Boolean Algebra & Karnaugh Map





 
 
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Karnaugh Map (K map)


Karnaugh map

–a graphical method Boolean logic expression reduction.

-a Boolean expression can be reduced to it’s simplest form through the four simple steps involved in Karnaugh mapping.

 
Four simple steps:

1. Populate Karnaugh Map with 1s as they relate to the truth table.

2. Group the adjacent 1s.

3. Analyze the groups.

4. List the reduced Boolean expression

First step:

A
B
C
X
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
1
1
1

 

 
C
C’
A’B’
1
0
A’B
1
1
AB
1
1
AB’
0
0

 

Second step:


Group the 1, using the following rules:

-zero may not be used.

-group must contain 2, 4 or 8 ones.

-grouping may only be done side to side or top to bottom, not diagonally.

-using the same “1” repeatedly is permissible.

-the goal is to find the fewest number of groups.

-the top row may wrap around to the bottom row.

 


 

Third step:


If the letter in each column are the same, then drop down. If there are different, then cancel each other out.

 

A’B’C

A’B  C

=A’C

 

 

A B ’C’

A’B C

A B C’

A B C

= B

 
Fourth step:

Then, F = A’C + B

 

 
 

 

 

 


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