Different Types of Logic Gates - Essay Example

NAND Gate states that output X is TRUE or 1 if and only if any one of the inputs is FALSE (0) or both are FALSE else it’s TRUE (ITL Education Solutions Limited, 2011). The truth table for X = NOT A AND B is mentioned.

XOR gate states Output X = A OR (NOT B) OR (NOT A) OR B.

Boolean algebra can be stated as a mathematical logic or a subarea of algebra. There are certain theorems included in this Boolean algebra that are utilized in solving mathematical operations. The truth values or values for variables used in this algebra are represented as 0 and 1. These numerical figures denote False and Truth respectively. In this type of elementary algebra variable values are represented as numbers. The main operations of Boolean algebra are denoted as conjunction, negation, and disjunction. It is a formal structure to describe a wide set of logical relations. Boolean algebra plays a critical role in structuring modern programming languages. The different laws of Boolean algebra have been given.

A Boolean function can be defined as a function ‘f’ associated with Cartesian product xn {0, 1} to {0, 1} (Khanna, 2008).  An example comprising of Boolean function and Boolean algebra is given below:
(~ (p^~q)) ^ (p V q) = (~p V~~q) ^ (p V q) (De Morgan’s rule);
                               = (~p V q) ^ (p V q) (double negotiation);
                               = (q V ~p) ^ (q V p) (commutative rule);
                               = q V (~p ^ p) (distributive rule);
                               = q V 0 (negation rule);
                               = q (bound rule).