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Karnaugh Map

Karnaugh map is an explanation of the truth table Bool function in the form of images. One purpose of the Karnaugh map to simplify the Bool function, up to five variables. Boolean function with more than five variables   it will be difficult to simplified using this method.

Karnaugh map contains several squares, each square-cage is representing one segment of the Boolean equation. The number of squares depending on the number of variables. Karnaugh maps for the two variables, it will contain four squares.For the 3 variables is composed by 8 squares, 4 variables are 16 squares, and for the 5 variables composed of 32 squares. In this page will be explained only for 2, 3 and 4 variables.

Karnaugh map for 2 variables

Examples for two-variable Boolean equation  is shown in Figure 1.

Figure 1. Karnaugh map to simplify the 2 variables Boolean function.

The process of simplification in Figure 1, done in a way that eliminate the does not same variable in the row / column which locked the red line.

Karnaugh map for 3 variables

Examples for the three variables Boolean equation is shown in Figure 2.

Figure 2. Karnaugh map to simplify the 3 variables Boolean function  .

The process of simplification in Figure 2, is the same as in Figure 1, namely by eliminating the variables that are not equal in the row / column is locked red line. Squares Boxes  are arranged in the order 00, 01, 11 and 10 (for the variable BC) and 0, 1 (for variable A).

Karnaugh map for 4 variables

Examples for four variable Boolean equation is shown in Figure 3.

Figure 4. Karnaugh map to simplify the 4 variables Boolean function.

The process of simplification in Figure 3, is the same as in Figure 1 and 2, namely by eliminating the variables that are not equal in the row / column is locked red line. Squares Boxes are  arranged in the order 00, 01, 11 and 10 (for variables AB and BC).

Tips for simplification

• Give the 1 mark in a square box in accordance with the Boolean equation.

• Give a circular line around each of the boxes adjacent to that is: for the two's 1 mark in a row or column, for  four's 1 mark in the form of squares 2 x 2 or the edge of the left and right or top and bottom edge, or line size of 1 x 4 or column size 4 x 1.

• Eliminates for every different variables in a loop.

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