Mapping a Standard SOP (Sum Of Production) Expression 



exercise 01 

Map the following standard SOP expression on a Karnaugh map:

Solution

Evaluate the expression as shown below. Place a 1 on the 3-variable Karnaugh map Figure for each standard product term in the expression.



exercise 02 

Map the following standard SOP expression on a Karnaugh map:

Solution

Evaluate the expression as shown below. Place a 1 on the 4-variable Karnaugh map for each standard product term in the expression.

Mapping a Nonstandard SOP (Sum Of Production)Expression

exercise 03 

Map the following SOP expression on a Karnaugh map:

Solution

The SOP expression is obviously not in standard form because each product term does not have three variables. The first term is missing two variables, the second term is missing one variable, and the third term is standard. First expand the terms numerically as follows:


Map each of the resulting binary values by placing a 1 in the appropriate cell of the 3-variable Karnaugh map 

exercise 04 

Map the following SOP expression on a Karnaugh map:

Solution

The SOP expression is obviously not in standard form because each product term does not have four variables. The first and second terms are both missing two variables, the third term is missing one variable, and the rest of the terms are standard. First expand the terms by including all combinations of the missing variables numerically as follows:

Map each of the resulting binary values by placing a 1 in the appropriate cell of the 4-variable Karnaugh map. Notice that some of the values in the expanded expression are redundant.


Karnaugh Map Simplification of SOP Expressions

exercise 05

Group the 1s in each of the Karnaugh maps:

Solution

The groupings are shown in Figure. In some cases, there may be more than one way to group the 1s to form maximum groupings.



exercise 06

Determine the product terms for each of the Karnaugh maps and write the resulting minimum SOP expression.



Solution

The resulting minimum product term for each group is shown in Figure.

 The minimum SOP expressions for each of the Karnaugh maps in the figure are: