NIMCET 2018 Question Paper with solutions

Karnaugh Map is used to simplify Boolean algebra expressions.
It is a graphical technique of simplifying Boolean expressions.
It is also known as K-map.
K-map contains two types of methods:
1. SOP (Sum Of Product): This produces logical expressions that contain OR of multiple AND terms.
Example: $\overline{\mathit{b}}\cdot \overline{\mathit{d}}+\overline{\mathit{d}}\cdot \overline{\mathit{c}}$
2. POS (Product Of Sum): This produces logical expressions that contain AND of multiple OR terms.
Example: $\left(\overline{\mathit{b}}+\overline{\mathit{d}}\right)\left(\overline{\mathit{d}}+\overline{\mathit{c}}\right)$
Explaination:
The first quad will form from the K-map:
$\left(\mathit{a}\mathit{b}-00,10,\mathit{c}\mathit{d}-00,10\right)$
Value is: $\overline{\mathit{b}}\cdot \overline{\mathit{d}}$
The second quad will form from the K-map:
$\left(\mathit{a}\mathit{b}-00,10,\mathit{c}\mathit{d}-00,01\right)$
Value is $\overline{\mathit{c}}\cdot \overline{\mathit{b}}$
So, the minimal form of the given K-map is $\overline{\mathit{b}}\cdot \overline{\mathit{d}}+\overline{\mathit{c}}\cdot \overline{\mathit{b}}$.
Hence, the correct answer is "option 2".