Question

How to get the minimum product of sums in a k map

Answer 1

To get the minimum product of sums in a K-map, identify groups of adjacent 1s, derive Boolean expressions for each group, simplify the expressions, and multiply them together.

Step-by-step explanation:

In a Karnaugh map (K-map), the minimum product of sums can be obtained by identifying groups of 1s in the map and deriving the corresponding Boolean expressions. Here are the steps to get the minimum product of sums:

1. Identify groups of adjacent 1s in the K-map. These groups can be in the form of 2, 4, 8, or 16 adjacent cells.
2. Write down the Boolean expression for each group by considering the variables that are common to all the cells within the group. Use OR operations between the variables and AND operations between different groups of 1s.
3. Simplify the boolean expressions by applying boolean algebra rules, such as complementation, absorption, and the distributive law.
4. Obtain the final minimum product of sums expression by multiplying the simplified expressions obtained in the previous step together.