KARNAUGH MAP

The Karnaugh map or K-Map provides a simple and straight-forward method of minimizing Boolean expressions. The only limitation is that it will be ineffective for more than four (4) inputs.

The K-Map can also be described as a grid-like representation of a truth table. The rows and columns correspond to the possible values of the function's inputs. Each cell represents the outputs of the function for those possible inputs.

Figure 1 :  It show trusth tablewith three input and one output.
X1, X2, X3 as input
F as output

Figure 2 : It show k-map

KMaps can be applied to expressions of more than two variables. We simply extend KMaps for two variables to three variables, as indicated by Figure 1.


Step 1 :

To use k-map, we must draw a truth table,
X1, X2, X3  is input in truth table. F is output in truth table.

F = X1'  X2  X3' +  X1  X2  X3'  + X1  X2  X3

You can simplify F = X1'  X2  X3' +  X1  X2  X3'  + X1  X2  X3 by using Karnaugh Map.

F = x1 x2 + x2 x3'