Solved Examples on Minterms and Maxterms
Example 1: For the Boolean variables A = 0, B = 1 and C = 0 obtain the minterm and maxterm for the variables.
Solution:
Given the values of Boolean variables as:
A = 0, B = 1 and C = 0
The required minterm for above values = A’BC’
The required maxterm for above values = A + B’ + C
Logic gate diagram for above minterm and maxterm
Example 2: Simplify the POS form and obtain the result in POS form only.
F(A, B, C, D) = (A + B + C + D)(A + B’ + C + D’)(A + B’ + C’ + D)(A + B’ + C’ + D’)(A’ + B + C + D)(A’ + B + C’ + D’)(A’ + B’ + C’ + D’)
Solution:
We draw K-Map to simplify the given POS
The simplified POS form F(A, B, C, D) = (B + C + D)(A + B’ + D’ )(A + B’ + C’)(A’ + C’ + D’)
Logic gate diagram for above maxterm:
Example 3: Simplify the SOP form and obtain the result in SOP only.
F(A, B, C, D) = A’BC’D’ + A’BC’D + A’BCD + AB’C’D’ + AB’C’D + ABC’D’ + ABCD’
Solution:
We draw K-Map to simplify the given SOP
The Simplified SOP form is F(A, B, C, D) = ABD’ + AB’C’ + A’BC’ + A’BD
Logic gate diagram for above minterm:
Minterm vs Maxterm
Minterms and Maxterms are important parts of Boolean algebra. Minterm is the product of N distinct literals where each literal occurs exactly once. The output of the minterm functions is 1. Minterm is represented by m. Maxterm is the sum of N distinct literals where each literals occurs exactly once. The output of the maxterm functions is 0. Maxterm is represented by M. In this article we will learn about minterms and maxterms, their difference, why we use minterms and maxterms along with the solved examples.