• Simplification of Boolean algebra is the process of reducing a Boolean expression to its simplest form.
Map methods
Map methods are a graphical way to simplify Boolean expressions. The most common map methods are the Karnaugh map and the Quine–McCluskey method.
Karnaugh map
The K-map is a systematic way of simplifying Boolean expressions. With the help of the K-map method, we can find the simplest POS and SOP expression, which is known as the minimum expression. The K-map provides a cookbook for simplification.
• A k-map is similar to a truth table because it presents all of the possible values of input variables and the resulting output for each value.
• In K-map, the number of cells is similar to the total number of variable input combinations. For example, if the number of variables is three, the number of cells is 23=8, and if the number of variables is four, the number of cells is 24.
• The K-map takes the SOP and POS forms.
• The K-map grid is filled using 0’s and 1’s. The K-map is solved by making groups.
Note:
Cell Adjacency: The cells that differ by only one bit are called as cell adjacency.2 Variable K-map
A 2-variable Karnaugh map (K-map) is a table with 4 cells, each representing a different combination of the two input variables, A and B. The value of each cell is the value of the output variable, F, for that combination of input variables.
3-variable K-map
A 3-variable Karnaugh map (K-map) is a table with 8 cells, each representing a different combination of the three input variables, A, B, and C. The value of each cell is the value of the output variable, F, for that combination of input variables.
4-variable k-map
A 4-variable Karnaugh map (K-map) is a table with 16 cells, each representing a different combination of the four input variables, A, B, C, and D. The value of each cell is the value of the output variable, F, for that combination of input variables.
5-variable K-map:
A 5-variable Karnaugh map (K-map) is a graphical method for simplifying Boolean expressions with five variables.
• A K-map for five variables (ABCDE) can be constructed using two 4-variable maps. Each map contains 16 cells with all combinations of variables B, C, D, and E. One map is for A = 0, and the other is for A = 1).
