Number System 

Any number system there is an ordered set of symbols known as digits with rules defined for performing arithmetic operation like addition, multiplication etc. A collection of these digits makes a number which in general has two parts -- integer and fractional, set apart by a radix point(.)

                

 

where N= a number

            b=radix or base of the number system

            n = number of digits in integer portion

            m=number of digits in fractional portion

          dn-1= most significant digit(msd)

          d-m=least significant digit(lsd)

Types of Number System

The four most common number system types are:

1. Decimal number system (Base- 10)
2. Binary number system (Base- 2)
3. Octal number system (Base-8)
4. Hexadecimal number system (Base- 16)

 Binary Number System:

The number system wit base(or radix) two is known  as the binary number system .Only two symbols   are used to represent numbers in this system and these are 0 and 1. These are known as bits. 

list of 20 number with decimal number and binary number

Decimal	Binary
1	01
2	10
3	11
4	100
5	101
6	110
7	111
8	1000
9	1001
10	1010
11	1011
12	1100
13	1101
14	1110
15	1111
16	10000
17	10001
18	10010
19	10011
20	10100

 

OCTAL  NUMBER SYSTEM:

The number system with base (or radix) eight is known as the octal number system. In this system, eight symbols ,0,1,2,3,4,5,6 and 7 are used to represent numbers. Similar to decimal and binary number systems, it is also a positional system and has, in general, two parts: integer and fractional, set apart by a radix(octal) point(.). 

                                            

                                                

Decimal	Octal
1	01
2	2
3	3
4	4
5	5
6	6
7	7
8	10
9	11
10	12
11	13
12	14
13	15
14	16
15	17
16	20
17	21
18	22
19	23
20	24

 

HEXADECIMAL NUMBER SYSTEM

Hexadecimal number system is very popular in computer uses. The base for hexadecimal number system is 16 which   requires 16 distinct symbols to represent the numbers. These are numerals 0 through 9 and alphabets A through F. Since numeric digits and alphabets both are used to represent the digits in the hexadecimal number system , therefore , this is an alphanumeric number system. 

 

                                                                      

Decimal	Hexadecimal
1	01
2	2
3	3
4	4
5	5
6	6
7	7
8	8
9	9
10	A
11	B
12	C
13	D
14	E
15	F
16	10
17	11
18	12
19	13
20	14