Chapter 2 : Computer System (Part 4)

2.4 Logic Gate & Simple Logic Circuit

An Intoduction to Boolean Algebra

-Boolean Algebra derives its name from the mathematician George Boole.

-It is the simplest way by which we can convert human ways of expressing logical processes into a mathematical and electronic form for computation known as symbolic logic or Boolean Algebra.

-Boolean Algebra is the basics of all modern computing.

-Because computers are built as collection of switches that either “on” or “off”, Boolean Algebra is a very natural way to represent digital information

-Since a Boolean algebra is a logic algebra, the variables take on two values corresponding to truth (1 or T) and false (0 or F). Hence:

·         Value 1 represents True (T)

·         Value 0 represents False (F)

Boolean Expression

-Variables are represented by letters and can have one of two values, either 0 or 1.

-Boolean algebra uses three basic logical operators AND, OR, and NOT.

-These basic operations can be combines to form a Boolean expression.

Logical Operators:  The AND Operation

-The AND operation is a binary operation, meaning that it needs two variables, A AND B.

-The Boolean expression for AND operation

Ø  Written as A.B or AB

Ø  Read “A and B”

-Truth table for AND operation

A	B	A . B
0	0	0
0	1	0
1	0	0
1	1	1

Logical OR operators : The OR Operation

-The OR operation is also binary operation with two variables. A OR B

-The Boolean expresstion for OR operation

Ø  Written as A + B

Ø  Read “A or B”

-The truth table for OR operation

A	B	A + B
0	0	0
0	1	1
1	0	1
1	1	1

Logical Operators : The NOT Operation

-The NOT operation is an unary operation with only one variable. NOT (A)

-The Boolean expression for NOT opreation :

Ø  Written as Ā

Ø  Read “NOT A”

-The Truth table for NOT operation

A	Ā
0	1
1	0