Terminology » Other Wireless » DeMorgan's Theorem: Simplifying Logical Expressions

DeMorgan's Theorem: Simplifying Logical Expressions

boolean algebra logic expression demorgan theorem digital logic rule simplification

This page covers the basics of DeMorgan’s Theorem and provides an example application.

DeMorgan’s Theorem essentially provides a way to simplify logical expressions. It comes in two key rules:

  • RULE-1: The complement of a product of terms is equal to the sum of the complements of each term.
  • RULE-2: The complement of a sum of terms is equal to the product of the complements of each term.

These rules can be expressed mathematically as follows:

DeMorgan Theorem

How to Remember?

A simple mnemonic to remember DeMorgan’s Theorem is:

“BREAK THE LINE, CHANGE THE SIGN”

Break the line (the overbar representing the complement) over the variables, and change the sign (AND to OR, or OR to AND) directly under the original line.

Example Application of DeMorgan’s Theorem

Here’s an example demonstrating how DeMorgan’s Theorem can be applied:

Boolean and DeMorgan Rules

Let’s see how to simplify a Boolean expression using DeMorgan’s Theorem. Consider the following example:

Boolean and DeMorgan EXAMPLE

The goal is to use Boolean algebra and DeMorgan’s Theorem to simplify the expression and write the final answer in Sum of Products (SOP) form.