The document provides an overview of boolean logic, explaining its fundamental concepts and operators such as 'and', 'or', and 'not', which relate to true and false values expressed as 1 and 0. It discusses the creation and interpretation of truth tables and evaluates boolean expressions using these tables. Additionally, it includes methods for constructing truth tables based on the number of variables involved.

1. BOOLEAN LOGIC
CLASS: XI
COMPUTER SCIENCE -083

2. INTRODUCTION TO BOOLEAN LOGIC
Boolean Logic is a form of algebra which is centered around three simple words
known as Boolean Operators: “Or,” “And,” and “Not”. At the heart of Boolean
Logic is the idea that all values are either true or false MEANS 1’s [TRUE] or
0’s[FALSE].
Boolean logic was originally developed by George Boole in
mid-1800s.Boolean logic is a very easy way to figure out
the truth of a expression using True or False.
10 > 5 TRUE

3. Boolean logic is very easy to explain and to understand.
The values that expressed only in the form of 1’s means TRUE/YES or 0’s
means FALSE/NO.
Consider the example:
• Should I go to restaurant or not?
• Should I purchase a new mobile or not?
All these statements have only one answer, either in the form of yes/no,
True/False.

4. Boolean Variable.
It is also known as binary variable or logical variable that takes values from
Boolean algebra. A Boolean variable can take only one binary – valued
quantity out of two possible values i.e., YES/TRUE/1 or NO/FALSE/0.
One bit represents one Boolean variable.
So in electrical circuit, if the signals passes, it represents 1, else
represented through 0.

5. Boolean Constant:
The values which are stored in binary variables are known as Boolean
Constants. Therefore, the values are YES/TRUE/1’s or NO/FALSE/0’s.
Boolean Operators:
And Or Not
(Dot) + (Plus) ( ) or ( ‘ )
^ (caret) ( ~ )
स्थिर ,stable, static, stationary, constant, stagnant, still
()^Reversed caret

6. And (Dot)
AND operator is a binary operator that operates on two variable and the
operation performed by AND operator is known as logical multiplication.
( ^ )
Consider the following two variable values and find the result using AND
operator:
A B A . B
0
0
1
1
0
1
0
1
0
0
0
1
A B A ^ B
F
F
T
T
F
T
F
T
F
F
F
T
A B^

7. OR
OR operator is a binary operator that operates on two variable and the
operation performed by OR operator is known as logical addition.
Consider the following two variable values and find the result using OR
operator:
A B A + B
0
0
1
1
0
1
0
1
0
1
1
1
A B A + B
F
F
T
T
F
T
F
T
F
T
T
T
+ (Plus)
^
A B
^

8. NOT
NOT operator is a unary operator that operates on one variable and the
operation performed by NOT operator is known as Negation or
complementation..
Consider the following one variable values and find the result using NOT
operator:
A
0
1
1
0
A A’
F
T
T
F
~A
( ) or ( ‘ ) , ( ~ )
A’
A
TRUE NOT = FALSE

9. TRUTH TABLE:
A truth table is a mathematical table used to determine if a compound
statement is true or false. In a truth table, each statement is typically
represented by a letter or variable, like p, q, or r, and each statement also
has its own corresponding column in the truth table that lists all of the
possible truth values
Three types of truth table form:
1) Two variable form
2) Three variable form
3) Four variable form

10. How to Create a Truth Table
The first step in creating a truth table is to determine the number of
variables.
Draw COLUMNS for each unique variable. For example if two variable A,B
then two columns
Draw ROWS which can be calculated as 2n where n is total number of
variables.
Write 0’s in the first half for the number of rows in the first column and 1’s in
the next half in the first column
Similarly, Write 0’s in the first half for number of rows which have 0’s in the
first column and 1’s in the same number. Repeat this pattern till it written for
all.

11. Let us discuss First two variable form A,B :
It means two variable so number of rows are 22=4
A B
Write 0’s in the first half for the number of rows in the
first column and 1’s in the next half in the first column0
0
1
1
Draw the 2 column for A, B variable
Similarly, Write 0’s in the first half for number of rows
which have 0’s in the first column and 1’s in the same
number. Repeat this pattern till it written for all.
0
1
0
1
Method 1:
LEFT To RIGHT

12. Let us discuss First two variable form A,B :
It means two variable so number of rows are 22=4
A B
0
0
1
1
Draw the 2 column for A, B variable
0
1
0
1
Start from the last column and put 0,1,0,1……upto
the last row
Now go to next column at the left and now again
write 0,1 but double it like : 0,0,1,1,0,0,1,1………
Method 2:
RIGHT To LEFT

13. It means two variable so number of rows are 23=8 rows
A B C Draw the 3 column for A, B, C variable A B C
First column half 0’s
and half 1’s
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
Three variable form A,B,C.
LEFT To RIGHT RIGHT To LEFT
Method 1: Method 2:
Write 0’s in the first
half for number of
rows which have 0’s
in the first column
and 1’s in the same
number. Repeat same
for next
Start from
the last
column
and put
0,1,0,1
next column at
the left and
now again
write 0,1 but
double it like :
0,0,1,1,….

14. Three variable so number of rows are 24=16 rows
A B C D
0
0
0
0
0
0
1
1
1
1
0
0
Four variable form A,B,C,D.
LEFT To RIGHT RIGHT To LEFT
Method 1: Method 2:
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
First column half 0’s
and half 1’s
Write 0’s in the first
half for number of
rows which have 0’s
in the first column
and 1’s in the same
number. Repeat same
for next
A B C D
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
next column at
the left and
now again
write 0,1 but
double it like :
0,0,1,1,….
Start from
the last
column
and put
0,1,0,1

15. Now you know how to draw truth table
Let us solve the Boolean expression using truth table
Rules to evaluating Boolean expression:
Evaluate the Boolean expression from left to right
Evaluate the expression in parenthesis first
Perform all NOT expression
Perform all AND expression
Perform all OR expression

16. Evaluate the Boolean expression A+BC’ using truth table.
How many variable 3 A,B,C mean 23=8 rows.
A B C
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
C’ BC’ A + BC’
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
1
1.Perform all NOT expression
2.Perform all AND expression
3.Perform all OR expression
BC’ means B.C’

17. Evaluate the Boolean expression A+ABC’+A’C’ using truth table.
How many variable 3 A,B,C mean 23=8 rows.
A B C
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
A’ C’ ABC’ A’C’ A+ABC’+A’C’
1
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1

18. Verify using truth table that ( X + Y ) ‘ = X’ Y’ for each X,Y{0,1}.
X Y
0 0
0 1
1 0
1 1
X + Y
0
1
1
1
(X + Y)’
1
0
0
0
X’.Y’
1
0
0
0
X’
1
1
0
0
Y’
1
0
1
0
(LHS) (RHS)
It is proved that LHS = RHS