# Data Representation

By Suresh Chand

Data refers to the symbols that represent people, events, things, and ideas. Data can be a name, a number, the colors in a photograph, or the notes in a musical composition

Data Representation refers to the form in which data is stored, processed, and transmitted.Devices such as smartphones, ipodsand computer store data in digital formats that can be handled by electronic circuitry.

Digitization is the process of converting information, such as text, numbers, photo, or music, into digital data that can be manipulated by electronic devices.

The Digital Revolution has evolved through four phases, beginning with big, expensive, standalone computers, and progressing to today’s digital world in which small, inexpensive digital devices are everywhere.

### Introduction

Data stored in different kinds

1. Numeric (0,1,2..9)
2. Alphabetic (A, B, C…Z)
3. Alphanumeric
4. Special Characters

All of them is represented in terms of 0s and 1sAnd their unique combinations

Our discussion is focus on following number systems

1. Decimal number
2. Binary number system,
3. Octal number system, and

 Base / Radix Name 2 Binary system 8 Octal system 10 Decimal system 16 Hexadecimal system

## NUMBER SYSTEM

Face value

Face value of a digit in a number is the value of the digit itself. Wherever it appears.

Place value/Position Value

Place value of a digit in a number is the value of the digit where it to appear.

Eg

1. 768534, find place value and face value of 5 in given no;

Face Value of 5 is ; 5

Place Value of 5 is; 5*100= 500

2. 0.03721; find place value of 3.

Another way;

The Place Value/Position value of a digit is 【BasePosition

In 768534 Place Value/Position valueof 5 is = 102–>5*102

A number in a particular base is written as 【(number)base of number】For example, (23)10 means that the number 23 is a decimal number(345)8 shows that 345 is an octal number.

### A. Decimal Number System

It consists of 10 digits number—0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

probably the most commonly used number system

All number in this numbering system are combination of 0-9 digits

Represented by base or radix 10/ base 10 number system

 Position 3 2 1 0 -1 -2 -3 Position Value 103 102 101 100 10-1 10-2 10-3 Quantity 1000 100 10 1 1/10 1/100 1/1000

### B. Binary Number System

The binary number system consists of two digits—0 and 1.

All binary numbers are formed using combination of 0 and 1.

All number in this numbering system are unique combination of 1s & 0s

Represented by base or radix 2

 Position 3 2 1 0 -1 -2 -3 Position Value 23 22 21 20 2-1 2-2 2-3 Quantity 8 4 2 1 1/2 1/4 1/8

### C. Octal Number System

The octal number system consists of eight digits—0 to 7.

All octal numbers are represented using these eight digits

Also called“oct”in short, is the base-8 number system

 Position 3 2 1 0 -1 -2 -3 Position Value 83 82 81 80 8-1 8-2 8-3 Quantity 512 64 8 1 1/8 1/64 1/512

The hexadecimal number system consists of sixteen digits—0 to 9, A, B, C, D, E, F, where (A is for 10, B is for 11, C-12, D-13, E-14, F-15).

All hexadecimal numbers are represented using these 16 digits.

In short “hex”

Base 16 Number System

 Position 3 2 1 0 -1 -2 -3 Position Value 163 162 161 160 16-1 16-2 16-3 Quantity 4096 256 16 1 1/16 1/256 1/4096

 Decimal Binary Octal Hexadecial 0 0000 0 0 1 0001 1 1 2 0010 2 2 3 0011 3 3 4 0100 4 4 5 0101 5 5 6 0110 6 6 7 0111 7 7 8 1000 10 8 9 1001 11 9 10 1010 12 A 11 1011 13 B 12 1100 14 C 13 1101 15 D 14 1110 16 E 15 1111 17 F

## Signed And Unsigned Number

Important Questions