you studied the minimization of an SOP expression using a Karnaugh map. In this section, we focus on POS expressions. The approaches are much the same except that with POS expressions, 0s representing the standard sum terms are placed on the Karnaugh map instead of 1s.

Karnaugh Map POS Minimization

Mapping a Standard POS Expression

For a POS expression in standard form, a 0 is placed on the Karnaugh map for each sum term in the expression. Each 0 is placed in a cell corresponding to the value of a sum term. For example, for the sum term A +B + C, a 0 goes in the 010 cell on a 3-variable map. When a POS expression is completely mapped, there will be a number of 0s on the Karnaugh map equal to the number of sum terms in the standard POS expression. The cells that do not have a 0 are the cells for which the expression is 1. Usually, when working with POS expressions, the 1s are left off. The following steps and the illustration in Figure : 

Step 1: Determine the binary value of each sum term in the standard POS expression. This is the binary value that makes the term equal to 0. 

Step 2: As each sum term is evaluated, place a 0 on the Karnaugh map in the corresponding cell.

Example of mapping a standard POS expression.

Map the following standard POS expression on a Karnaugh map:


Evaluate the expression as shown below and place a 0 on the 4-variable Karnaugh map.


Karnaugh Map Simplification of POS Expressions

Use a Karnaugh map to minimize the following standard POS expression:


The combinations of binary values of the expression are:


Map the standard POS expression and group the cells as shown in Figure:

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