2. Table of contents
1.History of boolen algebra
2. Boolen algebra
3.Rules of boolen algebra
4.Boolen laws
-Commutative law
- associative law
- Distribute law
5. Important Boolen theory
6.Truth table formation
3. HISTORY OF BOOLEAN ALGEBRA
BooleanAlgebra
is used to analyze
and simplify the
digital (logic)
circuits. It uses
only the binary
numbers i.e. 0
and 1. It is also
called as Binary
Algebra or logical
Algebra. Boolean
algebra was
invented
by George
4. BOOLEAN ALGEBRA
Boolean Algebra is used to analyze and
simplify the digital (logic) circuits. It uses only
the binary numbers i.e. 0 and 1. It is also
called as Binary Algebra or logical Algebra.
Boolean algebra was invented by George
Boole in 1854. Following are the important
rules used in Boolean algebra.Variable used
can have only two values.
5. RULES OF BOOLEAN ALGEBRA
Following are the important rules used in
Boolean algebra.
Variable used can have only two values. Binary 1 for HIGH
and Binary 0 for LOW.
Complement of a variable is represented by an overbar (-).
Thus, complement of variable B is represented as .Thus if B
= 0 then = 1 and B = 1 then = 0.
OR of the variables is represented by a plus (+) sign
between them. For example OR ofA, B, C is represented as
A + B + C.
Logical AND of the two or more variable is represented by
writing a dot between them such asA.B.C. Sometime the
dot may be omitted like ABC.
6. Boolean Laws
There are six types of Boolean Laws.
1.Commutative law
Any binary operation which satisfies the
following expression is referred to as
commutative operation.
Commutative law states that changing the
sequence of the variables does not have any
effect on the output of a logic circuit.
For example; (i). A.B =B.A
(ii).A+B=B+A
7. 2.Associative law
This law states that the order in which the logic
operations are performed is irrelevant as their effect is
the same.
For example; (i) (A.B).C=A.(B.C)
(ii) (A+B)+C=A+(B+C)
3.Distributive law
Distributive law states the following condition.
For example; (i) A.(B+C)=A.B+B.C
8. AND law
These laws use the AND operation.Therefore they are called
as AND laws.
For example; (i) A.0=0
(ii) A.1=A
(iii) A.A=A
OR law
These laws use the OR operation.Therefore they are called
as OR laws.
For example; (i) A+0=A
(ii) A+1=1
(iii) A+A=A
9. INVERSION law
This law uses the NOT operation.The inversion law
states that double inversion of a variable results in the
original variable itself.
For example; A =A
10. Important Boolean Theorems
Following are few important Boolen theorem
ems.
Boolean function/theorems
Boolean Functions
De Morgan'sTheorems
Description
Boolean Functions and
Expressions, K-Map and
NAND Gates realization
De Morgan'sTheorem 1
andTheorem 2
11. Truth Table Formation
A truth table represents a table having all
combinations of inputs and their
corresponding result.
It is possible to convert the switching
equation into a truth table. For example,
consider the following switching equation.
F(A,B,C) = A+(BC)
12. The output will be high (1) if A = 1 or BC =
1 or both are 1.The truth table for this
equation is shown byTable (a).The
number of rows in the truth table is
2n where n is the number of input
variables (n=3 for the given equation).
Hence there are 23 = 8 possible input
combination of inputs.
