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Logic gates

Logic gates:

“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 off state and one corresponds with the circuit in on state. So if we are dealing with true or false statements zero is considered as 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 voltage more than zero. 

Logic gates


Types of logic gates:

There are basically seven types of logic gates which are further classified into three groups:

      Basic gates

      Logic gates

      Arithmetic gates

 

Basic Gates:

Basic gates are the type of gates that can not do anything individually. They have to combine with other gates to design a circuit. that is why they are called basic gates because they can not pass the voltage alone they have to combine with other gates to complete the circuit.  Types of basic gates are

    OR

    AND

    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:

Logic gates

 

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 and gate will be one only when all inputs will be one

      The mathematical equation of this gate is:

                        Y=A-B

Symbol:

Logic gates



Truth table:

 

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:

Logic gates


Truth table:

 

A

Y

0

1

1

0

 

 Universal Gates:

        Universal gates are formed by the combination of two basic gates. Types of universal gates are

    NAND gate

    NOR gate

 

NAND gate:

      A 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:

Logic gates



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:

Logic gates



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:

Logic gates


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

                       Y=A.B+A’B’.

Symbol:



Truth table:

 

A

B

Y

0

0

1

0

1

0

1

0

0

1

1

1

Uses:

      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 these 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, or Transistor-Transistor Logic, CMOS, or Complementary Metal-Oxide-Silicon and chips (ICs)

De-Morgans Theorem:

  • First Theorem:

Logic gates

 


  • Second Theorem:

Logic gates

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