8th Class Computers Science Data Representation Introduction to Data Representation

Introduction to Data Representation

Introduction

Classification of computers are basically divided according to their speed, memory capability, peripheral support etc. Different types of computers are used in different sectors. Microcomputer is the personal computer, whereas mini and super computers are more advanced and used in the sectors where big amount of data is processed. Number system in computing are used for coding characters in numbers. There are four type of number systems in digital system. They are Binary, Octal, Decimal and Hexadecimal. This chapter includes the classification of computer's number system.

Binary Number System

A number system with a base-2 is known as binary number system. The whole binary number system depends on two digits, these are 0 and 1 respectively. By using these two digits, the numbers in binary number system are written. Thus the place value of a digit in a number increases in the power of 2 from right to left.

Characteristics

• A positional number system.
• Has only 2 symbols or digits (0 and 1) hence its base = 2.
• The maximum value of a single digit is 1 (one less than) value of the base.
• Each position of a digit represents a specific power of base (2).
• This number system is used in computers.

The following example shows how to convert binary number 1010101 into decimal number:

• The place value of 1 is : 1*2⁰ = 1
• The place value of 0 is : 0*2¹
• The place value of 1 is : 1*2² = 4
• The place value of 0 is : 0*2³ = 0
• The place value of 1 is : 1*2⁴ = 16
• The place value of 0 is : 0*2⁵ = 0
• The place value of 1 is : 1*2⁶ = 64
• The decimal number = 1 + 4 + 16 + 64 = 85

Example

Decimal Number System

A system with base = 10 is a decimal number system. Thus, it means that there are ten basic digits on which the decimal number system depends. The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. By using these ten digits, all the numbers in decimal number system are .written. Thus, the place value of a digit in a number increases the power from right to left.

Characteristics

• A positional number system.
• Has 10 symbols or digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) Hence, its base =10.
• The maximum value of a single digit is 9 (one less than the value of the base).
• Each position of a digit represents a specific power of the base (10).

The following are the place value of each digit of number 5471:

• The place value of 1 is : 1* 10⁰ = 1
• The place value of 7 is : 7*10¹ = 70
• The place value of 4 is : 4*10² = 400
• The place value of 5 is : 5*10³ = 5000

Example:

Decimal Binary Conversion Table

Steps to convert Decimal to Binary conversion by short division by two with remainder:-

1. Divide the decimal number to be converted by the value of the new base. In this case divide it by 2.
2. Record the remainder from step 1 as the rightmost digit.
3. Divide the quotient of the pervious by the new base.
4. Record the remainder from step 3 as the next digit (to the left) of the new base number.
5. Bottom to top sequence of remainder will be the required converted number. Repeat Step 3 & Step 4, recording remainders less than the digit of new base so that it cannot be divided.

Example:

Octal Number System

Octal number system consists of eight digits from 0 to 7 the base of Octal system is 8. Each digit position in this system represents the power of 8. Any digit in this system is always less than 8.

Characteristics

• A positional number system.
• Has total 8 symbols or digits (0, 1, 2, 3, 4, 5, 6, 7). Hence its base =8.
• The maximum value of a single digit is 7 (one less than the value of the base).
• Each position of a digit represents a specific power of the base (8).
• Since there are only 8 digits, 3 bits are sufficient to represent any octal number in binary.

Example:

Hexadecimal Number System

The Hexadecimal number system is based on base 16. Therefore, it means, there are 16 basics digits on which whole hexadecimal number system depends. These digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 and 15, whereas the numbers 10, 11, 12, 13, 14, and 15 are also represented as A, B, C, D, E and F. By using these 16 digits all the numbers in Hexadecimal number system are written. Thus the place value in hexadecimal system is increased in the power of 16 from right to left.

Characteristics

• A positional number system.
• Has total 16 symbols or digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F). Hence its base =16.
• The symbols A, B, C, D, E and F represent the decimal value 10, 11, 12, 13, 14, and 15 respectively.
• The maximum value of a single digit is 15 (one less than the value of the base).
• Each position of a digit represents a specific power of the base (16).
• Since there are only 16 digits, 4 bits are sufficient to represent any hexadecimal number in binary.

Example

Introduction to ASCII

ASCII (American Standard Code for Information Interchange) is a seven bit code which includes 128 characters. Basically it is a method of character encoding. In 128 characters. Basically it is a method of character encoding. In 128 characters, 33 are printable characters and 95 are non-printable characters. The ASCII code assigns an integer value for each symbol in the character set, such as letters, digits, punctuation marks, special characters and control characters.