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**Home ⇒ Overview Courses ⇒ PLC ⇒ ****Karnaugh map**

## Simplification of logical circuits by Karnaugh-map

Table of Contents

ToggleIn 1952, Edward Veitch developed a graphic method from set theory to simplify digital switching functions, which was expanded a year later by Maurice Karnaugh. Hence the name KV diagrams.

Rules for simplification:

• Adjacent fields can be grouped into "small packages" in the size of 2, 4, 8, ... fields.

• Fields are considered to be adjacent if their entire edge touches one another.

• Packets can have one or more fields in common.

### Karnaugh-map with 2 input variables

The Karnaugh-map has as many fields as the lines in the Truth table. This means that each line of the table of values is assigned to a field in the Karnaugh-map. In this script we limit ourselves to the Disjunctive normal form.

### Karnaugh-map with 3 input variables

With three input variables, the KV díagram already has 8 fields.

### Karnaugh-map with 4 input variables

The two-dimensional Karnaugh-map for 4 variables can be converted into the three-dimensional torus by convolution and curvature. Thus also a package "over the corners" as shown, is allowed.

### Karnaugh-map with 5 input variables

With 5 input variables, there are already 2^{5} possible combinations. This means that our truth table now has 32 rows and our KV diagram has 32 cells:

... soon coming more