Digital Logic :
The word Logic is used to describe the circuits which can
duplicate specific function of decision making performed by the human mind. In
the logic relevant to computers we know that there can be only two states. This
logic is thus called two state logic or bivalent logic. Such a logical method
was developed by ARISTOTAL for getting at the truth. The method was
subsequently developed by mathematician DE-MORGAN and GEORGE BOOLE into a very powerful
mathematical tool.
A Gate is a simple electronic circuit or device that performs
logical functions. It has one or more inputs and output. Gates are called
binary logic gates 1 and 0 are inputs and outputs.
Truth Table
Truth Table is a table which shows all inputs and outputs
possibilities of a logical circuits or gate.
Types of
Logic Gates
1. AND Gate
2.
OR Gate
3.
NOT Gate
4.
NAND Gate
5.
NOR Gate
AND Gate
This is an electronic decision making element with one or more
inputs and single outputs. Its function is to implement the AND operation
(i.e., Logical Multiplication). The logical symbol for AND Gate is
A
Q
B
Two inputs
AND Gate truth table
|
Input A |
Input B |
Output Q=A.B |
|
0 |
0 |
0 |
|
0 |
1 |
0 |
|
1 |
0 |
0 |
|
1 |
1 |
1 |
Three inputs
AND Gate truth table
|
Input A |
Input B |
Input C |
Output Q=A.B.C |
|
0 |
0 |
0 |
0 |
|
0 |
0 |
1 |
0 |
|
0 |
1 |
0 |
0 |
|
0 |
1 |
1 |
0 |
|
1 |
0 |
0 |
0 |
|
1 |
0 |
1 |
0 |
|
1 |
1 |
0 |
0 |
|
1 |
1 |
1 |
1 |
AND Gate
Rule
1. Logic 1 when all inputs are 1
2.
Logic 0 when
any input is 0
OR Gate
This is an electronic decision
making element with one or more inputs and single output. Its function is to
implement the OR operation (i.e., Logical Addition). The logical symbol for OR
Gate is
Two inputs
OR Gate truth table
|
Input A |
Input B |
Output Q=A+B |
|
0 |
0 |
0 |
|
0 |
1 |
1 |
|
1 |
0 |
1 |
|
1 |
1 |
1 |
Three inputs
OR Gate truth table
|
Input A |
Input B |
Input C |
Output Q=A+B+C |
|
0 |
0 |
0 |
0 |
|
0 |
0 |
1 |
1 |
|
0 |
1 |
0 |
1 |
|
0 |
1 |
1 |
1 |
|
1 |
0 |
0 |
1 |
|
1 |
0 |
1 |
1 |
|
1 |
1 |
0 |
1 |
|
1 |
1 |
1 |
1 |
OR Gate Rule
1. Logic 1 when an inputs is 1
2.
Logic 0 when
all inputs are 0
NOT Gate
This is an electronic decision making element with one input and
one output. Its function is to implement the NOT operation (i.e., Inversion or
Logical Complement) . The logical symbol for NOT Gate is
Truth table of NOT Gate is
Two inputs
OR Gate truth table
|
Input A |
Output Q (Complement of A) |
|
0 |
1 |
|
1 |
0 |
NOT Gate
Rule is
1. Logic 1 when input is 0
2.
Logic 0 when
input is 1
NAND Gate
This is combination of NOT and AND Gates. This is like AND Gate
but with the output complimented.
The logical
symbol for NAND Gate is
Two inputs NAND Gate truth table
|
Input A |
Input B |
A.B |
Output Q=NOT(A.B) |
|
0 |
0 |
0 |
1 |
|
0 |
1 |
0 |
1 |
|
1 |
0 |
0 |
1 |
|
1 |
1 |
1 |
0 |
NAND Gate rule is
1. Logic 1 when any input is 0
2.
Logic 0 when
all inputs are 1
NOR Gate
This is combination of NOT and OR Gates.
This is like OR Gate but with the output complimented.
The logical symbol for NOR Gate is
Two inputs
NOR Gate truth table
|
Input A |
Input B |
A+B |
Output Q=NOT(A+B) |
|
0 |
0 |
0 |
1 |
|
0 |
1 |
1 |
0 |
|
1 |
0 |
1 |
0 |
|
1 |
1 |
1 |
0 |
NOR Gate rule is
1. Logic 1 when all inputs are 0
2.
Logic 0 when
any inputs is 1
Universal
Gates
NAND and NOR gates are called universal gates because the other
gates (i.e., AND, OR and NOT) can realized these individual gates.
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