Karnaugh maps

Boolean functions and its functioning can be explained well using graphs. This method was first developed by Veitch. Later Karnaugh modified this very effectively and since then it is called as Karnaugh maps. This method involves a diagrammatic representation of a Boolean function. Normally a truth table is used to represent the function of a Boolean function. A Karnaugh map is a geometrical configuration of cells such that each of the n-tuples corresponding to the row of a truth table uniquely identifies a cell on the map. The exact functional values of these n-tuples are placed as entries in the cells. If the functional value is ‘0’, a ‘0’ is placed in the associated cell. If the functional value is ‘1’, a ‘1’ is placed as cell entry. In this way, we can represent a truth table diagrammatically. In a Karnaugh map, two cells are physically adjacent within the configuration if and only if their respective n-tuples differ in exactly one element.  There exist one-variable, two-variable, three-variable and four-variable karnaugh maps. These maps consists of 2, 4, 8 and 16 cells respectively.