Module 2 - Boolean Algebra & Basic Logic Gates

Objective
1. Proof Boolean Algebra statements using basic logic gates. 2. Understand how to use Integrated Circuits (IC).

Theory
Boolean algebra is a mathematical system that describes the notations and operations on Boolean values. Boolean values are things that take on one out of two possible values. For example, a bit that can be a 1 or a 0.  

 Boolean algebra can be used to describe digital systems because digital signals are Boolean values: HIGH/VCC = 1 and LOW/GND = 0. So, a function of a digital system can be analyzed by using boolean algebra. 

 The laws of Boolean algebra are: 

 

 Those laws are used to simplify Boolean algebra expressions. The result is that the amount of components needed to implement a function into a digital system shrinks and so the cost for that system decreases. For example: 

 (A̅ + B) ∗ (A + B) = B ∗ (A̅+ A)        Inverse of Distributive Law for AND over OR = B ∗ (1)              Idempotent Law for OR = B                      Identity Law for AND 

 Logic gates are the basic components that make up a digital system. A logic gate implements a logic operation. Below is a list of logic gates with its symbol, function, and truth table: