Digital and microprocessors (cc442)
Eng. Ayatallah Ahmed
Karnaugh map (K-map)

The Karnaugh map (K-map) is a tool for simplifying combinational
logic with 3 or 4 variables. For 3 variables, 8 cells are required
(2^3), For 4 variables, 16 cells are required (2^4).
Example:
Read the terms for the yellow cells.
1
1
1
1
1
1
1
Karnaugh map (K-map)
Karnaugh map (K-map)
Groups must contain 1, 2, 4, 8, or in general 2n cells.
Karnaugh map (K-map)
Karnaugh map (K-map)
• Groups may overlap.
Karnaugh map (K-map)
• Groups may wrap around the table. The leftmost cell in a row
may be grouped with the rightmost cell and the top cell in a
column may be grouped with the bottom cell.
Group the 1’s
Group the 1’s
Group the 1’s
Group the 1’s
0
Simplify the following using kmap:
Simplify the following using kmap:
Simplify the following using kmap:
Simplify the following using kmap:

F(P,Q,R,S)=∑(0,2,5,7,8,10,13,15)
QS+Q’S’
Simplify the following truth table using
k-map:
1
1
1
1
Thank you!