Circuit Simplification
When designing more complex logic circuits, the circuits can get very long and intricate. Therefore, three different methods were developed in order to simplify and make logic circuits use less gates but still produce the same logic expression.
Boolean Algebra
Boolean Algebra is a mathematical technique that provides the ability to algebraically simplify logic expressions. Boolean algebra uses 20 different theorems in order to simplify logic expressions.
Example.
Simplify the following logic expression using Boolean Algebra.
Simplify the following logic expression using Boolean Algebra.
DeMorgan's Theorems
DeMorgan’s Theorems are two additional simplification techniques that can be used to simplify Boolean expressions. Here are the theorems:
Example.
Simplify the following logic expression using DeMorgan's Theorems.
Simplify the following logic expression using DeMorgan's Theorems.
Karnaugh Mapping
The Karnaugh mapping, or K-Map, uses a graphical technique in order to simplify a logic expression. K-Mapping is done by translating a truth table or a logic expression onto a K-Map and simplifying adjacent cells. Here are three ways to simplify a K-Map: