Simplification of Boolean expressions using Karnaugh Map

The Karnaugh map or the K-map takes both SOP and POS into consideration, therefore there are two possible outcomes: minterm and maxterm. 

Minterm Solution of K-map

Step 1: Define the expression in its canonical form.

Step 2: Create the K-map by entering 1 to each product-term into the K-map cell and fill the remaining cells with zeros. 

Step 3: Groups are formed by considering each of them in the K-map. 

Step 4: The boolean expression is found for each group.

Step 5: The boolean expression is found for the output. 

For example,

Expression: Y=A’B’ + A’B+AB

Simplified expression: Y=A’+B 

Maxterm Solution of K-map

Step 1: populate the K-map by entering the value of 0 to each sum term into the K-map cell and fill the remaining cell with one. 

Step 2: Group the zeroes.

Step 3: Define the boolean expression for each group. 

Step 4: Write the simplified boolean expression in POS form and combine the sums of the groups. 

Reference

Simplification of Boolean expressions using Karnaugh Map