Digital Teaching Aid (DED Philippinen, 86 p.)
 Karnaugh Mapping II - Lesson 5
 Lesson Plan
 (introduction...) Introduction Product of sums method Don't care conditions

### Don't care conditions

In some digital systems, certain input conditions never occur during normal operations; therefore, the corresponding output never appears.

Þ It is indicated in the truth table by an X.

Fig. 5-5: Don't care conditions

 A B C D Z 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 1 0 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 0 X 1 0 1 1 X 1 1 0 0 X Don't care conditions 1 1 0 1 X 1 1 1 0 X 1 1 1 1 X

Don't care conditions are like wild cards, you can let them stand for what ever you like:

Fig. 5-6: Karnaugh map and simplified equation

HO: Simplify the following Boolean function:

That has the don't care conditions:

Solution:

First we have to translate the function into a truth table:

 W X Y Z F 0 0 0 0 X 0 0 0 1 1 0 0 1 0 X 0 0 1 1 1 0 1 0 0 0 0 1 0 1 X 0 1 1 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1 1 1 1 0 0 0 1 1 0 1 0 1 1 1 0 0 1 1 1 1 1

Now we have to convert it into a Karnaugh map and simplify it:

Figure