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Logic gates
The gates operation is based on Boolean algebra, which involves variables that have only two possible values: true (1) and false (0).Logic gates are fundamental building blocks used in digital circuits.
“Logic gates are digital circuits or
electronic circuits that manipulate voltages, so, in effect, they manipulate
the binary ones and zeros which are moving around inside your
computer.”
Logic gates,
and the innovative ways in which they may be combined, are thus necessary for
the proper functioning of a digital computer.
Boolean expression
“The relationship between input and
output is called Boolean expression and is represented in binary numbers.”
Binary numbers have only two possibilities. Zero and one. When dealing
with the circuits, zero corresponds with the circuit in the off state and one corresponds
with the circuit in the on state.
So, if we are dealing with true or false
statements zero is considered false and one is considered true. If you
are dealing with voltage an off-state would have zero volts and an on-stage
will have a voltage more than zero.
Types of logic gates
There
are basically seven types of logic gates which are further classified into
three groups:
1- Basic gates
2- Logic gates
3- Arithmetic gates
2- Logic gates
3- Arithmetic gates
Basic Gates:
Basic
gates are the type of gates that cannot do anything individually. They have to
combine with other gates to design a circuit. that is why they are called basic
gates because they cannot pass the voltage alone, they have to combine with
other gates to complete the circuit.
Types of basic gates:
There are three basic types of logic gates, other types are originated from the basic,
1- OR
2- AND
3- NOT
OR Gate:
OR gate requires two inputs (A, B) and gives one output (Y). The basic logic of this gate is that if at least one input is 1,
the output will be 1. The mathematical equation of this gate is:
Y = A + B
Symbol: 
Truth table:
|
A |
B |
Y |
|
0 |
0 |
0
|
|
0
|
1 |
1 |
|
1
|
0 |
1 |
|
1
|
1
|
1 |
AND Gate:
Just like or gate and gate requires single output and two
inputs. The output of the gate will be 1 only when all inputs
will be 1. The mathematical equation of this gate is:
Y = A - B
Symbol:
|
A |
B |
Y
|
|
0 |
0 |
0
|
|
0 |
1 |
0
|
|
1 |
0 |
0
|
|
1 |
1 |
1
|
NOT Gate:
NOT gate consists of one input and one output. The output and input of this gate will be reversed from each
other. That is why it is also called the inverter. The mathematical equation of this gate is
Y = A’
Symbol:
Truth Table:
|
A |
Y |
|
0 |
1 |
|
1 |
0 |
Universal Gates:
Universal gates are formed by the
combination of two gates. Types of universal
gates are
- NAND gate
- NOR gate
NAND gate:
NAND gate essentially operates as an and gate followed by a
not gate. that is why it is also sometimes called the ‘NOT-AND’ gate. The output of this gate will be zero only if both of the
inputs will be one. The mathematical equation of this gate is
Y = (A . B)’
Symbol:
Truth Table:
|
A |
B |
Y |
|
0 |
0 |
1 |
|
0 |
1 |
1 |
|
1 |
0 |
1 |
|
1 |
1 |
0 |
NOR gate:
A nor gate is also sometimes called a ‘NOT-OR’ gate, which
is essentially, or gate filled by not gate. The output of this gate will be one only if both of the
inputs will be zero otherwise the output will be false. The mathematical equation of this gate is
Y = ( A + B )’
Symbol:
Truth table:
|
A |
B |
Y |
|
0 |
0 |
1 |
|
0 |
1 |
0 |
|
1 |
0 |
0 |
|
1 |
1 |
0 |
Arithmetic Gates:
Arithmetic
gates are the special type of gates that can be used in the half adder, full
adder, and subtractor. Types of these gates are
➢ XOR gate
➢ XNOR gate
XOR Gate:
The XOR gate or ‘Ex-OR’ basically consists of two inputs and
one output. The output of this gate will be false if both of the inputs
are true. The mathematical equation of this gate is
Y = A’. B + A . B’
Symbol:
Truth table:
|
A |
B |
Y |
|
0 |
0 |
0 |
|
0 |
1 |
1 |
|
1 |
0 |
1 |
|
1 |
1 |
0 |
XNOR Gate:
The XNOR gate or ‘Ex-NOR’ accepts only one output but
more than one input. The output of this gate will be one if both of the inputs are
the same and it will be zero if both inputs are different. The mathematical equation f this gate is
Symbol:
Truth table:
|
A |
B |
Y |
|
0 |
0 |
1 |
|
0 |
1 |
0 |
|
1 |
0 |
0 |
|
1 |
1 |
1 |
Logic Gates Usage in Electronics:
Nearly every digital device we use on a regular basis contains logic gates. Such as laptops, smartphones, tablets, memory devices, etc.
Logic gates can be combined in a million different combinations and the number of combinations can be used to make different technologies like robots etc.
Logic gates are basically the main component of a chip that is used in different electronic devices.
Commonly used logic gates are TTL, Transistor-Transistor Logic, CMOS, or Complementary Metal-Oxide-Silicon and chips (ICs)
De-Morgan's Theorem:
De Morgan's theorem explain Boolean algebraic expression. It used in digital designing of logics. first and second theorem explain below as
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