Chapter  - 2 

                                     Number System 

( D ) Answer the following questions:- 

Ques:-1 Describe Decimal number system with example ?

Ans:- Some examples of decimal numbers are:- A number system which uses digits from 0 to 9 to represent a number with base 10 is the decimal system number. The number is expressed in base-10 where each value is denoted by 0 or first nine positive integers. 

Ques:-2 Briefly explain the hexadecimal number system ?

Ans:- Number systems are the technique to represent numbers in the computer system architecture, every value that you are saving or getting into/from computer memory has a defined number system.

Computer architecture supports following number systems.

• Binary number system
• Octal number system
• Decimal number system
• Hexadecimal (hex) number system

Table of the Numbers Systems with Base, Used Digits, Representation, C language representation:

Number system	Base	Used digits	Example	C Language assignment
Binary	2	0,1	(11110000)2	int val=0b11110000;
Octal	8	0,1,2,3,4,5,6,7	(360)8	int val=0360;
Decimal	10	0,1,2,3,4,5,6,7,8,9	(240)10	int val=240;
Hexadecimal	16	0,1,2,3,4,5,6,7,8,9, A,B,C,D,E,F	(F0)16	int val=0xF0;

Number System Conversions

There are three types of conversion:

• Decimal Number System to Other Base
  [for example: Decimal Number System to Binary Number System]
• Other Base to Decimal Number System
  [for example: Binary Number System to Decimal Number System]
• Other Base to Other Base
  [for example: Binary Number System to Hexadecimal Number System]

Decimal Number System to Other Base

To convert Number system from Decimal Number System to Any Other Base is quite easy; you have to follow just two steps:
A) Divide the Number (Decimal Number) by the base of target base system (in which you want to convert the number: Binary (2), octal (8) and Hexadecimal (16)).
B) Write the remainder from step 1 as a Least Signification Bit (LSB) to Step last as a Most Significant Bit (MSB).

Decimal to Binary Conversion	Result
Decimal Number is : (12345)10	Binary Number is (11000000111001)2

                                                             Make by Aakash

Decimal to Octal Conversion	Result
Decimal Number is : (12345)10	Octal Number is (30071)8

Decimal to Hexadecimal Conversion	Result
Example 1 Decimal Number is : (12345)10	Hexadecimal Number is (3039)16
Example 2 Decimal Number is : (725)10