Advance Digital Technique - Karnaugh Map (K-MAP) Recall Notes

KARNAUGH MAP (K-MAP)

- The K-map provides a graphical technique for reducing logic equations to minimal form.
- It is an array of cells which contains all the information in the truth table arranged in a way that
allows a quick visual simplification of the logic equation.
- The usefulness of the K-MAP lies in the fact that ADJACENT CELLS can be grouped visually to
eliminate redundant variables

TWO INPUT VARIABLE MAP (2^2 = 4 CELLS)

1. A GROUP OF TWO ADJACENT CELLS COMBINES TO YIELD A SINGLE VARIABLE
2. A SINGLE CELL WHICH CANNOT BE COMBINED REPRESENTS A TWO VARIABLE TERM.

EX.

TRUTH TABLE

A B X Solution:
0 0 1
0 1 1
1 0 1
1 1 0

, THREE INPUT VARIABLE MAP (2^3 = 8 CELLS)

1. A GROUP OF FOUR ADJACENT CELLS (IN LINE OR SQUARE) COMBINES TO YIELD A SINGLE
VARIABLE
2. A GROUP OF TWO ADJACENT CELLS COMBINES TO YIELD A TWO VARIABLE TERM
3. A SINGLE CELL WHICH CONTROL BE COMBINED REPRESENTS A THREE VARIABLE TERM

EX.

TRUTH TABLE

A B C X Solution:
0 0 0 1
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 1