DATA REPRESENTATION - BASIC CONCEPT (CLASS - XI) - IP

DATA REPRESENTATION - BASIC CONCEPT

CHAPTER - 02

CLASS - XI

Introduction

In general term computer represent information/data in different types of data forms i.e. number, character, picture, audio, video etc.

Computers are made of a series of switches/ gates. Each switch has two states: ON(1) or OFF(0).That's why computer works on the basis of binary number system(0/1). But for different purpose different number systems are used in computer world to represent information. E.g. Octal, Decimal, Hexadecimal.

NUMBER SYSTEM
SYSTEM	BASE	DIGIT
Binary	2	0  1
Octal	8	0  1  2  3  4  5  6  7
Decimal	10	0  1  2  3  4  5  6  7  8  9
Hexadecimal	16	0  1  2  3  4  5  6  7  8  9  A  B  C  D  E  F

 

Binary Number: In the binary system there are only two symbols or possible digit values, 0 and 1. Even so, this base-2 system can be used to represent any quantity that can be represented in decimal or other number system.

The binary number system is also a positional-value system, where in each binary digit has its own value or weight expressed as a power of 2.

Example

For above example, place to the left of the binary point are positive powers of 2 and place to the right are negative powers of 2.

To find the decimal equivalent of above binary number, we simply take the sum of the products of each digit value (0 and 1) and its positional value:

1010.0101 = (1x2³) + (0 x 2²) + (1 x 2¹) + (0 x 2⁰) + (0 x 2^-1) + (1 x 2^-2) + (0 x 2^-3) + (1 x 2^-4)

                    = 8 + 0 +2 + 0 + 0 + 0.25 + 0 + 0.0625 = 10.3125₁₀

Characteristics

Two symbols

0  1

Positional

Positional

1010₂ ¹ 1100₂

Most (digital) computers use the binary number system Why?

Computers are made of a series of switches/ gates. Each switch has two states:  ON(1) or OFF(0).That's why computer works on the basis of binary number system(0/1).

Decimal Number System: The decimal system is composed of 10 numerals or symbols. These 10 symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; using these symbols as digit of a number, we can express any quantity. The decimal number system, also called the base-10 system because it has 10 digit.

2512.1971 = (2x10³) + (5 x 10²) + (1 x 10¹) + (2 x 10⁰) + (1 x 10^-1) + (9 x 10^-2) + (7 x 10^-3) + (1 x 10^-4)

 In general, any number is simply the sum of the products of each digit value and its positional value.

 Octal Number System: This number system represents number using eight unique symbols: 0, 1, 2, 3, 4, 5, 6, 7. So numbers in octal system go as: 0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23……… As you must have noticed that digit 8 and 9 are not regonised by octal number system.

 Hexadecimal Number System: This number system represents numbers using sixteen unique symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8 ,9, A, B, C, D, E, F. So numbers in Hexadecimal number system go as 0, 1, 2, 3 ……,8, 9, A, B, C, D, E, F, 10, 11, 12,………,18, 19, 1A, 1B, 1C, 1D, 1E, 1F, 20, 21, …….,28, 29, 2A, 2B, 2C, 2D, 2E, 2F and so on.

The letters other than A-F are not recognized by the hexadecimal number system. So ACE, FACE, CAFÉ etc. are valid Hexadecimal number system.

 String Representation

String is any finite sequence of characters. Any string includes letters, numerals, symbols and punctuation marks.

Computers are designed to work internally with numbers. In order to handle characters, we need to choose a number for each character. There are many ways to do this

Following are some form of character set

ASCII (American Standard Code for Information Interchange): The ASCII code is used for the transfer of alphanumeric information between a computer and input/output device such as video terminal or printers. A computer also uses it internally to store the information that an operator types in at the computer’s keyboard.

 ISCII (Indian Standard Code for Information Interchange): In 1991, the bureau of Indian Standard adopted ISCII, the ISCII standard that was evolved by standardization committee. This is an eight-bit code capable of coding 256 characters. ISCII code retains all ASCII characters and offering code for Indian scripts also. Thus, it is also called Indian Scripts Code for Information Interchange.

 UNICODE: It is a worldwide character-encoding standard. It’s main objective is to enable a single, unique character set that is capable of supporting all characters from all scripts, as well as symbols, that are commonly utilized for computer processing throughout the world.

Indian Language on Unicode: The Unicode Standard has incorporated Indian scripts under the group named Asian Scripts. The Indian scripts included are Devnagari, Bengali, Gurumukhi, Gujarati, Oriya, Tamil, Telugu, Kannada, Malayalam. The Indian language block of Unicode Standard is based in ISCII-1988.

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