PHYS345 Electricity and Electronics

Example of Karnaugh Mapping

Boxing Ones for Sum of Products:

Consider the following truth table for three inputs:
 A   B   C     O 
0 0 0   0
0 0 1   0
0 1 0   1
0 1 1   1
1 0 0   1
1 0 1   0
1 1 0   1
1 1 1   0

The truth table expressed in a form suitable for Karnaugh mapping:

 BC 00  01  11  10 
A\  
 0     0   0   1   1 
 1     1   0   0   1 

Boxing the ones:

 BC 00  01  11  10 
A\  
 0     0   0   1   1 
 1     1   0   0   1 

The red cells form a 1x2 supercell represented by A'.B.
The green cells form a 1x2 wrapped supercell represented by A.C'.
The resulting Boolean expression for this truth table, a sum of products, is A'.B + A.C'.

This realization requires five gates as shown below:

SOP example


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Last updated Nov. 4, 1999.
Copyright George Watson, Univ. of Delaware, 1999.