Logic Gates and its types

Logic Gate

A logic gate is the most basic digital circuit that is used to perform logical operations on binary inputs. It can have many inputs but a single output.

There are 3 basic gates:

  1. OR Gate
  2. AND Gate
  3. NOT Gate

There are two Universal Gates:

  1. NAND Gate
  2. NOR Gate

There are two Derived Gates:

  1. Ex-OR Gate
  2. Ex-NOR Gate

Basic Gates

OR Gate

The OR is used to perform the Logical addition operation also known as OR function. Let A and B are two independent variables. If the OR operation of A and B is Z then,

Z = A+B

Where A and B are the input variables and Z is the output Variable.

0R Gate Symbol
OR Gate Symbol
OR gate equivalent electronic circuit
The electrical equivalent of OR gate

The truth table of OR Gate is shown below:

The Truth Table of OR Gate

Important OR Operation

The important points to remember regarding OR gate & OR operation are:

  1. The OR gate produces output 1 when any of the input variables is 1.
  2. The OR gate produces output 0 when all the input variable is 0.
  3. With the OR operation, 1+1=1, 1+1+1+1+……………= 1 and so on.

AND Gate

The AND gate is used to perform the logical multiplication, also known as AND function. The AND gate can have more than two inputs but a single output.

Z = A.B

Where A and B are the input variables and Z is the output Variable.

Logic AND Gate Symbol
AND Gate Symbol
AND GATE ELX CKT Diagram
The Electrical circuit equivalent of AND gate

The AND GateTruh table is shown below:

The Truth Table of AND Gate

Important AND Operation

The important points to remember regarding AND gate & AND operation are:

  1. The AND operation is performed exactly like ordinary multiplication of 1s and 0s.
  2. An output of the AND gate is equal to 1 only if all the inputs are 1.
  3. The output of AND gate is 0 if any of the input is 0.

NOT Gate or Inverter

The NOT Gate also known as Inverter is used for the operation of inversion or complementation. This means that an inverter or Not gate changes High(1) to Low(0) and Low(0) to High(1) . NOT gate is the only gate that has only one input and one output.

The logical equation for a NOT gate is

The logic output Equation of Not Gate

Where A is the input variable and Z is the output variable.

NOT GATE symbol
Symbol of NOT gate.
NOT GATE ELX CKT diagram
Electrical circuit equivalent of NOT gate

The NOT gate Truth table is drawn below:

TRUTH TABLE OF NOT GATE

Universal Gates

There are two Universal Gates:

  1. NAND Gate
  2. NOR Gate

NAND and NOR gate are also known as Universal gates because they can be used individually as the universal building blocks to build any logic circuit. Also the logic circuit. Also the logic functions like AND , OR ,NOT etc can be easily constructed using only NAND or NOR gates. Further, any boolean expression can be implemented either by the use of NAND gates only or NOR gates only.

NOR gates

The word NOR implies an OR function with an inverted output. The output of a NOR gate is high (1) only if all inputs are L.ow(0). The output logic equation of NOR Gate is given as

Logic Output of Nor Gate

where A and B are input Variables and Z is the output variable.

Logic NOR Gate Symbol
NOR Gate symbol

The NOR gate Truth table is drawn below:

TRUTH TABLE OF NOR GATE

Construction of AND , OR , NOT gate by NOR Gate

(i) OR gate by NOR Gate

OR GATE BY NOR GATE

(ii) AND gate by NOR gate

NEW AND GATE BY NOR GATE

(iii) NOT gate by NOR Gate

NOT GATE BY NOR GATE

NAND Gate

The word NAND implies an AND function with an inverted output. The output of a NAND gate is Low(0) only if all the inputs are high(1). The logic equation of the NAND gate is

NAND Gate Output

where A & B are input variables and Z is the output variable

NAND Gate
NAND Gate Symbol

The NAND GateTruth Table is shown below:

TRUTH TABLE OF NAND GATE

Design of AND , OR and NOT gate by NAND gates only

(i) AND Gate by NAND Gate

AND GATE BY NAND GATE

(ii) OR Gate by NAND Gate

OR GATE BY NAND GATE

(iii) NOT Gate by NAND Gate

NOT GATE BY NAND GATE

Derived Gates

Exclusive OR gate (EX-OR Gate)

The output of EXOR gate is high only if both inputs are different. The output is Low if both inputs are same i.e. either both inputs are 1 or both are 0. The output logical equation of the EX-OR gate is

Output Equation of ExOR Gate

Where A & B are input variables and Z is output Variable.

exor gate
Symbol of EX-OR Gate

The truth Table of EX-OR Gate is shown below:

TRUTH TABLE OF EXOR GATE

Exclusive -NOR Gate( EX-NOR Gate)

The output of the EX-NOR gate is high if both the inputs are same. The output is low if both inputs are different. The logical equation of the EX-NOR gate is

outpur equation of ExNOR Gate
Exnor gate 1
Symbol of EX-NOR gate

The truth Table of EX-NOR gate is shown below:

TRUTH TABLE OF EXNOR GATE

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