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