Logic Gates - Essay Example

MODULE 2 BACKGROUND of the of the Different types of logic gates There are six types of logic gates such as NOT, AND, OR, NAND, NOR and XOR. NOT gate is most primarily form of logic gate. This logic gate’s output is reverse of its input. For instance, output (X) is regarded as true if and only if Input (Y) is NOT True. Truth table for X=NOT Y is given below.
Input Y
Output X=NOT Y
0
1
1
0
Input Y Output X=NOT Y
The AND gates states that if both inputs are true then only the output will be true else it would be false. Where 1 represents TRUE and 0 represents FALSE. For instance, if inputs A and B both are true then output X is true or 1. Truth table given below represents X=A AND B.
Input A
Input B
Output X = A AND B
0
0
0
0
1
0
1
0
0
1
1
1
Output X = A AND B or A.B
The OR gate considers output to be true if any one of the inputs is true else it is false. For example, output X is 1 or true if input A or B is 1 or true. Truth table for X= A OR B is outlined below-
Input A
Input B
Output X= A OR B
0
0
0
0
1
1
1
0
1
1
1
1
Output X = A OR B
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). Truth table for X = NOT A AND B is-
Input A
Input B
X=NOT A AND B
0
0
1
0
1
1
1
0
1
1
1
0
NOR gate outlines output X = NOT A OR B. Truth table is –
Input A
Input B
X=NOT A OR B
0
0
1
0
1
0
1
0
0
1
1
0
XOR gate states Output X = A OR (NOT B) OR (NOT A) OR B.
Input A
Input B
Output X
0
0
0
0
1
1
1
0
1
1
1
0
Laws of Boolean algebra
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 basically 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 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 in figure 1.
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)
References
ITL Education Solutions Limited. (2011). Introduction to computer science. UK: Pearson Education India.
Khanna, R. (2008). Basics of computer science. USA: New Age International. Read More