--------------------------------------------------------------------------------------------------------------------------
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
= B
Fourth step:
Then, F = A’C + B
0 comments:
Post a Comment