Algorithms & Flowcharts with Examples.PDF - Google Drive

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ALGORITHMS,!' FLOWCHARTS

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What is an Algorithm? An Algorithm is a step-by-step method of performing any task' (Or)

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An Algorithm cafibe defined as a finite set of rules, which gives a sequellce of operations for solving a specific type of problern. (Or) An Algorithm is awell-developed, detailed ancl organized approach to solving a ccmplex problem. (Or) An Algorithm is ageneral, language independent set of action intended to perform a specific task.

It has the following five features (conditip4l): Finiteness: An algorithm should always terminate after a.finite number of steps. Each step must be (2) Definiteness: Each step of a n algorithm must be ctear AfalmUiguous' | definite" It must be perfectly clear what should be done. (3) Effectiveness: Each step must be effective. T'hat is it should be easil.v convertible into program statement and can be performed exactly in a finite amount of time. (4) Generality: The algorithm must be complete in itself. So that it can be used to solve all

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problems of a specific type for any input data. (5) Input/output: Each algorithm must take zero, one or more i/p quantities and produce one or more o/p quantities. Consider shopping cxamPle Step 1: Going to shoP Step 2: Selecting and purchasing the required items Step 3: Returning back

We can fuither subdivide the f,rrst step of above algorithm Consider going to shoP examPle Step 1: Go to the bus stoP Step 2: Board the approPriate bus Step 3: Get the ticket Step 4: Reach the destination

Like this we can write the algorithms in English like sentences.

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An Algorithm is one of the most basic tools that are used to der el.-,p --r :r- ,:, :':r , - l logic. An algorithm is designed for a problern that is solved using a computer. Different algorithms may accomplish the same task, with a different set of in--s.-r:r=- : more or less the same time, space, and efforts. For developing an effective algorithm, flowchafts and pseudo codes are used b1' programmers. They are further expressed in programming language to develop computer programs.

isr The word algorithm comes from the name of fameous arad mathematician"abu jafar mohammed ibn musa Al-khowarizml" hterally meaning is father ofjafar mohammed, of moses native of Al-Khowarizm. The

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son

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Devising the algorithm

Validating the algorithm Expressing the algorithm Devising an algorithm is a method of solving a problem. Each step of an algorithm must be precisely defined and no vague statements should be used. Pseudo code is used to describe the algorithm, in less formal language than a programming language. The next step in developing algorithm is validating the algorithm is (i.e. proof of correctness of an algorithm) a human must be able to perform each step using paper and pencil by giving the required input, use the algorithm and should get the required output

in a finite amount of time. The next step is to implement the algorithm in programming language.

Algorithm properties Algorithms are not computer programs, as they cannot be executed by a computer. Properties of Algorithm are: 1. There must be no ambiguity in any instruction. 2. There should not be any uncertainty about which instruction is to be executed next. 3. The description of the algorithm must be finite. An algorithm cannot be open-ended. 4. The execution of the algorithm should conclude after a finite number of steps" 5. The algorithm must be general enough to deal with any contingency. 6. The algorithm should use less memory space as much as possible. 7 " An algorithm takes zero or more inputs and results in one or more oulputs. 8. An algorithm should be efficient and flexible. Three basic operations that the statements of an algorithm have the following type

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- A series of steps that we perform one after the other Selection - making a choice from multiple available options Iteration - Perfonning repetitive tasks Sequence

By combining these three we can write any algorithm.

Structure of an algorithm: The structure of an algorithm must starts with the step of Start/ Begrn and ends with End/Stop Step as shown below. In between steps of an algorithm from Begin to End has must follow any of the types such as Sequence, Selection or Iteration. Each and every algorithm has a name so we should place it at the top/ before start Step of an algorithm. We can also put comments for the steps of an algorithm whenever an instruction/ statement of an algorithm is complex.

/Alame of the algorithm Step L: StarU Begin Step 2: ....:... Step 3:

(comments)

Step n-1: Step n: Stop/End

Twes of an aleorithm: The steps of an algorithm is not only limited to a linear sequence of statements. During it is process it may diverge, repeat code or take decisions. For these pu{poses, control structures specify what has to be done to perform an algorithm. An algorithm statement that effects the order in which statements are executd or that effects whether the statements are executed, are called control structures. It affects the flow of controi-

Control structures are used to express algorithms, flowcharts, and pseudo codes as actual computer programs. Essentially there are three types of algorithms:

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Sequence Algorithms

2. Selection Algorithms 3. Iteration Algorithms

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Sequence Algorithms: Sequence Algorithms follows the sequence control

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nhere the

information flows in a straight line.

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Flowchart

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Action n The actions are performed in the same sequence (Top to bottom) in which they are written. Example: Simple sequence control structure that adds two numbers. Selection Algorithms: Selection Algorithms follows the Selection control structure as shown below. It allows a choice between two alternative paths, whether it is true or false. The first statement of a selection structure is a conditional statement. Once the sequence of steps in the selected path has been carried out, the paths are rejoined and then next instruction is carried out. Thus the selection structure has only single entry and single exit. Example: Selection control structure to find out larger of two numbers.

Flow chart

If condition

Pseudocode

If (.onAition

is true) THEN

List of actions ELSE

true?

List of different actions End-if Iteration Algorithms: lterative or repetitive Algorithms use the iterative control structure, which causes the intemrption to normal sequence of processing" It directs the system to loop back to previous statements, repeating the same sequence over and again, usually with new data.

When sequence of statements is repeated against a condition, it is said to be in a loop. Using looping the programmer avoids writing the same set of instructions again. The looping process may be one time or more times until the desired output is obtained with

inasingleprogram. Example: Iterative control structure to print first 10 natural numbers. pseudocode

Flowchart

REPEAT Sequence

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Sequence 2

Sequence n

LJNTIL Condition is false Sequence Example #

Algorithm to find out sum of two (a' b) numbers

Step 1: Begin Step 2: Read the numbers a, b Step 3: Compute the sum of a, b Step 4: Store the result in c Step 5: Print c Step 6: End

#Algorithm to find out average of four numbers (p' q' r' Step 1: Begin Step 2: Read the values

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Step 3: Add the values of p, q, r

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Step 4: Store the result in the variable 'sum' Step 5: Divide the sum by 4 St€p 6: Store the result in variable Step 7: Print avg

Step 8: End

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Selection Examples: #

Algorithm for smallest among three

Step 1: Begin Step 2: Read a, b, c Step 3:

If

a0 and y max then

then go to step 9 assign n to max

Step 8: Increment count

by I

Step 9: Print max

Step 10: End

A Flow chaft is a blueprint for an algorithm. A Flow chartis a diagrammatic or pictorial representation of an algorithm.

A "Flow Chart" is a Snap Shot of our Process of solving a problem A " Flow Chart" is a Zoom

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Lens

for your Business Pracesses.

(Dictionary) A schematic representation of a sequence of operations, as in a manufacturing process or computer program.

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(Technical) A graphical rqrresentation of the sequence of operations in an information system or program. Information system flowcharts show bow data flows from source documents through the computer to final distribution to users. Program flowcharts show the sequence of instructions in a single program or subroutine. Different symbols are used to draw each tlpe of flowchart.

A Flowchart can

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shows logic of an algorithm emphasizes individual steps and their interconnections e.g. control flow from'one action to the next

TABLE OF F'LOWCIIART SYMBOLS I$}Ef ol,iilt.li!i'!:'.i:=,iiilrl"=,,,rr1:.,=ii.'$@._-$

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Symht{ii Desoiytion

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(alias) Terminator (Terminal Point, Oval)

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This symbol is used to indicate where the flowchart begins or ends. When used to start it is labeled "start "and the label "end'7'stop"is used at the termination of the flowchart. A flowchart should always begin and end with this

synbol. Process

Show a Process or action step. This symbol is used forrepresenting arithmetic and data movement instructions. It can represent a single step('add 2 cups of flow')or an entire sub-

(make bread') with in a larger process. This is the most common symbol in both process flowcharts and business process maps. process

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Data Input/Output

The Data flowchart shape indicates inputs to and outputs from a process. As such, the shape is more often referred to as an VO shape than a Data shape.

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(Arrow,

process flows.Flow lines are used to connect

Connector)

symbols. These lines indicate the sequence of steps and the direction offlow ofa process.

Decision

Decision symbol denotes a decision (or branch) to be made. The program should continue along one of the two routes (IF/ELSE). This symbol has one entry and trvo exit paths. The path

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chosen depends

Annotation

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on whether

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about another flowchart symbol. The content may be in the form of descriptive comments, reinarks or explanatory notes.

Connector

(Inspection)

Connectors are usual'ly labeled with capital letters (A, B. AA) to shorv matching jump points. They are handy for avoiding florv lines

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that cross other shapes and flow lines. They are also handy forjumping to and from a sub-

On-page

process defined in a separate area than the main

connector

flowchart. [Just to confuse things further, same people will use a circle to indicate an operation and a square to indicate an inspection. That's why it's irnportant to include a symbol key in the

flov'chart.J Off-Page Connector

Or

Off-Page Connector shows continuation of a process flowchart onto another page. When using them in conjunction with Connectors, it's best to differentiate the labels, e.g. use numbers for Off-Page Connectors and capital letters for Connectors. In actual practice, most flowchads just use the Connect shape for both on-page and off-page references. The logical Or symbol shows when a process diverges - usually for more than 2 branches. When using this symbol, it is important to label the out-going flow lines to indicate the criteria to follow each branch.

Summing Junction

The logical Summing Junction flowchart shape is shows when multiple branches converge into a single process. The merge symbol is more common for this use, though. This symbol and the Or symbol are really more relevant in data processing flow diagrams than in process

flowcharts. Document

Pretty self explanatory - the Document flowchad symbol is for a process step that produces a document.

ai Docu.ent, except, well, multiple

Multi-

Same

Document

documents. This shape is not as commonly used as the Document flowchart shape, even when

multiple documents are implied. Display

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displayed to a person (e.g., PC user, machine operator).

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Manual lnput

Manual Input flowchad shapes show process steps where the operator/ user is prompted for information that must be manually input into a system.

Card

This is the companion to the punched iape flowchart shapes. This shape is seldom used.

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Stord Data

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Sto*ag.i

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for any process st€p that stfr€s data

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good at stretching all the life out of a maching you may still have use for the Punched Tape symbol - usd fc input into old computers and CNC machines.

Punched Tape

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Disk

data storage location, this

(Database)

depicts a database.

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Storage

Hard Drive'

Process

indepe'ndently defined process' To reduce complexity, some gtoup of instructions is specifred elsewhere as a function or subroutine'

(Subroutine)

which can be called for execution using this sYmbol.

uirlelines for Prep*ring Florvcharts a flowchart: The following guidelines should be used for creating S

1.

2. 3.

The flowchart shouldbe clear, neat, and easyto follow' The flowchart must have a logical start and finish' should be listed in logical In drawing a propef flowchart, all necessary requirements order.

4. The direction 5.

or top to of the flow of aprocedure should always be from 1eft to right

bottom. Only one flow line should come out from a process syrnbol'

of

6.

two or three flow lines Only one flow line should€nter a decision synbol. However, (one for each possible answer) may leave the decision symbol. :

7. Only one flow line is used with a terminal symbol' t

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Or

8.

Within standard symbols, write briefly. If necessary, use the annotation symbol to describe data or process more clearly.

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g. In case of complex flowcharts,

pt**s will add two numbers

and store the value in SUM

connector slmrbols are used to reduce the number

of

flow lines. 10. Intersection of

flow lines should be avoided to make it

a more effective and better

way

of representing communication. 11. It is useful to test the validity of the flowchart by passing through it with normaVunusual test data.

Benefits of a Flow chart: are currently working and also find outs the key elements of a process by drawing clear lines between the end of one process and the start of next one.

A flowchart helps to clarifu how things

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Makes Logic Clear: A flowchart makes logic clear. Communication: It is the better way of communicating the logic of a system to all concerned.

Efrective Analysis: A proble,m can be analyzed in an effective u'ay by using a flowchart. Useful in Coding It is acting as a guiCe or blueprint during the analysis and program development phase.

Proper Testing and Debugging: By nature the flowchart helps in detecting the errors in a program, shows exactlywhat the logic should do. Appropriate Documentation: Flowcharts serve as a good proglam documentation tool. Limitations of

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a

Flowchart:

Complex: when a program is very large the Flowchart tend to be large quickly and it is difficult to follow. Costly: If flowcharts are to be drawn for a huge application, the time and cost factor of program development may get out ofproportion, making it costly.

Difficult to Modify:

Due to its synbolic nature, any changes or rnodifrcations to a flowcharl usually require redrawing the entire logic again, and redrarving a complex flowchart is not a simple task.

No Update: Usually programs are updated regularly. However the corresponding update of flowcharts may not take place, especially in the case of large programs. As a result the logic in the program

PSETIDOCODE:

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Pseudo code (pronounced as soo-doh-kohd) made up two words: pseudo and code. Pseudo means imitation and code refers to instructions, written in programming languages.

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Pseudo code is not real proqramminq code but

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It is eeneric wa)' of describine an aleorithm without using any specific programming

it is look like a programming

code.

language related notations.

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Simply, we can say that it is an outline of a proqram written in the form i.e. easily converted into real programming statements. It uses plain Enelish like statements rather than symbols to represent the process of computer program

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It is also known as PDL (Program Design Language).It emphasis more on the design aspect of a computer program or structured English because usually pseudo instructions are written in normal English like statements but in a structured way. x& It is somewhat halfway between English and a programming language. sk The goal of writing pseudo code is to provide a high level description of an algorithm. It also suppresses many of the details that are insignificant. qL Example: Pseudocode to calculate an area of a rectangle PROMPT the user to enter the height of the rectangle PROMPT the user to enter width of the rectangle COMPUTE the area by multiplying the height with width

DISPLAY the area STOP *jl& Pseudocode uses some keywords to denote programming process

.f. Input : READ, OBTAIN,

{. * * *

GET, and pROMpT Output : PRINT, DISPLAY and SHOW Compute : COMPUTE, CALCULATE. and DETERMINE Initialise : SET and INITIALISE Add One : INCREMENT

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Since, Pseudocode is detailed yet readable, and programmers.

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Once pseudocode is accepted,

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it can be inspected by the tearn of designers

it is transformed into actual program code using the

vocabulary and syntax of the chosen programming language. The benefit of pseudocode is that it enables the programmer to concentrate on the algorithms without worrying about all the syntactic details of particular programming language.

Benefits of a pseudocode:

* * * *

Pseudo code is language independent so

it

can be use by most programmers

It is easier to develop a program from a pseudocode than with a flowchart. It is easy to translate pseudocode into a programming language, this can be accomplished by less experienced prograrnmers. Unlike flowcharts, pseudocode i5 sompact and does not tend to run over many pages. It is a simple structure and readability makes it easier.

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The main disadvantage of using pseudocode is that representation of the program's logic.

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There are no accepted standards for writing pseudocodes. Programmers use their own style of writing pseudocode.

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Pseudocode cannot be compiled and not be executed, and there are no real formatting or syntax rules. It simply one step, an important one, in producing the final code.

it does not provide visual

fnere

are

diferent wavs

1. 2. 3. 4.

Step form Pseudo code

Flow chart

Nassi-Shneiderman Step-form: o Problem solved with written statements. o One statement is logically related to preceding statement. o Each statement performs an action.ie solves apart of problem together these statements complete the solution.

'Why learn about programming?

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// Write an Algorithm and Flow chart for making

a tea

Begin Step 1: Boil water. Step 2: Put tea powder in the kettle. Step3: Pour boiled water in the kettle.

Stq4: Wait for three minutes. Step5: Boil milk. Step6: Put boiled milk in a cup. StepT: Add sugar to the cup. Step8: Empty the kettle in the cuP.

Step9: Stii the cup with a spoon. End

Flow Chart for the above algorithm:

Put tea powder in the kettle

Pour boiled water in the kettle

Wait for three minutes

Put boiled milk in a cup

Add suear to the cup

Empty the kettle in the cup

Stir the cup with a spoon

Example 1:

//Algorithm to find whether a student has to pass or fail by reading four subjects marks. Begin

Ml, M2, M3, M4

Step 1:

Input

Step 2:

GRADE

Step 3:

if (GRADE 0 then calculate sqrt(d)/2iandstore calculate r 1 :real*imag and tT:real-imag Siep 11: Otherwise print "Roots are imaginary arrdrl't2" Step 12: end-if Step 13: end-if Step 14: end-if Step 15: StoP

FLOWCHART:

Read a,b,c

Print "equation is lineaC'

Print "roots are real & Equal" Print real

Rl: (-b+sqrt(d)l2a P2: (-b-sqrt(d))/2a

d:_d

imag: sqrt(d)/2a

rl :

real* imag 12: real- imag

Print "roots are real& uffeal" Print r1 & 12

Print'toots are imaginary''Print

rl

and12

FLOWCHART:

Print'oequation is linear"

Print "roots are real & Equal" Print real

P1: (-b+sqrt(d)Y2a R2: (-b-sqrt(d)l2a

d:_d

imag: sqrt(dl2a

:

real* imag 12: real- imag

r1

Print'oroots are real& unreal" Print 11 & 12

Print "roots are imagina4y''Print rl andr?

SUMMARY of Proerammins Lanzuases The Evolution of Programming Languages

To build programs, people use languages that are similar to human language. The results are translated into machine code, which computers understand. Programming languages fall into three broad categories:

.

Machine languages

.

Assembly languages

.

Higher-level languages

The Evolution of Programming Languages

-

Machine Laneuages Machine languages (first-generation lanzuaees) are the most basic type of computer languages, consisting of strings of numbers the computer's hardware can use.i.e. the program is in binary form 0's and I's.

Different types of hardware use different machine code. For example, IBM computers use different machine language than Apple computers. i.e. it is a Machine dependent language.

The Evolution of Programming Languages

-

Assembly Languages Assembly languages (second-generation lanzuaees) are only somewhat easier to work with than machine languages" To create programs in assembly language, developers use cryptic English-like phrases called mnemonics (: an abbreviated OPeration CODE) to represent strings of numbers. The code is then translated into object code, using a translator called an assembler.

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There is a one-to-one correspondence betvzeen assembly language program and the machine language program.

The Evolution of Programming Languages Hiqher-Level Lanzuaqes

HigherJevel languages are more powerful than assembly language and allow the programmer to work in a more EnglishJike environment. Higher-level programming languages are divided into three "generations," each more powerful last: than the a

c o

Third- generation languages Fourth- generation languages Fifth- generation languages

Higher-Level Languages Third-Generation Lanzuases . Third-generation languages (3GLs) are the first to use true English-like phrasing, making them easier to use than previous languages"

3GLs are portable, meaning the object code created for one type of system can be translated for use on a different tlpe of system.

-

The following languages are 3GLs:

FORTAN, COBOL, BASIC, Pascal , C, C++, Java,ActiveX ...

Higher-Level Languages Fourth-Generation Lansuases Fourth-generation languages (4GLs) are even easier to use than 3GLs. 4GLs may use a text-based environment (like a 3GL) or may allow the programmer to work in a visual environment, using graphical tools. The following languages are 4GLs:

Visual Basic (VB), Visual Age and Authoring environments

Higher-Level Languages Fifth-Generation Languases Fifth-generation languages (5GLs) are an issue of debate in the programming community - some prografirmers cannot agree that they even exist. These high-level languages would use artificial intelligence to create software, making 5GLs extremely difficult to develop. Solve problems using constraints rather than algsritluns, used in

Prolog

Features of good programming language: Ease

ofuse

Portability Naturalness for the application

Reliability Safety Performance Cost

Promote strucfural programming

Artificial Intelligence

I

I

Cornpact code

Maintainability Reusability Provides interface to other languages

Concurrency suppofi Standardization

Types of programming language

BASIC

are Hundreds of high level languages have been developed and designed alnong these which is (Beginner, All purpose Symbolic Instruction code) FORTRAN, COBALT,

PASCAL, DBASE, C-Language JAVA etc. FORTRAN (Fortran Translator) was developed by IBM Corporation between 1954 and mathematical 1957 to be used for scientific and engineering application that require complex coml.iutation but it is a text base programming language'

Dennis Richie

in

1972

at Bell laboratories developed a C- programming language, C

language is a very popular package among the computer user,

it was first

used

to develop the

UNIX Operating system. C* is an extension of C, developed by Bjarne stroustrup in the early C language 1980,s at Bell laboratories. C* provicles a number of features that " spruce up" the people fiast the capabilities for doing so called object- oriented programming (OOP) Many the believe that (OOP) can greatly improve the software development process C* has become

dominant system implementation language. Java was developed

by SUN Micro system and released in 1995. Java is based on C and

and incorporates a number of features from other object oriented language" Java includes access extensive libraries for doing multimedia, networking, multi reading graphics data base

C*

and much more. Microsoft version

visual

of Java is called visual J* many people believe that Java and

J* will be the most significant

long-term competitor to Visual Basie'