variables $\text{A, B and C}$ when expressed as sum of products is given by

$$F=\overline{A}\:.\overline{B}\:.\overline{C}+\overline{A}\:.B\:.\overline{C}+A\:.\overline{B}\:.\overline{C}$$

where, $\overline{A}\:,\overline{B}\:,and\:\overline{C}$ are the complements of the respective variables. The product of sums $\text{(POS)}$ form of the function $F$ is 

• A. $F=\left ( A +B+C\right ).\left ( A+\overline{B} + C\right ). \left ( \overline{A}+B+C \right )$
• B. $F=\left ( \overline{A} +\overline{B}+\overline{C}\right ).\left ( \overline{A} +B+ \overline{C}\right ). \left (A+ \overline{B}+\overline{C} \right )$
• C. $F=\left ( A +B+\overline{C}\right ).\left ( A+\overline{B} + \overline{C}\right ). \left (\overline{A}+ B+\overline{C} \right ).\left ( \overline{A}+\overline{B}+C\right ).\left ( \overline{A}+\overline{B} +\overline{C}\right )$
• D. $F=\left ( \overline{A}+\overline{B}+C\right ).\left (\overline{A} +B+ C\right ). \left (A+\overline{B}+ C \right ).\left (A+B+\overline{C}\right ).\left ( A+B+C \right )$

Answer 1

For any function $f,$ we can convert Canonical Sum of Product(CSOP) form to Canonical Product of Sum(CPOS) form by simply doing two things:

1. Change $\Sigma$ to $\Pi.$

&

2. Write the missing indexes of CSOP form.

Given function $F$ in the CSOP form = $\Sigma (0,2,4)$

So, function $F$ in CPOS form = $\Pi (1,3,5,6,7)$ which is same as Option C.

Conversion of "Sum of Minterms" to "Product of Maxterms"