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
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
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