Minimization Technique by Rishov Mal

The Karnaugh Map, also known as the K-map, is a method to simplify
boolean algebra expressions.
The Karnaugh Map reduces the need for extensive calculations by
taking advantageof humans’ pattern-recognition capability.
These terms can be used to write a minimal boolean expression
representing the required logic.

The Karnaugh Map uses the following rules for the simplification of expressions
by grouping together adjacent cells containigng ones.
1. Groups may not include any
cell containing a zero.
2. Groups may be horizontal
or vertical, but not diagonal.

3. Groups must contain 1,2,4,8 or in general 2^n cells.
That is if n=1, a group will contain two 1’s since 2^1=2.
If n=2, a group will contai four 1’s since 2^2=4.

4. Each group should be as large as possible.
5. Each cell containing a one must be in at least one
group.

7. 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.

8. There should be as few groups as possible, as long as this does not
contardict any of the previous rules.

Four variable Karnaugh Map
 Karnaugh map can be extended to 4 variables:
 Top cells are adjacent to bottom cells. Left-edge cells are
adjacent to right-edge cells.
 Note variable ordering(WXYZ).

Don’t Cares in K-map
 Don’t cares can be treated as O’s or 1’s:
 Example: minimize F(A,B,C,D)=∑m(1,3,5,7,9)+d(6,12,13)
 With and without using don’t cares
 Use X==“1”
 allows a 2-cube rather than a 1-cube
F=A’D+B’C’D without using don’t cares
F=A’D+C’D using don’t cares

•No zeros allowed.
•No diagonals.
•Only power 0f 2 number of cells in each group.
•Groups should be as large as possible.
•Every one must be in at least one group.
•Overlapping allowed.
•Wrap around allowed.
•Fewest number of groups possible.

Minimization Technique by Rishov Mal

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