UNIT 1
BOOLEAN LOGIC
Boolean Logic, also known as boolean algebra was developed by
mathematician “George Boole”.
By using Boolean logic computer can do logical thinking very fast.
Complete logic is based on True(T) or False(F).
Boolean logic is helped in developing circuits .
Boolean Algebra: The algebra which deals with only two values
ie, either True or False. The truth value of True is denoted by 1 and
the truth value False is denoted by 0.
Boolean Variable: The variables which can take only two values
either True or false ie, 1 or 0
Boolean Constants: True and False are the Boolean constants
Truth Table
It is the tabular representation of all the possible values of logical
variables with all the possible outcomes for the given combination
of values. A truth table consists of rows and columns.
Rows
The horizontal lines of truth table are called rows. The number of
rows depends upon the number of input variables. 2n rows are there
for ‘n’ number of input variables.
For 3 input variables , 23 = 8 rows
Columns
The vertical lines in a truth table are called columns.
Boolean Operators
NOT operator’s truth table.
AND operator’s truth table.
OR operator’s truth table.
Logic Gates
A Gate is a basic electronic circuit which operates on one or more
signals to produce an output signal.
1.Basic logic gates: NOT gate , AND gate , OR gate
Not gate symbol
OR gate symbol
AND gate symbols
2.Derived Logic Gates :
Derived logic gates are derived from three basic gates. Derived
gates are more popular than basic gates because they are widely
used in industry. They are NOR gate , NAND gate , XOR gate
NOR gate is inverted OR gate.
X NOR Y = (X+Y)’
NOR gate symbol
Truth table of NOR gate
X Y X+Y X NOR Y = (X+Y)’
0 0 0 1
0 1 1 0
1 0 1 0
1 1 1 0
NAND gate is inverted AND gate.
X NAND Y = (X .Y)’
NAND gate symbol
Truth table of NAND gate
X Y X.Y X NAND Y = (X .Y)’
0 0 0 1
0 1 0 1
1 0 0 1
1 1 1 0
XOR gate (Exclusive OR gate) has two or more inputs but
produces one output signal.
XOR gate produces output 1 for only those input combination that
have odd number of 1’s.
⊕Sign stands for XOR operation
A XOR B = A⊕B
DEMORGAN’s LAW
DEMORGAN’s FIRST LAW
a)(X+ Y)’ = X’ . Y’
X Y X+Y (X+Y)’ X’ Y’ X’.Y’
0 0 0 1 1 1 1
0 1 1 0 1 0 0
1 0 1 0 0 1 0
1 1 1 0 0 0 0
DEMORGAN’s SECOND LAW
b) (X. Y)’ = X’ + Y’
X Y X.Y (X.Y)’ X’ Y’ X’+Y’
0 0 0 1 1 1 1
0 1 0 1 1 0 1
1 0 0 1 0 1 1
1 1 1 0 0 0 0
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