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1.9 BOOLEAN ALGEBRA
Boolean Algebra gets its name from the famous mathematician George Boole who developed symbolic logic which
states the relation between mathematics and logic. Like Algebra, it also has variables, but they can store only two
values 0 (off) and 1 (on). They are termed Boolean variables.
Boolean algebra has laws that help in simplifying a complex Boolean expression, which further reduces the number of
digital gates required to represent a circuit.
1.9.1 Logical Operators and Logic Gates
An operator is a symbol used to perform different operations. The operators used in Boolean algebra are logical
operators which join two or more relational statements.
There are three types of logical operators: NOT, AND and OR.
Logical NOT
This operator is used to complement a Boolean variable or expression. NOT inverts 1 to 0 and 0 to 1. If A is a Boolean
variable then NOT A is represented as A' or A.
The truth table for NOT is as follows:
A A'
0 1
1 0
Truth table for Logical NOT
Logical OR
This operator returns 0 (false) when all the operands are 0 (false). It A B A+B
returns 1(true) if any one operand is 1 (true). It is represented using the 0 0 0
symbol + (plus). This operator works on two or more operands. It does not
check the second condition if the first condition is true. 0 1 1
1 0 1
Let us consider the following logical expressions 1 1 1
Expression 1: A%2 == 0 Truth table for OR operation
Expression 2: A%3 == 0
Value of A A%2==0 A%3==0 A+B
A%2==0 OR A%3==0
25 False False False
16 True False True
39 False True True
24 True True True
Logical AND
A B A.B
This operator produces 1 (true) when all operands are 1 (true). If any one 0 0 0
operand is 0 (false) then the result is 0 (false). It is represented by a dot (.)
symbol. This operator works on two or more operands. It does not check 0 1 0
the second condition if the first condition is false. 1 0 0
1 1 1
Truth table for AND operation
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