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INTRODUCTION

Digital signal and logic levels A digital signal (pulse) is shown in Fig. It has two discrete levels,

‘High’ and ‘Low’. In most cases, the more positive of the two levels is

called HIGH and is also referred to as logic 1. The other level

becomes low and also called logic 0. This method of using more

positive voltage level as logic 1 is called a positive logic system. A

voltage 5V refers to logic 1 and 0 V refers to logic 0. On the other

hand, in a negative logic system, the more negative of the two

discrete levels is taken as logic 1 and the other level as logic 0. Both

positive and negative logic are used in digital systems. But, positive

logic is more common of logic gates. Hence we consider only positive

logic for studying the operation of logic gates.

Logic gates Circuits which are used to process digital signals are called logic gates. They are binary in nature. Gate is a digital circuit with one or more inputs but with only one output. The output appears only for certain combination of input logic levels. Logic gates are the basic building blocks from which most of the digital systems are built up. The numbers 0 and 1 represent the two possible states of a logic circuit. The two states can also be referred to as ‘ON and OFF’ or ‘HIGH and LOW’ or ‘TRUE and FALSE’.

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Basic logic gates using discrete components The basic elements that make up a digital system are ‘OR’, ‘AND’ and

‘NOT’ gates. These three gates are called basic logic gates. All the

possible inputs and outputs of a logic circuit are represented in a

table called TRUTH TABLE.

Logic gates are primarily implemented using diodes or transistors acting as electronic switches, but can also be constructed using electromagnetic relays (relay logic), fluidic logic, pneumatic logic, optics, molecules, or even mechanical elements. With amplification, logic gates can be cascaded in the same way that Boolean functions can be composed, allowing the construction of a physical model of all of Boolean logic, and therefore, all of the algorithms and mathematics that can be described with Boolean logic.

Logic circuits include such devices as multiplexers, registers, arithmetic logic units (ALUs), and computer memory, all the way up through complete microprocessors, which may contain more than 100 million gates. In practice, the gates are made from field-effect transistors (FETs), particularly MOSFETs

(metal–oxide–semiconductor field-effect transistors).

Boolean algebra Boolean algebra, named after a mathematician George Boole is the algebra of logic, which is applied to the operation of computer devices. The rules of this algebra is simple, speed and accurate. This algebra is helpful in simplifying the complicated logical expression. Laws and theorems of Boolean algebra.

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The fundamental laws of Boolean algebra are given below which are necessary for manipulating different Boolean expressions. Basic laws : Commutative laws : A + B = B + A ; AB = BA Associative Laws: A + (B + C) = (A + B) + C ; A (BC) = (AB) C Distributive law: A (B+C) = AB + AC Special theorems : A + AB = A (A + B) (A + C) = A + BC A (A + B) = A A + A B = A + B A ( A + B) = AB (A + B) ( A + C) = AC + A B AB + A C = (A + C) ( A + B)

Theorems involving a single variable can be proved by considering every possible value of the variable.

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EXPERIMENT

AIM: To demonstrate the working of logic gates using torch

bulb, battery and switches.

APPARATUS: Torch bulb, battery, switches, connecting

wires.

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1. THE ‘OR’ GATE

PROCEDURE: Consider a parallel combination of two

switches connected in a series with a bulb and battery.

The bulb will glow when either or both of the switches S₁ and S₂

are closed but it will not glow when both are open. The

functioning of the circuit may be summarized in tabular form as

follows:

Switch S₁ Switch S₂ Bulb glows

Open Open No

Open Closed Yes

Closed Open Yes

Closed Closed Yes

This action of the switches is called OR operation. Now let S₁ be

called as input A and S₂ input B. Let the state of bulb be called

output Y. Then the OR operator may be described by

Which is read as ‘Y equals A or B’ .Now if it ON value of Boolean

variable is denoted by 1 and OFF value by 0, then the above table can

be rewritten as follows:

INPUT A INPUT B OUTPUT Y = A+B

0 0 0

0 1 1

1 0 1

1 1 1

Y = A+B

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This table is called the truth table of the OR operation. Obliviously

the output is 1 when any of the input is 1.

OR GATE symbol

Circuit diagram

.

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2. THE ‘AND’ GATE

PROCEDURE: Consider two switches S₁ and S₂ connected in

a series with a bulb and a battery.

The bulb can glow only if both the switches S₁ and S₂ are closed. The

operation of the circuit is summarised in the following table :

SWITCH S₁ SWITCH S₂ Bulb Glows

Open Open No Open Closed No

Closed Open No

Closed Closed Yes

This action of the switches is called the AND operation. The AND

operator relates two input variables A and B to give a new output

variable Y and is described by the Boolean expression:

Which is read as ‘Y equals A and B’ .Thus the truth table of AND

operator will be as follows:

Input A Input B Output Y = A.B

0 0 0

0 1 0

1 0 0

1 1 1

Y = A.B

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Obviously, the output of AND operator is 1 only when both the

inputs are 1.

AND GATE symbol

Circuit diagram

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3. THE ‘NOT’ GATE

PROCEDURE: Consider a bulb short circuited by a switch.

When the switch S is open, the current flows through the bulb as it

glow. When the switch S is closed, the current goes through the

switch and the bulb is off (assuming zero resistance of the closed

switch). The function of the circuit can be summarized in the

following table.

Switch S Bulb glows

Open Yes

Closed No

This action of the circuit is called NOT operation .Let the switch S be

called input A and the state of bulb be called output Y. Then the NOT

operator may be described by the Boolean expression:

Which is read as ‘Y equals not A’ or ‘Y equals negotiation A’. Thus the

truth table is NOT operator will be as follows:

Input A Output Y= A

0 1

1 0

Y = A

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NOT GATE symbol

Circuit diagram

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CONCLUSION

NAND and NOR as Universal gates NAND and NOR gates are called Universal gates because they can

perform all the three basic logic functions. Table gives the

construction of basic logic gates NOT, OR and AND using NAND and

NOR gates.

1) AND gate examples:

Electronic door will only open if it detects a person and the switch is

set to unlocked.

Microwave will only start if the start button is pressed and the door

close switch is closed.

2) NOT gate examples:

Microwave will stop if the door is not closed.

House alarm will go off if the door is not closed.

Traffic light will operate normally if it's not in maintenance mode.

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EXPERIMENT’S IMAGES

AND gate and NOT gate

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OR gate

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BIBLIOGRAPHY

The necessary information for the project is collected from

the references stated below:

ARYA publication physics lab manual

http://en.wikipedia.org/wiki/Logic_gate#Implementations

http://en.wikibooks.org/wiki/Practical_Electronics/Logic

http://www.gneet.com/notes/np21//semiconductor.pdf