Minimization using K-Mapp

Minimization of Boolean expressions using Karnaugh maps.
Given the following truth table for the majority function.

To use a Karnaugh map we draw the following map which has a position (square) corresponding to each of the 8 possible combinations of the 3 Boolean variables. The upper left position corresponds to the 000 row of the truth table, the lower right position corresponds to 101.


Now for 4 Boolean variables. The Karnaugh map is drawn as shown below.

Grouping the 1s together results in the following.

Minimization of Boolean expressions using Karnaugh maps.
Given the following truth table for the majority function.

To use a Karnaugh map we draw the following map which has a position (square) corresponding to each of the 8 possible combinations of the 3 Boolean variables. The upper left position corresponds to the 000 row of the truth table, the lower right position corresponds to 101.


Now for 4 Boolean variables. The Karnaugh map is drawn as shown below.

Grouping the 1s together results in the following.

Minimization of Boolean expressions using Karnaugh maps.
Given the following truth table for the majority function.

To use a Karnaugh map we draw the following map which has a position (square) corresponding to each of the 8 possible combinations of the 3 Boolean variables. The upper left position corresponds to the 000 row of the truth table, the lower right position corresponds to 101.


Now for 4 Boolean variables. The Karnaugh map is drawn as shown below.

Grouping the 1s together results in the following.