Karnaugh Maps / Tables

The Karnaugh map, also known as a Veitch diagram (KV-map or K-map for short), is a tool to facilitate the simplification of Boolean algebra integrated circuit expressions. The Karnaugh map reduces the need for extensive calculations by taking advantage of human pattern-recognition and permitting the rapid identification and elimination of potential race hazards.

The Karnaugh map was invented in 1952 by Edward W. Veitch. It was further developed in 1953 by Maurice Karnaugh, a physicist at Bell Labs, to help simplify digital electronic circuits.

In a Karnaugh map the boolean variables are transferred (generally from a truth table) and ordered according to the principles of Gray code in which only one variable changes in between squares. Once the table is generated and the output possibilities are transcribed, the data is arranged into the largest even group possible and the minterm is generated through the axiom laws of boolean algebra. - Wikipedia

Karnaugh Map (also known as the Veitch Diagram) reduction was developed as a graphic method of minimizing Boolean function. The 4-variable Karnaugh Map reduction shown here applies to any size map.

Example 4-Variable Map Problem

4-Variable Karnaugh Map - RF Cafe

F(w,x,y,z) = ∑(0,1,2,4,5,6,8,9,12,13,14) = y+w·z+x·z Minterms must be boxed in the smallest number of groups which results in all minterms being enclosed.

Generic 4-Variable Map

Generic 4-Variable Karnaugh Map - RF Cafe

Note that w,x,y,z terms (and their compliments) are arranged in positions corresponding to the axis labels. One unique minterm exists in each square.

Generic 2-Variable Map

2-Variable Karnaugh Map - RF Cafe

Generic 3-Variable Map

3-Variable Karnaugh Map - RF Cafe

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