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INFORMATION TECHNOLOGY
COMPUTER AND ITS EVOLUTION
PART-A
MADE BY :KSHITIJ BISHT
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Necessity is the mother of invention. The saying
holds true for computers also because computer were
invented as a result of mans search for fast andaccurate calculating devices.
The earliest device that qualifies as a digital
computer is the abacus also known as soroban.
This device permits the users to represent numbersby the position of beads on a rack. Simple addition and
subtraction can be carried out rapidly and efficiently by
positioning the beads appropriately.
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C BH AA BR BL AE GS E
A nineteenth century Professor at
Cambridge University, is considered to
be the Father of modern digital
computers.
Babbage designed a Difference
Engine in the year 1822 which could produce
reliable tables.
In 1842, Babbage came out with his new
idea ofAnalytical Engine that was
intended to be completely automatic. It was
capable of performing the basic arithmetic
functions for any mathematical problem and it
was to do so at an average speed of 60
additions per minute..
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1. The Mark I Computer (1937-44)
Also known as Automatic Sequence
Controlled calculator, this was the first fullyautomatic calculating machine designed by
Howard A. Aiken of Harvard University in
collaboration with IBM (InternationalBusiness Machines) corporation. Its design
was based on the techniques already developed
for punched card machinery.
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2. THE ATANASOFF-BERRY
COMPUTER (1939-42)
This electronic machine was developed byDr. John Atanasoff to solve certain
mathematical equations. It was called theAtanasoff-Berry Computer, or ABC, after itsinventors name and his assistant, Clifford
Berry. It used 45 vacuum tubes for internallogic and capacitors for storage.
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3. The ENIAC (1943-46)
The Electronic
Numerical Integrator And
Calculator (ENIAC) was
the first electronic
computer. It wasconstructed at the Moore
School of Engineering of
the University of
Pennsylvania, U.S.A. bya design team led by
Professors J. Presper
Eckert and John
Mauchly.
It could store and
manipulate only a
very limited
amount of
information, and
Its programs were
wired on boards.
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The operation of ENIAC was seriously handicapped
by the wiring board. This problem was later overcome by
the new concept of stored program developed by Dr.
John Von Neumann. The basic idea behind the stored
program concept is that a sequence of instructions aswell as data can be stored in the memory of the
computer for the purpose of automatically directing the
flow of operations. The stored program feature
considerably influenced the development of moderndigital computers and because of this feature we often
refer to modern digital computers as stored program
digital computers. The Electronic Discrete Variable
Automatic Computer (EDVAC) was designed on stored
program concept.
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5. EDSAC (1947-49)Almost simultaneously with EDVAC of U.S.A.,the Britishers developed the Electronic Delay StorageAutomatic Calculator (EDSAC). The machineexecuted its first program in May 1949. In thismachine, addition operation was accomplished in1500 microseconds, and multiplication operation in4000 microseconds. The machine was developed bya group of scientists headed by Professor MauriceWilkes at the Cambridge University MathematicalLaboratory.
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This computer was a small experimentalmachine based on the stored program concept.It was designed at Manchester University by a
group of scientists headed by Professor M.H.A.Newman. Its storage capacity was only 32words, each of 31 binary digits. This was toolimited to store data and instructions. Hence,the Manchester Mark I was hardly of anypractical use.
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7. The UNIVAC I (1951)
The Universal Automatic Computer (UNIVAC) was thefirst digital computer which was not one of a kind. ManyUNICAC machines were produced, the first of which was
installed in the Census Bureau in 1951 and was usedcontinuously for 10 years. The first business use of acomputer, a UNICAC I, was by General Electric Corporationin 1954.
In 1952, the International Business Machines (IBM)Corporation introduced the 701 commercial computer. Inrapid succession, improved models of the UNICAC I andother 700-series machines were introduced. In 1953, IBMproduced the IBM-650 and sold over 1000 of thesecomputers.
The commercially available digital computers, that
could be used for business and scientific applications, hadarrived.
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Data are raw facts and figures. Data are represented by values. These values may benumbers, characters, or sequence of any symbols that carry meaning in certain context.
Example:-20, 60, 98 are the marks of student out of 100. The passing percentage is40. Evaluate how many students have passed?
Sol. Data is 20, 60, 98.
Context marks of student out of 100.
Instructioncompare each data with 40 to find if student has passed or not?
Information2 students passed (obtained after processing instruction)
Data Instruction used
For processing
Information
Data storage
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The word Computer comes from the word Compute which meansto calculate. So, a computer is considered to be a calculating device that canperform arithmetical, logical as well as relational operation at very high speedand with approximately zero error.A computer can be defined asAn electronic device used to process data, convert that data into information which
can be useful to user.
A general purpose machine that processes data according to a set of instructions thatare stored in it.
A programmable computing machine.
A system of hardware
a) Which can accept data (facts, figures, observations) in prescribed form (in specificsequence)
b) Which can process the data according to the stored set of instructionsc) Supply the results of processing in a specific format
i. As an information which cab assist in decision-making
ii. As signals to control automatically further machines or processes.
iii. Store the results in a primary or secondary storage for safe keeping or later reuse.In simple terms, a computer is an electronic device for accepting and processing of data,
convert that data into information, which can further be used in decision-making.
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CHARACTERISTICS OF COMPUTERS
1. Speed2. Accuracy3. Versatility4. Power of Remembering5. Diligence6. No IQ7. No Feelings
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A computer is a very fast device. It can
perform in a few seconds the amount of work the human
being can do approximate in a week.
The speed of computer is measured in
microseconds (10-6), nanoseconds (10-9), and in
picoseconds (10-12). A powerful computer is capable of
performing about 3 to 4 million simple arithmetic
operations per second.
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The accuracy of a computer is consistently high. The degree ofaccuracy depends on designing of the computer. But for a particular
computer, each and every calculation has to be performed with certainaccuracy.
Errors can occur in a computer but these are mainly due to humanrather than technological weakness as:
due to imprecise thinking of programmer due to inaccurate data
It is the most wonderful thing about the computers. At a time, a
computer can be busy preparing electricity bill, at another preparingresume (biodata), and at still another drawing images and animation. Acomputer is capable of performing almost any task provided that the task
can be reduced to a service of logical step.
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As a human being acquires new knowledge, the brain subconsciously select what it
feels is important and worth retains in its memory and neglects the unimportant details orjust forgets them. But with computers this is not the case. A computer can store andretrieve any amount of information because of its secondary storage device capability.Every small information can be retained from the computer as and when required evenafter several years. Computer does not forget unless it is crash or it is explicitly told to do so.
Unlike human being the computer is free from monotony, tiredness of concentrationetc. and hence can work for hours together without creating any error and withoutgrumbling. Due to this property, computers obviously score more over human being indoing routine type of jobs which require great accuracy.
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Computer is not a magical device. It can perform only the task
which a human being can, the difference is that it performs these taskswith unthinkable speed and accuracy. It possess no intelligence of its
own. Till date its IQ is zero. It is told by human beings through a set of
instruction what to do and in what sequence. It depends on the users
decision and not on computers wish what task to perform.
Computers have no feelings and no instincts because they are
made line. Based on feelings, taste, knowledge and experience certain
judgements are made which is not possible with computers. Computers
judgements are based on the instructions given to them in the form of
programs, that are written by programmers.
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APPLICATIONS OF
COMPUTERS
Scientists usecomputers to develop
theories, to collect and testdata and to exchangeinformation electronicallywith colleagues around theworld. Researchers can
access databases indistant locations. Scientistrequires complexcomputation of very highdegree of accuracy andprecision.
In business, where the
computer simply replicated the
previous manual tasks, it nowautomates fully. The process and the
procedures have been improved.
Office automation is defined as
using computer and communication
technology to help people to better
use and manage information. Office
automation technology includes all
types of computers, telephones, e-
mail and office machines that use
microprocessors or other high-
technology components.
COMPUTERS IN SCIENTIFIC
RESEARCHCOMPUTERS IN BUSINESS AND
INDUSTRY
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COMPUTERS IN EDUCATION COMPUTERS IN SCHOOL
Most educational application
packages incorporate interesting and colorfulgraphics to hold the students attention andinclude programs to increase readingcomprehension, improve spelling, buildvocabulary, and develop thinking and otherspecial skills.
In todays world computer will be acommon place as telephones and dictionaries.
To prepare for outside world the studentshould learn how to work comfortably with allkinds of knowledge tools including pencils,
books, calculators, computers and otherinformation utilities.
Students need to have a clearunderstanding of the limitations of thetechnology and the ability to assess the
benefits and risks of applying technology to aproblem. They need to be able to questiontechnology.
The information age clearly makesnew demands on the educational system,
requiring major changes in what and howpeople learn. Many educators believe thatcomputers and IT are essential parts. Manyof the elementary and secondary schools arenow introducing computers. Students andteachers are using these computers in avariety of ways to learn.
Computers allow student to learnbased on drill and practice principle. The
computer based training software allowsstudent to learn at their own pace. Givesfeedback about how much they have learned.
Tutorial software provides directinstruction in a clearly specified skill orproject. Drill-and-practice software andtutorial software are often referred to asComputer Aided Instruction (CAI) software.
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COMPUTERSINENTERTAINMENTAPPLICATIONS
The use of computers in the entertainment field-movies, music, presentation, sports and gameshas
increased over the last decades and now computer play a vital role in these fields.
Computers help in improving productivity by automating time consuming, repetitive and monotonous
processes. They give the movie makers a lot of options by giving them the power to create the kind of special
effects they wantthose that were not possible in early times. The computers can create outer space, alien
characters, extinct animals and so on without the creating of their physical models. The filmmakers can then
integrate these backgrounds and characters with real characters. Computers are used in almost all phases of
movie making may it be writing scripts, creating special effects, editing, adding sound effects and so on.
Computer technology has given the ability to create special effects. Any musical composition i.e., when a piece
of music is treated, when it is played, or when it is reproduced.
COMPUTERSINWEATHERFORECASTING
Weather forecasting is one of the important areas of application of IT. With the advancement of IT,
weather forecasting has become very reliable, accurate and simpler. It is combination of science and art
both. In the modern and scientific techniques, it is possible to read the weather maps in digital medium and
these maps may be processed in such a way that a pattern for the next day is obtained.
Based on the forecasters experience and projected weather maps, the forecasting is done. Use of
computer has facilitated the job of data processing related with weather. The size of data used for weather
forecasting is normally huge, therefore the use of computers for processing these data is essential. There
are several methods used for weather forecasting such as Persistence method, Trends method, Analog
method, Numerical Weather Prediction, Textual examination etc.
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COMPUTER IN BANKINGAPPLICATIONS
APPLICATIONS INSPORTS
Banking is yet anothertype of business application thatbenefits from computerisationand information technologybecause of the repetitiveness ofthe transactions, the accuracyrequired, and the speed required
to handle the large volume ofdaily transactions.
Electronic FundsTransfer. To reduce demandsfor handling of paperdocuments, banks have deviseda number of computer
applications that make itpossible to transfer fundsthrough communication betweencomputers. This technique isknow as Eelctronic FundsTransfer (EFT).
In most sports, computerscompile statistics, sell tickets,create training programs anddiets for players and athletes,and suggest game plans andstrategies based on thecompetitors past performance.
Computers are used insports to analyze themovements of sports personsand to find faults in themovements and optimize themovements so that maximumefficiency is achieved.
Computers are used by sportsprofessionals to analyze theirtechniques to find theirstrengths and weaknesses.Computers are used to simulategames and to try out differentgames strategies.
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COMPUTER IN MULTIMEDIAThe term multimedia refers to the integration of multiple media
such as visual imager, text, video, sound and animationwhichtogether can multiply the impact of the message.
Multimedia systems can be used in training the students, teachersand employees located at different places. Through the use of video
conferencing systems, great savings in travel time and cost can beachieved. In modern organisations, video conferencing provides bettercommunication between persons separated by space and time who need towork together on common projects.
Multimedia has also improved interpersonal communicationbetween people. Another use for which multimedia is often used is making presentations in groups. It provides the
presenter with a powerful tool that can enhance communication by
delivering a multi-sensory experience.
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VARIOUS FIELDS OF
COMPUTERS1) Hardware:-Hardware is the jargon term given to the machinery itself and to the
various individual pieces of equipment. It referes to the physical devices of acomputer system.
2) Software:-A computer cannot do anything on its own. It must be instructed todo a desired job. Hence it is necessary to specify a sequence of instructionsthat a computer must perform to solve a problem. Such a sequence of
instructions written in a language that can be understood by a computer iscalled a Computer Program.
3) Firmware:-With the advancement in technology and the reduction in hardwarecost, today software is also being made available by many computermanufacturers on read-only memory (ROM) chips. These ROM chips can beeasily plugged intothe computer system and they form a part of the hardware.Such programs (software) made available on hardware are known firmware.
1) Humanware:-The personnel involved in using and maintaining the computersystem form the Humanware.
Hardware Engineer who takes care of the various components loaded computer.
Software Engineer who manages and handles the softwares loaded onto the computer.
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Accuracy:--Computers provides very highlevel of accuracy or correctness incomputing without doing any errors incomputing.
No fat igue:--A computer is free fromtiredness, lack of concentration at fatigueetc.
Memorising effect:--A computer is alsocalled as a Store Houses has the power of
storing huge amount of information or data. Analysis of d ata:--Computer cantransform data into meaningful information.
Speed:--Computers can work very fast. Ittakes only few seconds for calculations thatwe take hours to complete.
Dynamic ro le:-- Computer are capable ofplaying a versatile job.
Intangible benefits:-- Computers givemany intangible benefits like flexibility,
ability to accommodate changes andexpansion.
No psyc ho log ica l prob lems:--Ascomputers are machines they do not comewith any emotional ego and psychologicalproblems, which are otherwise destructive innature.
Cost reduct ion:-- Inspite of the cost ofcomputerisation, which is coming downdrastically over the years, the benefits whichcomputer give override the cost, thereby
making the cost incurred to be recoveredwithin no time, in turn reducing the effectivecost, thus one can have competitive edgeover others.
Works automat ically (Autom at ion):--Computer is a device, which is much morethan a calculator which is not able to dovarious automatic operations and need ahuman operator to press the necessary keysfor any operation to be performed.
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LIMITATIONS OF COMPUTERS
1) Computer does not work on it self, it receives aset of instructions and only then it can function.
2) Computers are not intelligent, they have to be
instructed about each and every step which they
have to perform i.e., each and every task to be
performed by them should be given in detail.
3) Computers cannot take decisions on its won, one
has to programme the computer to take an action
if some conditions prevail.
4) Data handling through computers is prone to the
loss of information and being tampered. Thus, it
requires special protection routines.
5) Computers, unlike humans, cannot learn by
experience.
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Processor
Memory
Input and Output device
Storage
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INPUT OUTPUTPU
MEMORY
STORAGE
PROCESSOR MEMORY
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PROCESSOR MEMORY
Processoris the brain of thecomputer that organizes andcarries out instructions that comefrom either the user or the
software.1) The function ofArithmetic
and Logical Unit(ALU) is toperform.a. Arithmetic operations as adding,
subtracting, multiplying, anddividing one set of data with
anotherb. Logical Operations (AND, OR,
NOT, exclusive OR) which is doneby analyzing and evaluating databy matching it with the set ofknown data that are included in the
program or called from memory.This unit also performs increment,
decrement, shift, and clearanceoperations.
2) Control Unit(CU) generatescontrol and timing signalsnecessary for the processing of aninstructions. It controls all theoperations of the computers.
The CPU of small computers is aMicroprocessor.
Memory is also known as
storage, Memory is like an
electronic scratch pad inside the
computer.When new data is entered
into the computer it is stored into
memory but only temporarily.
The most common type of
memory is Random Access
Memory (RAM). Unit ofmeasurement of computers
memory is the bytethe amount
of memory it takes to store a
single character.
Secondary or Auxiliarymemory is used to store
operating system, compiler,
assembler, application programs,
data files etc. which are not read
by CPU directly.
Another kind of memory which isplaced between the CPU and the
O
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Without interaction with user thecomputer is useless. Input devices accept
data and instructions from the user orfrom another computer system. Outputdevices return processed data back to theuser or to another computer system.
The mouse, trackball and touchpadenable to draw or point on the screen.
The joystick is especially well suited forplaying fast moving video games.
A scanner can copy a printed page of text
or a graphic into the computers memory,eliminating the time consuming step of typinginput or creating an image from scratch.
Digital cameras record live images thatcab viewed and edited on the computer.
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CLASSIFICATION OF COMPUTERS2) On the basis of Processing Speed and
Storage CapacityAccording to the processingspeed and storage capacity computers can beclassified as follow:
i) Micro Computer. Micro computer is a small sizedand an inexpensive computer which was originatedin late 1970s.
The most familiar kind of computer is themicrocomputer. The past, microcomputers havebeen considered to be of two types:
a) Personal computers
b) Workstations
ii) Mini Computer. A mini computer is a small generalpurpose computer with computing power largerthan a microcomputer their capacity lies betweenmicrocomputers and the mainframes.Minicomputers are usually designed to handlemultiple client requests.
iii) Mainframe Computer. Mainframe computer aremore powerful than a minicomputer. Themainframe computers have word length of 32-bits,48-bits or 64-bits.
iv) Super Computer. Super computers are the mostpowerful computers. These system have extremelyhigh processing speed and a very large size. Thefastest super computers can perform more than 1
trillion calculations per second.
1) On the basis of
Technology Computerscan be classified on the
basis of technology i.e., onthe basis of type of data
processing for which they
are designed
i. Analog Computers. These
computer operates on the
data which are continuously
varying with respect to samephysical quantity.
ii. Digital Computers. These
computer manipulates
discrete data and can perform
arithmetic and logical
operation. The data which are
countable and discrete data
iii. Hybrid Computers. Hybrid
computer is the combination
of analog and digital
computers. In hybrid
computers some calculations
are performed in the analog
portion of the computer and
some are performed on the
digital portion of the computer.
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3) On the basis of Purpose
General purpose computers. These computers areused to perform as many task as possible. Thesecomputers are store different programs and can beused to execute counters applications.
Specific purpose computers. These computers are
designed to perform only one specific task. Theprograms or instructions are wired into or permanentlystore in these machines. These machines lacksversatility but performs their single task quickly andefficiently.
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DIFFERENT GENERATION OF COMPUTERS
FIRST GENERATION (1942-1955) SECOND GENERATION (1955-1964)
This generation include:- ENIAC,EDVAC, EDSAC, MANCHESTER MARK I, theUNIVAC I. These machines used VacuumTubes which was delicate glass device thatcould control and amplify electronic signals.
Advantages :
Vacuum tube technology made possible the
advent of electronic digital computers.
These computers were the fastest calculatingdevice of that time, performed operation inmillisecond.
Disadvantages :
Too big in size.
Non-portable.
Requires air-conditioners to run.
Prone to frequent hardware failure.
Unreliable.
Requires constant maintenance.
Commercial use is limited.
Costly and difficult to use for commercial
production.
The second generation was revolutionized by theuse of transistors in lieu of vacuum tubes.Transistors are smaller and more reliable and socalled the brain of computers. This reduced thesize of computer.
Advantages :
Smaller in Size
More reliable.
Can be ported.
Generates less quantity of heat.
Hardware failure is less.
Wider commercial use.
Reduction of computational time from
milliseconds to microseconds.Disadvantages :
Requires air conditioners to run.
Requires regular maintenance.
Commercial production is difficult andcostly.
Individual components have to be manually
assembled into functional units.
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Advancement in electronictechnology made possible to
integrate large number of circuit
elements into very small surfaces of
silicon called Chips, calling this new
technology as Ics (Integrated
Circuits).Advantages :
Smaller in size.
Generates still less amount of heat.
Easily portable.
More reliable.
Requires less power to run.
Low cost of maintenance.
General purpose machines.
Cheaper and easier commercial
production.
Disadvantages : Sometimes re uires air-conditions.
This era came with the integration of over30,000 components over a single chip
called large scale integration
technology (LSI). Fourth generation
computers has LSI chips as its brain.
Advantages :
Compact, with high components density.
Generates negligible amount of heat.
Very reliable.
Cheapest as compared to all generation
computers.
Least air conditioner required.
Much faster in computation.
Hardware failure is minimum.
Less maintenance is required.
Easily portable as size is small.
Totally used as general purpose machine.
Assembling stage requires minimum laborcost and difficulty.
THIRD GENERATION (1964-
1975)
FOURTH GENERATION (1975-
1995)
TYPES OF SOFTWARE
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TYPES OF SOFTWARE
Application
software, also known
as an application
package, is a set of
one or more programs
designed to carry out
operations for aspecified application.
System software,
also known as system
package, is a set of one
or more programs,designed to control the
operation of a computer
system. These
programs do not solvespecific problems.
a) Application software b) Systems software
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COMPILER INTERPRETERA computer hardware is
capable of only understanding
machine level instructions andso it becomes compulsory to
convert the instructions written
in high level languages to
machine level instruction before
the execution of the program.
Assembleris used to
convert assembly language
instructions to machine level
instructions. Compileris usedto translate the program written
in high level language into
machine language. Compiler is
a translating program which is
much more sophisticated thanan assembler.
An interpreter is a typeof translator used for
translating high-levellanguage into machine code.It takes one statement of ahigh level language andtranslates it into a machineinstruction which is
immediately executed.Advantages :1. Fast response to change in
the source program.
2. Interpreter eliminates theneed for separate compiling
run after each programchange to add features orcorrect errors.
3. Compiler is a complexprogram as compared tointerpreter.
4. Interpreters are easy to write.
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NUMBERSYSTEM
PART - B
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NUMBER SYSTEMNumber systems are basically of two types :
Non-positional and positional number system.
Non positional : In early days , humanbeings counted on fingers. When the fingers
were not adequate then on stones , pebbles orsticks were used to indicate value. This methodis Non positional or additive approach.
Positional : In this number systemthere are only a few symbols called digits. Thesesymbols represents different values dependingupon the position they occupy in the number.
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Decimal number system Binary number systemThis number system, consists
of ten digits. 0, 1, 2, 3, 4, 5, 6, 7,8, and 9. A decimal number can berepresented in combination of
these 10 digits. The positions ofdigits are represented according toplace value of the digits. The basevalue for decimal number is 10and so the number is representedas (6734)10. The expanded form is
(6734)10= 6*1000+7*100+3*10+4*1(6734)10=6*103+7*102 +3*101 +4*100The power of ten indicate therelative position of the digits of
the number from right to left.
In the binary number system thebase is 2. So we have only 2digits and these digits are 0 and1 which can be used in binarysystem.
(11011)2=1*24+1*23+0*22+1*21*1*20(11011)2=1*16+1*8+0*4+1*2+1*1= 16+8+0+2+1(11011)2= (27)10
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OCTAL NUMBER SYSTEMHEXADECIMAL NUMBER
SYSTEM
In the octal numbersystem the base is 8. So wehave 8 digits starting from 0and ending with value (8-1)=7 i.e., 0, 1, 2, 3, 4, 5, 6 and 7,
(4621)8=4*83+6*82+2*81+1*80
=4*512+6*64+2*8+1*1=2048+384+16+1
(4621)8 =(2449)10
As there are only 8 digits inthe octal number system, so 3bits (23=8) are sufficient torepresent only octal numberin binary. Following tableshows 3 bit number with theirdecimal values :
In the hexadecimalnumber system the base is16.
(A31)16= A*162+3*161+1*160
(A31)16= A*162+3*16+1*160
= 10*256+3*16+1*1= 2560+48+1
(A31)16= (2609)10
As there are only 16 digits inthe hexadecimal numbersystem, so 4-bits (24=16) aresufficient to represent anyhexadecimal number in binaryform.
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CONVERSION AMONG VARIOUS NUMBER SYSTEM
1) Converting
any base number
to decimal
The three steps which are
used to convert any base
number to decimal.
Step i. Determine the
positional value of eachdigit. This depends on the
position of the digit and the
base of the number system.
Step ii. Multiply the obtained
positional values from Step
1 by the digits in the
corresponding columns.
Step iii. Sum the product
obtained from step 2. The
total is equivalent to the
decimal value.
2) Converting
from base 10
3) Converting
from a base other
than 10 to a baseother than 10
Decimal number to a new
base (Division Remainder
Technique)
Step i. Divide the decimal
number to be converted bythe value of the new base.
Step ii. Record the remainder
from the step 1 on the right
most digit of the new base
number.
Step iii. Divide the Quotient
by the new base.Step iv. Again, record the
remainder of step 3 as the
next digit of the new base
number.
The three steps which are
used to convert any base
number to decimal.
Step i. Convert the original
number to a decimalnumber i.e., base 10.
Step ii. Convert the decimal
number to the new base
number.
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(a) Converting binary number to an octal numberStep 1. Divide the binary digits into groups of three, starting from the right. If the
left most group fall short of digits then insert required number of zeros to the left
of most significant bit (MSB).
Step 2. Convert each group of three binary digits into one octal digit.
(b) Converting binary number to hexadecimal numberStep 1. Divide the binary digits into groups of four, starting from the right. If the left
most group fall short of digits then insert required number of zeros to the left ofmost significant bit (MSB).
Step 2. Convert each group of four binary digits to one hexadecimal digit.Hexadecimal digits 0 to 9 are equal to decimal digits 0 to 9 and hexadecimal digitsA to F are equal to decimal digits 10 to 15
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(c) Converting octalnumber to binary
number
(d) Convertinghexadecimal number
to binary number
Step 1. Convert each octal digit toa 3 digit binary number.
Step 2. Combine all the resultingbinary number into a singlebinary number.
Step 1. Convert the decimalequivalent of each hexadecimaldigit to 4 binary digits.
Step 2. Combine all the resultingbinary groups into a singlebinary number.