The Map method involves a simple, straightforward procedure for simplifying Boolean expressions.
Map simplification may be regarded as a pictorial arrangement of the truth table which allows an easy interpretation for choosing the minimum number of terms needed to express the function algebraically. The map method is also known as Karnaugh map or K-map.
Each combination of the variables in a truth table is called a mid-term.
Note: When expressed in a truth table a function of n variables will have 2^n min-terms, equivalent to the 2^n binary numbers obtained from n bits.
There are four min-terms in a two variable map. Therefore, the map consists of four squares, one for each min-term. The 0's and 1's marked for each row, and each column designates the values of variable x and y, respectively.
Representation of functions in the two-variable map:
Three variable map
There are eight min-terms in a three-variable map. Therefore, the map consists of eight squares.
Three variable map: