Page 27 - Computer science 868 Class 12
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Let us consider the following logical expressions
Expression 1: A>=50
Expression 2: A<=80
Value of A A>=50 A<=80 A.B
A>=50 AND A<=80
25 False True False
72 True True True
90 True False False
1.9.2 Boolean Laws
The postulates and laws of Boolean algebra are helpful in minimising Boolean functions which we will understand later
in this chapter. The postulates and laws of Boolean algebra are listed below.
1. Properties of 0 and 1
• If 1 is added to a Boolean variable, the final result of the expression is 1.
• If 0 is multiplied to a Boolean variable, the final product of the expression is 0.
• If 1 is multiplied to a Boolean variable, the final product of the expression is the binary value stored in that
variable.
• If 0 is added to a Boolean variable, the final sum of the expression is the binary value stored in that variable.
The above expressions in equation form are given as follows:
• A+1 = 1
• A.0 = 0
• A.1 = A
• A+0 = A
The above equations can be proved using a truth table as given below.
A 1 0 A+1 A.0 A.1 A+0
0 1 0 1 0 0 0
1 1 0 1 0 1 1
2. Complement Law
This law states that the logical addition of a Boolean variable and its complement results in 1 and the logical
multiplication of a Boolean variable with its complement results in 0.
The expression can thus be represented as
A+A' = 1
A.A' = 0
The following truth table proves the above expressions:
A A' A+A' A.A'
0 1 1 0
1 0 1 0
The second last column A+A' has all 1’s while the last column A.A' has all 0’s. Hence proved.
3. Idempotent Law
This law states that logically adding or multiplying a variable to itself results in the same variable. It can be expressed
algebraically as:
25
Boolean Algebra 25

