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Logic Gates:

Definition:

A logic gate is a circuit with one or more input voltages but only one output voltages.

logic gates are fundamental building blocks of the digital system. NOT, OR, and AND Gates are the basic types of gates.

The interconnection of gates to perform a variety of logical operation is called logic design. A truth table lists all possible combination of inputs and the corresponding outputs. All logic gates obey their truth table.

Types of Logic Gates:

NOT GATE:

A NOT gate produces an output that is the complement of the input. It has only one input signal.

It produces a 1 output when the input is 0. and

It produces a 0 output when the input is 1.

The four commonly used methods of expressing the NOT operation as shown in the figure.

In the English language	Output Y is the complement of Input A
As a Boolean expression	Y=Ā (“-” indicates NOT symbol)
As a symbol
as a truth table	A Y 0 1 1 0

The schematic diagram shows the idea of the NOT gate using a switch. The lamp (Y) will glow when the switch (A) is open. The lamp (Y) will not glow when the switch (A) is closed.

Logic Gates

The two possible switch position is shown below. The truth table shows that NOT function of the switch and lamp circuit. The output of the NOT  circuit will be enabled (lamp lit) when the input switch is open.

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OR GATE:

An OR gate is sometimes called the “any or all gate”. It has 2 or more input signals.

It produces a 1 output of any or all inputs are 1.

It produces a 0 output when all inputs are 0.

An OR gate corresponds to the action of parallel switches for the input.

The below table shows the four commonly used methods for expressing the OR operation.

In the English language	Input A is ORed with input B to yield output Y
As a Boolean expression	A + B = Y  (‘+’ Indicates OR symbol)
As a symbol
as a truth table	A B Y 0 0 0 0 1 1 1 0 1 1 1 1

The schematics diagram shows the idea of the OR gates using switches.

The lamp (Y) will glow when either switch A or switch B is closed. 

The lamp will also glow when both switches A and B are closed. 

The lamp will not glow when both switches A and B are open. 

All the possible switch combination are shown.

Switch Combination:

AND GATE:

An AND gate is sometimes called the “all or nothing gate”. It has 2 or more input signals.

It produces a 1 output only when all inputs are 1. Otherwise, it produces a 0 output (nothing).

In other words, it produces a 0 output when any input is 0.

An AND gate corresponds to the action of series switches for the input.

The below table shows the four commonly used methods for expressing the AND operation.

In the English language	Input A is ANed with input B to yield output Y
As a Boolean expression	A.B = Y  (‘.’ Indicates AND symbol)
As a symbol
as a truth table	A B Y 0 0 0 0 1 0 1 0 0 1 1 1

It shows the idea of the AND gate using switches.

The lamp (Y) will light only when both input switches (A and B) are closed.

All other possible combinations for switches A and B are shown in the below table.

Switch Combination:

NOR GATE:

A NOR gate represents an OR gate followed by an inverter. It has 2 or more input signals.

It produces a 1 when all the inputs are 0.

It produces a 0 output when any or all of the inputs are 1.

It therefore also acts as a negative (bubbled) AND gate.

The below table shows the four commonly used methods for expressing the NAND operation.

In the English language	Input A is NORed with input B to yield output Y
As a Boolean expression	A + B = Y  (‘+’ Indicates OR symbol)
As a symbol
as a truth table	A B Y 0 0 1 0 1 0 1 0 0 1 1 0

NAND GATE:

A NAND gate presents an AND gate followed by an inverter. It has 2 or more input signals.

It produces a 0 output only when all the inputs are 1.

It produces a 1 output when any of the inputs is 0.

De Mergon’s second theorem says that the NAND gate is equivalent to a negative (bubbled) OR gate.

The below table shows the four commonly used methods for expressing the NAND operation.

In the English language	Input A is Nanded with input B to yield output Y
As a Boolean expression
As a symbol
as a truth table	A B Y 0 0 1 0 1 1 1 0 1 1 1 0

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X-OR GATE:

An exclusive-OR (X-OR) gate is an anti-coincidence gate. It produces a 1 output only when the odd number of 1 is present at a time.

A 2-input X-OR gate is an inequality detector.

It produces a 1 output only when its two inputs are not equal i.e when one input is 1 or 0. An X-NOR gate can be used as a controlled inverter by connecting one input terminal to logic 1 and feeding the signal to be inverted to the other terminal.

The below table shows the four commonly used methods for expressing the X-OR operation.

In the English language	Input A and input B are X-ORed Yielding output Y
As a Boolean expression
As a symbol
as a truth table	A B Y 0 0 1 0 1 0 1 0 0 1 1 1

X-NOR GATE:

An exclusive-NOR (X-NOR) gate is a coincidence gate. It produces a 1 output only when even number of 1 is present at the input.

A 2-input X-NOR gate is an equality detector.

It produces a 1 output only when its two inputs are equal i.e when both inputs are 1 or 0. An X-NOR gate can be used as a controlled inverter by connecting one input terminal to logic 0 and feeding the signal to be inverted to the other terminal.

The below table shows the four commonly used methods for expressing the X-NOR operation.

In the English language	Input A and input B are XNORed Yielding output Y
As a Boolean expression
As a symbol
as a truth table	A B Y 0 0 1 0 1 0 1 0 0 1 1 1

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