12 cbse physics proj

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ACKNOWLEDGEMENT

My acknowledgement goes out to Mr. Parminder Singh ,

our physics teacher who motivated and guided me incompletion of this project. He provided me required

material and information that helped me in completion

of this project.

Shraddha Verma

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CERTIFICATE

This is to certify that MAYANK KAUSHIK of class XII-

A has performed as well as completed this project under my

supervision.

(Mr. Parminder Singh)

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AIM

TO STUDY THE FUNCTIONING OF

VARIOUS LOGIC GATES

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INTRODUCTION

Logic gates are building blocks of digital electronics. They are

used in digital electronics to change input voltage to output

voltage, according to some logical statement relating them. A

logic gate may have one or more inputs, but it has only one

output. The relation between the possible values of input andoutput voltages are expressed in the form of a table called

truth table or table of combinations.

Logic gates are related with BOOLEAN ALGEBRA,

which is different from both ordinary and binary algebra.

In this logical statements can have only two values, such asHIGH or LOW, ON or OFF, CLOSED or OPEN, YES or

NO and TRUE or FALSE. The two values of the logic

statements are denoted by the binary numbers 1 and 0. The

logic statements that the logic gates follow are called

BOOLEAN EXPRESSIONS.

The operations of logic gates are normally done by logic

digital integrated circuits (ICs). In other words digital ICs or

logic circuits are the building blocks of digital computers and

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calculators. The basic digital circuits are rather simple and

will serve as an introduction to digital ICs.

LOGIC CIRCUITSWe know the unidirectional characteristics of a solid state

semi conductor diode. When forward biased this diode acted

like a close switch. That is, it permitted current to flow in a

complete circuit. When reverse biased it acted like an open

switch and permitted a small current, if any to flow. This

unique characteristic of diode is employed in the designing of

basic logic circuits. In digital electronics a gate is a logic

circuit with one output and one or more inputs. An output

signal occurs for certain combinations of input signals.

Modern computers do many jobs from scientific computation

to business accounting. Computers are also used in the

automatic control of manufacturing processes. These devices

perform highly complex jobs. They consist of an arrangement

of simple logic circuits.

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To solve problems a computer has to make decisions as it

progresses through the steps in the problem solving. Computer

circuits that make decisions and comparisons are called logic

circuits. Computer decisions are of the YES/NO variety, also

known as two-state logic. Logic circuits can be in one of the

two states such as an ON or OFF, CLOSED or OPEn, YES

or NO, TRUE or FALSE.

BINARY SYSTEM AND ORDINARY SYSTEMBinary means two. Computers use the binary number

system. Rather than having digits from 0 to 9, a binary

number system, has only digits 0 to 1. This is better suited to

digital electronics where the signals are LOW or HIGH,

switches are OPEN or CLOSED and lights are ON or OFF.

In our experiments we will use positive logic. This means

binary 0 represents the LOW state and binary 1 represents

HIGH state. With this in mind table-2 is the truth table of a

two inputs and GATE as it is usually shown. This gives the

same information as table-1 except is uses a binary code.

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TABLE-1 TWO INPUT AND GATE IN ORDINARY SYSTEM INPUT OUTPUT

A B Y LOW LOW LOW

LOW HIGH LOW

HIGH LOW LOW

HIGH HIGH HIGH

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TABLE-2TWO INPUT AND GATE IN ORDINARY SYSTEM

INPUT OUTPUT

A B Y 0 0 0

0 1 0

1 0 0

1 1 1

AND GATE NOR GATE

NOT GATE OR GATE

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NAND GATE XOR GATE

LOGIC GATES DETAILS

Logic gate is a digital circuit, which works according to some logical

relationship between input and output voltages. Truth table of a logic gate is

a table that shows all the input and output possibilities for the logic gate.

BOOLEAN ALGEBRA

1. Addition sign is referred as OR.

Y=A+B

It is read as Y equal OR B

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2. Multiplication sign (.) is referred as AND.

Y=A.B It is read as Y equal A AND B

3. The bar sign (-) is referred as NOT.

Y=A

It is read as Y equal NOT A.

1) The OR GATE-

The OR gate is a two inputs and one output logic gate. It combines the

inputs A and B with output Y following the Boolean expression.

Y=A+B

OR gate is realized with the help of electronic circuit using two diodes D1

and D2. Negative terminal of the battery is grounded and positive terminalof battery is at high voltage. The output is voltage at C w.r.t earth.

When both A and B are connected to earth i.e. A=0 and B=0 both

diode do not conduct and hence no voltage develops across resistor i.e.

Y=0.

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When input A is connected to earth and B is connected to the terminal

of the battery then junction diode D1 does not conduct while D2

conducts being forward biased. If both are ideal diodes then there will

be no voltage drop across D2 and at same voltage as that of +veterminal of battery i.e. Y=1.

When A is connected to +ve terminal and B is earthed then D1 will

conduct while D2 will not conduct and there will be no voltage drop

across D1 i.e. Y=1

When both are connected to +ve terminal then both will be no voltage

drop i.e. Y=1.

Therefore, if both input are low then output is low. But if either input is

high, or both are high, the output is high. Table-3 summarizes the operation

of a two input OR gate in terms of binary 0s and 1s.

TABLE-3 TRUTH TABLE OF OR GATE

INPUT OUTPUT

A B Y=A+B

0 0 0

0 1 1

1 0 1

1 1 1

2 THE NOT GATEThe Not gate is a one input and one output logic gate. It combines the input

A with the output Y by following Boolean expression.

Y=A

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i.e. Y equals not A. it can be realized by using a transistor. The base of

transistor is connected to A through a resistor Rb while the emeter is

earthed. The collector is earthed through a resistor Rc and a 5V battery.

A=0 The base of the transistor also gets earthed. Therefore base

emitter junction is not forward biased. Since the base current is

zero, the collector current is also zero. The transistor is said to be in

cut- off mode. The output Y will be equal to voltage of attery,

connected to collector i.e. Y = 1.

A=1 When A is connected to +ve terminal of battery the base-

emitter junction gets forward biased and it leads to a large collector

current. The transistor is said to have gone to saturation i.e. Y=0.

Basically NOT gate is invert OR. If we give a low input the

resultant is high and if the input is high then output is low.

TABLE-4 TRUTH TABLE OF NOT GATE INPUT OUTPUT

A B

0 1

1 0

3 THE AND GATE

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The AND gate is a two inputs and one output logic hate. It combines

input A and B with the output Y following Boolean expression.

Y=A.B

i.e. Y equals A and B. it can be realized by electronic circuit by using twoideal p-n junction diodes D1 and D2. the resistance R is connected to +ve

terminal of a 5V battery. The output Y is the voltage at C w.r.t earth.

When both A and B are connected to earth i.e. A=0 and B=0 both

D1 and D2 gets forward biased hence conduct. The diodes being

ideal, no voltage drop across D1 and D2. Hence output will be 0.

When A is earthed and B is connected to +ve terminal of battery,

then diode D1 will conduct while D2 not conduct. D1 being ideal,

no voltage drop takes place across it. Therefore voltage drop of 5V

takes place across R having D at voltage 5 and C at 0V w.r.t earth

i.e. Y=0.

When A is connected to +ve terminal and B is earthed i.e. A=1 and

B=0 then D2 will conduct while D1 not. D2 being ideal no

voltage drop across it takes place. Therefore a voltage drop takes

place across R which equals 5v, having terminal D at +5V and C

at 0V w.r.t earth i.e. Y=0.

When both D1 and D2 are connected to + ve terminal i.e. A=B=1

then none will conduct. There will be no current through R. now

potential at C = potential at D i.e. +5V w.r.t earth i.e. Y=0.

The action of logic gate AND is summarized in form of truth table

given below-

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TABLE-3 TRUTH TABLE OF AND GATE

INPUT OUTPUT

A B Y=A.B

0 0 0

0 1 0

1 0 0

1 1 1

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COMBINATION OF GATESVarious combinations of three basic gates provides large number of

complicated digital circuits. Few combinations of basic gates are following-

THE NOR GATE-

It is a logic circuit in which OR gate is followed by a NOT gate. If

output(Y) of OR gate is connected to input of NOT gate, the gate so

obtained is called NOR gate. Boolean expression of NOR gate is-

Y=A+B

i.e. A or B neglected or Y equal NOT( A or B)

TABLE-3 TRUTH TABLE OF NOR GATE INPUT OUTPUT

A B Y=A+B

0 0 1

0 1 0

1 0 0

1 1 0

THE NAND GATE-

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It is a logic gate in which AND gate is followed by a NOT gate. If output

Y of AND gate is connected to input of NOT gate, the gate so obtain is

called NAND gate.

TABLE-3

TRUTH TABLE OF NAND GATE INPUT OUTPUT

A B Y=A+B

0 0 1

0 1 0

1 0 0

1 1 0

6) THE XOR: GATE-

It is called exclusive OR gate. XOR gate can by-

Y=AB+AB

It can be realized by making the circuit shown in the figure.

In XOR gate the output is 1 if one of the input is 0 if both the inputs are

0 or 1 then output is zero.

Truth table for XOR gate-

TABLE-6

TRUTH TABLE OF XOR GATE

INPUT

A B A B Y=AB Y=A.B OUTPUT

0 0 1 1 0 0 0

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0 1 1 0 1 0 1

1 0 0 1 0 1 1

1 1 0 0 0 0 0

CONCLUSIONHence, we conclude that a gate is a logic circuit which has one ormore input but only one output. It follows a logical relationshipbetween input and output volage , and is hence called a logic circuit.

It forms the base of digital circuits an important part of digitalelectronics. Moreover it also provides a vast field for furtherresearch and study.

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12 cbse physics proj

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