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Different types of logic gates(AND,OR,NOT,NOR,NAND,XOR,XNOR)

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What are universal logic gates?

Digital systems:

A digital systems deals with quantities or variable which have only two discrete values or states. The examples of such quantities are:

  • A switch can be either open or close.
  • A certain statement can be either true or false.
  • The answer of a question can be either yes or no.
  • A bulb can be either off or on.

The mathematically manipulation of these quantities can be best carried if they are represented by binary digits 1 and o. In describing functions of the digital systems a closed switch will be represented by 1 and open switch will be represented by 0. Similarly a lighted bulb will be described as 1 and an off bulb will be described as 0.

We require a special algebra, known as Boolean algebra for the manipulation of the quantities which have the values 1 and 0. These values 1 and 0 are also known as Booolean variables. Boolean algebra is based on basic opearations, which are

(1) AND operation

(2) OR operation

(3) NOT operation.

Logic Voltage Levels (+ ve and –ve Logic):

To repeat the logic 1 and the logic 0 conditions in the e circuits the voltage are choosen as follows

+ve Logic: In +ve Logic 1-logic level is made more positive than the 0-logic. Usually +5 V is assigned for logic 1 leve and 0 V or ground for the 0-looogic level.

-ve Logic: in –ve logic 1-logic level is made more negative than the 0-logic. Usually -5 V is assigned for logic 1 level and 0 V for the 0-logic level.

In logic circuits given below +ve logic is used.

The electronics circuits which implement the various logic Operations are known as logic gates. A logic circuits has one output and one or more inputs. The output signals appear only for certain combinations for input signals. In these gates the high and the low states i.e. 1 and 0 repreasent certain voltage level. There are these fundamental logic gates are given below:

The OR Gate:

The OR gate has two inputs marked as A and B and output as C. Now A ,B and C can have one of the two states either 0 or 1. The electronic circuit for OR gate is given below. The OR gate has output 1 and either A or B or both A & B are at logic 1. Above circuit shows that the lamp will light up when either switch A and B or both A & B are closed. The output will be zero if and only if both the inputs or at logic zero. It means that lamp remain off when only when both the switches A and B are open. The OR gate represents the Boolean equation A+B = C. This equation shows the that output C will be at 1 when either A and B or both A &B are at 1. This above logic operation of the OR gate can be summarized with the help of the truth table. A truth table is a table which gives the output state for all posible input combinations. Truth table for OR gate is given below:

Table………………..

Diode OR Gate:

  1. When both A and B are at logic 0 i.e.connected to ground, both the diodes will be reverse baised at the out put will be at zero.
  2. If A is at logic 0 and B is at logic 1, then Diode D1 will be reverse baised and D2 forward baised . As D2 is forward baised so the output will be at logic1 i.e. at +5 V.
  3. If A is at logic i.e. connected to + 5 V and B is at logic 0,then D1 will be forward baised and D2 will be reverse baise. The output will be at logic 1.
  4. If both A and B are at logic 1, both the diodes will be forward baised and the output will be at logic 1.

AND Gate:

The AND gate has two inputs marked as A and B and output as C. Now A ,B and C can have only one of the two states either 0 or 1. The AND gate repreasents the Boolean equation A.B = C. From the above circuit it is clear that AND gates give an output only when both the switches A and B are closed. It means that the both A & B are at 1, the output will also at 1. For all other combinations of the values A and B output is zero .

Diode AND Gate:

  1. When both A and B are at logic 0 i.e.connected to ground, both the diodes will be forward baised at the out put will be at zero.
  2. If A is at logic 0 and B is at logic 1, then Diode D1 will be reverse baised and D2 reverse  baised . so the output will be at logic 0.
  3. If A is at logic 1 i.e. connected to +5 V and B is at logic 0, then D1 will be reverse baised and D2 will be forward baised. The output will be at logic 0.
  4. If both A and B are at logic 1, both the diodes will be reverse baised and the output will be at logic 0.

NOT Gate:

It performs the operation of inversion or complementation. That is why it is also known as invertor. It vhanges a logic level to its opposite level. i.e.it changes 1 to 0 and 0 to 1. The symbolic repreasentiop of the NOT gate . Whenever a bar is placed on any variable , it shows the value of the variable has been inverted. For example 1 = 0 and 0 = 1 .  The bubble (o) in symbol of NOT gate indicates the operation of the inversion.

A common emitter transmitter whose input and the output are 180⁰ out of the phase often supplies the NOT operation. If A is at logic 0 i.e. connected to ground, the transistor is off and +Vcc appears at output, the output is at logic 1. If A is connected to the +5 V i.e. point A is at logic 1 the transistor is on and total +Vcc drop across R and the output is at zero, i.e.at logic 0.

 

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