Computer - Number System

When we type some letters or words, the computer translates them in numbers as computers can understand only numbers. A computer can understand the positional number system where there are only a few symbols called digits and these symbols represent different values depending on the position they occupy in the number.

The value of each digit in a number can be determined using −

• The digit
• The position of the digit in the number
• The base of the number system (where the base is defined as the total number of digits available in the number system)

Decimal Number System

The number system that we use in our day-to-day life is the decimal number system. Decimal number system has base 10 as it uses 10 digits from 0 to 9. In decimal number system, the successive positions to the left of the decimal point represent units, tens, hundreds, thousands, and so on.

Each position represents a specific power of the base (10). For example, the decimal number 1234 consists of the digit 4 in the units position, 3 in the tens position, 2 in the hundreds position, and 1 in the thousands position. Its value can be written as

(1 x 1000)+ (2 x 100)+ (3 x 10)+ (4 x l)
(1 x 103)+ (2 x 102)+ (3 x 101)+ (4 x l00)
1000 + 200 + 30 + 4
1234

As a computer programmer or an IT professional, you should understand the following number systems which are frequently used in computers.

S.No.	Number System and Description
1	Binary Number System Base 2. Digits used : 0, 1
2	Octal Number System Base 8. Digits used : 0 to 7
3	Hexa Decimal Number System Base 16. Digits used: 0 to 9, Letters used : A- F

Binary Number System

Characteristics of the binary number system are as follows −

• Uses two digits, 0 and 1
• Also called as base 2 number system
• Each position in a binary number represents a 0 power of the base (2). Example 2⁰
• Last position in a binary number represents a x power of the base (2). Example 2^x where x represents the last position - 1.

Example

Binary Number: 10101₂

Calculating Decimal Equivalent −

Step	Binary Number	Decimal Number
Step 1	101012	((1 x 24) + (0 x 23) + (1 x 22) + (0 x 21) + (1 x 20))10
Step 2	101012	(16 + 0 + 4 + 0 + 1)10
Step 3	101012	2110

Note − 10101₂ is normally written as 10101.

Octal Number System

Characteristics of the octal number system are as follows −

• Uses eight digits, 0,1,2,3,4,5,6,7
• Also called as base 8 number system
• Each position in an octal number represents a 0 power of the base (8). Example 8⁰
• Last position in an octal number represents a x power of the base (8). Example 8^x where x represents the last position - 1

Example

Octal Number: 12570₈

Calculating Decimal Equivalent −

Step	Octal Number	Decimal Number
Step 1	125708	((1 x 84) + (2 x 83) + (5 x 82) + (7 x 81) + (0 x 80))10
Step 2	125708	(4096 + 1024 + 320 + 56 + 0)10
Step 3	125708	549610

Note − 12570₈ is normally written as 12570.

Hexadecimal Number System

Characteristics of hexadecimal number system are as follows −

• Uses 10 digits and 6 letters, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
• Letters represent the numbers starting from 10. A = 10. B = 11, C = 12, D = 13, E = 14, F = 15
• Also called as base 16 number system
• Each position in a hexadecimal number represents a 0 power of the base (16). Example, 16⁰
• Last position in a hexadecimal number represents a x power of the base (16). Example 16^x where x represents the last position - 1

Example

Hexadecimal Number: 19FDE₁₆

Calculating Decimal Equivalent −

Step	Binary Number	Decimal Number
Step 1	19FDE16	((1 x 164) + (9 x 163) + (F x 162) + (D x 161) + (E x 160))10
Step 2	19FDE16	((1 x 164) + (9 x 163) + (15 x 162) + (13 x 161) + (14 x 160))10
Step 3	19FDE16	(65536+ 36864 + 3840 + 208 + 14)10
Step 4	19FDE16	10646210

Note − 19FDE₁₆ is normally written as 19FDE.

See more on Computer Tutorial

Computer Overview

Computer Fundamental Tutorial

Computer Application 

Computer - Generation

Computer - Type 
Computer - Components
Computer - CPU 
Computer - Input Devices
Output - Devices 

Computer - Memory 

Random Access Memory

Computer Read Only Memory
Computer - Motherboard 

Computer - Memory - Unit

Computer - Port 
Computer - Hardware
Computer - Number System   

Always check for more updates. . .

If you would like to donate to Ykamazingworld please click here. 

Check for more updates on Ykamazingworld Business List.

Click to view Director's Profile

To meet your needs with Ykamazingworld click on: http://metyourneeds.blogspot.com/ 

[Home Page] [Met your needs] [About Ykamazingworld Nigeria Enterprises] [Footwear and Leather Production] [Computer & Businesses] [Media and Communication Studios] [Films and Theatre Production Studios] [Vegetable Oil Dealer] [Home Planning & Building Engineer]  Farm Food Production Fashion, Wears and Printing Production Home-made and Cosmetics Ice-block Depot, Drinks, Provision and Business Ventures [Ykamazingworld Search] [Carrier and Opportunity] [Company Overview] [Our Objectives] [Our Vision] [Our Goals] [Our Products] [Our Services] [Networking & Communications] [Consultancy] [Sales of Footwear and Leather Suppliers] [Computer Industrial Training (I.C.T)] [Footwear Industrial Training (F.I.T)] [Payment Rules and Regulation] [Sponsors or Fund Raising] [Ykamazingworld Proposals(for Partnerships)] [Ykamazingworld Banks & Accounts] [Social Media] [Our Address] [Our Contacts] [Ykamazingworld Weblinks] [GOto Blog] [GOto WebChatrooms] [GOto Books and Publishing] [GOto Word of Wisdom] [GOto Answers.com] [Notice for all our Clients]

Together, we rise to the future. . .