F.Y.B.Sc. (IT)


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Boyce-Code Normal Form (BCNF)

  • A relationship is said to be in BCNF if it is already in 3NF and the left hand side of every dependency is a candidate key.
  • A relation which is in 3NF is almost always in BCNF. These could be same situation when a 3NF relation may not be in BCNF the following conditions are found true.
  1. The candidate keys are composite.
  2. There are more than one candidate keys in the relation.
  3. There are some common attributes in the relation
Professor Code Department Head of Dept. Percent Time
P1 Physics Ghosh 50
P1 Mathematics Krishnan 50
P2 Chemistry Rao 25
P2 Physics Ghosh 75
P3 Mathematics Krishnan 100

Consider, as an example, the above relation. It is assumed that:

  1. A professor can work in more than one department
  2. The percentage of the time he spends in each department is given.
  3. Each department has only one Head of Department.
  4. The relation diagram for the above relation is given as the following:



The given relation is in 3NF. Observe, however, that the names of Dept. and Head of Dept. are duplicated. Further, if Professor P2 resigns, rows 3 and 4 are deleted. We lose the information that Rao is the Head of Department of Chemistry.

The normalization of the relation is done by creating a new relation for Dept. and Head of Dept. and deleting Head of Dept. form the given relation. The normalized relations are shown in the following.

Professor Code Department Percent Time
P1 Physics 50
P1 Mathematics 50
P2 Chemistry 25
P2 Physics 75
P3 Mathematics 100


Department Head of Dept.
Physics Ghosh
Mathematics Krishnan
Chemistry Rao

See the dependency diagrams for these new relations.







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  • In real-life, complex objects are often built from smaller, simpler objects. For example, a car is built using a metal frame, an engine, some tires, a transmission, a steering wheel, and a large number of other parts.
  • A PC is built from a CPU, a motherboard, some memory, etc. This process of building complex objects from simpler ones is called composition (also known as object composition).
  • Composition is used for objects that have a has-a relationship to each other.
  • A car has-a metal frame, has-an engine, and has-a
  • A personal computer has-a CPU, a motherboard, and other components.
  • Composition is nothing but relationships between the different objects. Sometimes Object made up from another objects like Airplane is Wings, Landing gears, engines etc. this relationship is called composition
  • Inheritance is extends one class to another class like

Public class A

{//Here methods and variable etc.}

public class B:A

{//here methods and properties variable etc}

public static void main()

{B b = new B();


b.Variable ..}


  • One of the most important concepts in object-oriented programming is that of inheritance. Inheritance allows us to define a class in terms of another class, which makes it easier to create and maintain an application.
  • This also provides an opportunity to reuse the code functionality and fast implementation time.
  • When creating a class, instead of writing completely new data members and member functions, the programmer can designate that the new class should inherit the members of an existing class. This existing class is called the base class, and the new class is referred to as the derived
  • The idea of inheritance implements the is a For example, mammal IS-A animal, dog IS-A mammal hence dog IS-A animal as well

            Base & Derived Classes:

  • A class can be derived from more than one class, which means it can inherit data and functions from multiple base classes.
  • To define a derived class, we use a class derivation list to specify the base class. A class derivation list names one or more base classes and has the form:

class derived-class: access-specifier base-class

  • Where access-specifier is one of public, protected, or private, and base-class is the name of a previously defined class. If the access-specifier is not used, then it is private by default.
  • Consider a base class Shape and its derived class Rectangle as follows:

#include <iostream.h>
// Base class
class Shape
{ public:
voidsetWidth(int w)
{ width = w; }
voidsetHeight(int h)
{ height = h; }
int width;
int height;};
// Derived class
class Rectangle: public Shape
{ public:
{ return (width * height); }};
void main()
{ Rectangle Rect;
// Print the area of the object.
cout<< “Total area: ” <<Rect.getArea() <<endl;}

      When the above code is compiled and executed, it produces the following result:

 Total area: 35

 Total paint cost: $2450

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Application of Zener diode as voltage regulator:

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  • Zener diode works on reverse bias or in zener region the voltage across it is substantially constant for a large change of current through it. This characteristic permits the zener diode to be used as a voltage regulator.
  •  The zener diode maintains a constant voltage across the load spite of any change in load current or input voltage. Above figure is a very simple voltage regulator circuit requiring just one zener diode and one resistor. As long as the input voltage is a few volts more than the desired output voltage, the voltage across the zener diode will b stable.
  • As the input voltage increase the current through the zener diode increases but the voltage drop remains constant-a feature of zener diodes.
  • Review Questions

1)      Define semiconductor.

2)      What is meant by biasing of p-n junction diode?

3)      What is meant by the term “barrier potential”? What is its value for silicon and germanium diodes?

4)      Explain the formation of Depletion region in the unbiased p-n junction.

5)      Explain the working and characteristics of p-n junction diode.

6)      Compare ideal and practical diode.

7)       Compare zener and p-n junction diode.

8)      Zener diode can be used as voltage regulator. Justify.

9)      What is rectifier? With the help of neat circuit diagram and waveform explain the operation of a half rectifier circuit. Why this circuit is called ‘half wave’ circuit?

10)  Compare HW, FW and bridge rectifier.


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Fig 1.13 Symbolic Representation of Zener Diode.

  • A conventional diode does not permit large current to flow when in reverse biased. When a p-n junction is reversing biased, the current through the junction is very small. However if the magnitude of reverse bias reaches a critical value, avalanche breakdown may take place. Thus a rapid avalanche breakdown occurs and the diode conducts a large current in the reverse biased mode and may get damaged permanently.
  • However, diodes may be specially built to operate in the breakdown region. By varying the degree of doping, diodes the specific breakdown voltages (ranging from about one to several hundred volts) can be fabricated. If the junction is well-designed, the breakdown will be very sharp and the current after the breakdown will be independent of voltages; such diodes designed for a specific breakdown voltage are shown as Zener diodes.
  • They are useful in voltage regular circuits. As the load current or supply voltage changes, the current through a Zener diode will accommodate itself to these changes to maintain a constant load voltage. The upper limit on the diode current is determined by the power dissipation rating of the diode.
  • Working Of  Zener Diode (Biasing of Zener Diode):
  • Forward Biasing of Zener Diode:
  • When the anode of the zener diode is connected to the positive terminal if DC Source and  the cathode is connected to the Negative terminal, the zener diode is said to be forward biased.
  • The forward biased zener diode is behaves identical to the forward biased diodeThe fig shows the forward biased connection of zener diode.


  • Zener diode generally not used in forward biased condition.
  • Reverse  Biasing of Zener Diode:
  • When the cathode is connected to the positive terminal of the dc source and the anode is connected to the negative terminal of the dc sourse, the zener diode is said to be reverse biased.
  • Zener diode in the reverse biased condition is used as a voltage regulator.


  • The breakdown voltage depends upon the following.

1)      Width of the depletion region.

2)      Doping level.


The characteristics curve has three regions viz. forward, leakage and breakdown. In the diode forward region, it starts conducting at 0.7 V as any other silicon diode. The region between zero and breakdown is the leakage region and only small reverse current flows in this region. The breakdown region is very sharp. When the voltage reaches – 15V, the characteristics becomes almost vertical and the voltage becomes constant at- 15V.

The minus sign in the specification of the breakdown voltage does not have any significance. It only indicates that the Zener diode is reversing biased. It is preferable to say that the Zener diode has a breakdown voltage of (say) 15 V.

The following mechanism is responsible for breakdown under increasing reverse voltage,

1)      Zener Breakdown: The Zener breakdown occurs in the junction which being heavily doped and has a very narrow depletion layers, very strong electric field of the order of 10^8 V/M is developed at breakdown voltage. This electric field is strong enough to break the covalent bonds thereby generating electron hole pairs. Further a very small increase in reverse voltage produces a very large number of current carriers.

2)      Avalanche breakdown: The avalanche breakdown occurs in junction which are lightly doped, have wide depletion layer where the electric field is not strong enough to generate zener breakdown. The avalanche breakdown occurs when the accelerated free electron acquire

sufficient energy to ionize atoms by bombardment. The additional free electrons created in this manner are accelerated by the reverse field causing more and more ionization.

                  The zener diode uses a p-n junction is reverse bias to make use of the zener effect, which is a breakdown phenomenon which holds the voltage close to a constant value called the zener voltage. It is useful in zener regulator to provide a more constant voltage, for improvement of regulated power supplies, and for limiter application. Characteristics of zener diode is quite similar to that of simple PN junction diode in forward bias and have a Sharpe breakdown in reverse bias condition.

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                                  Fig 1.12 Characteristics of PN Junction Diode

The generalized voltage-current characteristic for a p-n junction in Figure above shows both the reverse-bias and forward-bias regions.

  1. At zero voltage: The barrier does not permit any current to flow through it.
  1. Forward-bias: Current rises rapidly as the voltage is increased and is quitehigh.
  1. Reverse-bias: The junction offers a very high resistance called reverse resistance.

Some amount (very small) of free holes and electrons still manage to cross the junction and constitute a reverse curren

Other Important terms:

  1. If the reverse bias is made very high, a large number of electron-hole pairs are created and the reverse current increases to a relatively high value. The maximum reverse potential difference, which a diode can tolerate without breakdown is called reverse break down voltage or zener voltage.

In other words, the minimum reverse voltage at which a pn junction breaks down is called the breakdown voltage.

  1. Knee Voltage: The voltage at which the pn junction begins to conduct currentand shows rapid rise in the current.
  1. Maximum forward voltage: The highest forward current that the pn junctioncan conduct without any damage to the junction
  1. Peak Inverse Voltage(PIV): It is the maximum reverse voltage that can beapplied to a pn junction without any damage to the junction

Beyond PIV, the junction diode is destroyed due to excessive heat.

  1. Maximum power rating: It is the maximum power that can be dissipatedthrough the junction without damaging it.
  2. It is equal to the product of junction current and voltage across the junction.


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  • A rectifier which rectifies both halves of each A.C. input cycle is called a full wave rectifier.To make use of both the halves of input cycle, two junction diodes are used.
  • Principle. It also works on the principle that a junction diode offers lowresistance during forward bias and high resistance, when reverse biased. Here, two junction diodes are connected in such a way that if one diode gets forward biased during first half cycle of A.C. input, the other gets reverse biased but when the next opposite half cycle comes, the first diode gets reverse biased and the second forward biased. Thus, output is obtained during both the half cycles of the A.C. input.
  • Arrangement: The a.c. supply is fed across the primary coil P of a step-downtransformer. The two ends of the secondary coil S of the transformer are Connected to the p-sections of the junction diodes D1 and D2. A load resistance RL is connected across the n-sections of the diodes and the central Tapping of the secondary coil. The d.c. output will be obtained across load resistance RL.
  • Theory:
  • Suppose that during first half of the input cycle upper end of coil S isat positive potential and the lower end is at negative potential, the junction diode D1 will get forward biased, while the diode D2 reverse biased. The conventional current due to the diode D1 will flow along the path of full arrows.

1  2Full Wave rectifier (Center tap)               Input output Waveform Of Full wave  rectifier

                         Fig 1.11 Full Wave Rectifiers with its Waveform

  • When the second half of the input cycle comes, the situation will be exactly reverse. Now, the junction diode D2 will conduct and the conventional current will flow along the path of the dotted arrows
  • Since current during both the half cycles’ flows from right to left through the load resistance RL, the output during both the half cycles will be of the same nature. The right end load resistance RL will be at positive potential w.r.t. its left end.
  •    Thus, in a full wave rectifier, the output is continuous but pulsating in nature. However, it can be made smooth by using a filter circuit.

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An electronic device which converts A.C. power into DC. power is called a rectifier.

The junction diode offers a low resistance path, when forward biased and a high resistance path when reverse biased. This feature of the junction diode enables it to be used as a rectifier.

The two half cycles of alternating input e.m.f. provide opposite kinds of bias to the junction diode.

If the junction diode gets forward biased during first half cycle, it will get reverse biased during the second half cycle and vice-versa.


In other words, when an alternating e.m.f. signal is applied across a junction diode, it will conduct only during those alternate half cycles, which bias it in forward direction.


  • A rectifier, which rectifies only one half of each A.C. input supply cycle, is called a half wave rectifier.
  • Principle: It is based on the principle that junction diode offers low resistancepath, when forward biased and high resistance when reverse biased. When A.C. input is applied to a junction diode it gets forward biased during one half cycle and reverse biased during the next opposite half cycle. Thus output is obtained during alternate half cycles of the A.C. input.
  • Arrangement:  The A.C. supply is fed across the primary coil P of a step-down

Transformer. The secondary coil S of the transformer is connected to the junction diode and a load resistance RL shown in Fig. 1.11. The output D.C. voltage is obtained across the load resistance RL.

  • Theory:
  • Suppose that during the first half of the input cycle, the junction diode gets forward biased. The conventional current will flow in the direction of the arrow heads.
  • The upper end of RL will be at positive potential w.r.t. the lower end. The magnitude of output across RL during first half cycle at any time will be proportional to the magnitude of current through it.
  • Hence, during the first half of the input cycle, when junction diode conducts, output across RL vary in accordance with A.C. input

1     2


Half wave Rectifier                                       Input Output Waveform of H.rectifier

Fig 1.10 HW Rectifier with its waveform

  • During the second half cycle, junction diode will get reverse biased and hence no output will be obtained across RL·
  • Critically, a small current will flow due to minority carriers and a negligible output will be obtained during this half cycle also.
  • During the next half cycle, output is again obtained as the junction diode gets forward biased.
  • Thus a half wave rectifier gives discontinuous and pulsating output across the load resistance as shown in Fig. Hence half wave rectification involves a lot of wastage of energy and hence it is not preferred.

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