Algebraic method

It consists on the application of postulates, proprieties and theorems to minimize the algebra. For example:

 

Veitch - Karnaugh graphic method (Karnaugh maps)

The minimization method based on Veitch-Karnaugh is used when the number of variables to manage is not very high, reaching up to 6 variables.

As first point, it is important to take into account the Karnaugh map depends on the number of input variables used. The number of cell in the Karnaugh table corresponds to 2ⁿ, where n is the number of variables that we have.

The V-K map is nothing else that the truth table drawn as a panel to favour the visual minimization. Each row in the truth table corresponds to a cell in the V-K map.

To minimize the V-K map consists on surrounding all 1 using the minimum number of "circles", being those of the maximum possible size. The circles are configured in rectangles whose areas are power of two (e.g. 1, 2, 4, 8, ...) trying to group the maximum number of possible terms. The procedure to follow is:

- All the 1s are taken that are not part of a group of two since they are not adjacent to any other.

- Groups of two that cannot form groups of four are taken.

- Groups of four that cannot form groups of eight are selected.

- When all the 1s are covered, the process is concluded.

- You have to take into account that a 1 can be included in as many groups as needed.

Note: This section is easier to explain than to write. If there is a doubt regarding this section, the student may check the following video in Youtube: http://www.youtube.com/watch?v=nwRkIbkc03g