Map Simplification
The Map method provides a clear and straightforward approach to simplifying Boolean expressions.
Map simplification can be seen as a visual representation of the truth table, making it easier to identify the minimum number of terms required to express the function algebraically. This method is also referred to as the Karnaugh map or K-map.
Each combination of variables in a truth table is known as a minterm.
A two-variable map contains four minterms, so it consists of four squares, each representing a minterm. The 0's and 1's assigned to each row and column indicate the values of the variables \(x\) and \(y\), respectively.
Three-variable map
A three-variable map contains eight minterms, meaning the map is made up of eight squares.
The map shown in part (b) of the above image is labeled with numbers in each row and column to illustrate the relationship between the squares and the three variables.
The map depicted in part (b) of the above image is numbered in each row and column to demonstrate the connection between the squares and the three variables.
According to the postulates of Boolean algebra, the sum of two adjacent minterms can be simplified to a single AND term with only two literals. For instance, consider the sum of two adjacent squares, such as m5 and m7.
m5+m7 = xy'z+xyz= xz(y'+y)= xz.
