GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 30

Question

Consider the function $f\left(x_1, x_2, x_3\right)=x_1 \cdot x_2 \cdot x_3+\bar{x}_1 \cdot \bar{x}_2 \cdot \bar{x}_3+\bar{x}_1 \cdot x_2 \cdot \bar{x}_3+\bar{x}_1 \cdot x_2 \cdot x_3$, what is the product of sum(POS) expression for this function?

• A. $f\left(x_1, x_2, x_3\right)=\left(x_1+x_2+x_3\right) \cdot\left(\bar{x}_1+\bar{x}_2+\bar{x}_3\right) \cdot\left(\bar{x}_1+x_2+\bar{x}_3\right) \cdot\left(\bar{x}_1+x_2+x_3\right)$
• B. $f\left(x_1, x_2, x_3\right)=\left(\bar{x}_1+\bar{x}_2+\bar{x}_3\right) \cdot\left(x_1+x_2+x_3\right) \cdot\left(x_1+\bar{x}_2+x_3\right) \cdot\left(x_1+\bar{x}_2+\bar{x}_3\right)$
• C. $f\left(x_1, x_2, x_3\right)=\left(x_1+x_2+\bar{x}_3\right) \cdot\left(\bar{x}_1+x_2+x_3\right) \cdot\left(\bar{x}_1+x_2+\bar{x}_3\right) \cdot\left(\bar{x}_1+\bar{x}_2+x_3\right)$
• D. $f\left(x_1, x_2, x_3\right)=\left(\bar{x}_1+x_2+\bar{x}_3\right) \cdot\left(\bar{x}_1+x_2+x_3\right) \cdot\left(x_1+\bar{x}_2+\bar{x}_3\right) \cdot\left(\bar{x}_1+\bar{x}_2+x_3\right)$

Answer 1

The given function is in SOP Form with 111,000,010,011 as min terms ie $\sum_{}^{} m(7,0,2,3)$

The max terms will be $\prod_{}^{}(1,4,5,6)$ => 001,100,101,110 => $(x+y+\overline{z})(\overline{x}+y+z)(\overline{x}+y+\overline{z})(\overline{x}+\overline{y}+z)$