Algebraic Minimization

The goal of logic expression minimization is to find an equivalent of an original logic expression that has fewer variables per term, has fewer terms and needs less logic to implement. There are three main manual methods used for logic expression minimization; algebraic minimization, Karnaugh Map minimization and Quine-McCluskey (tabular) minimization

Algebraic Minimization

The algebraic minimization process is the application of the switching algebra postulates, laws, and theorems to transform the original expression. It is hard to recognize when a particular law can be applied and difficult to know if resulting expression is truly minimal. The incorrect implementation or dropped variables etc can easy lead to a mistake.

The following are two examples of the algebraic minimization process by exploiting the adjacency theorem. Look for two terms that are identical except for one variable in the following expression

Application removes one term and one variable from the remaining term

In the following example one can look for the adjacency

The first and third term differ only A and Ᾱ
The third and fourth term differ only A₀ and A₀
The second and third term differ only A₀ and A₀

Duplicate 3rd. term and rearrange

Apply adjacency on term pairs