Digital Teaching Aid (DED Philippinen, 86 p.) 
Karnaugh Mapping II  Lesson 5 
Lesson Plan 

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. 55: 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. 56: 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