What is a Number System?

Number System defines a set of values used to represent
quantity.There are different types of Number systems.

Decimal Number

Binary Number

Octal Number

Hexadecimal Number

What is Base/Radix ?

The base of number system is simply the number of
different digits , including zero that exist in the number
system.

A number system of radix r, typically has a set of r
allowed digits belongs to (0,1,2…..r-1).

Example

(N)r (0,1,2,…,r-1)

(195)10 (0,1,2,3,…,9)

Types of Number Systems

System	Base / Radix	Symbols / Digits
Decimal	10	0,1,2,3,4,5,6,7,8,9
Binary	2	0, 1
Octal	8	0, 1, 2, 3, 4, 5, 6,7
Hexadecimal	16	0, 1, … 9,A, B, C, D, E, F

Quantities/Counting

Decimal	Binary	Octal	Hexa- decimal
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
16	10000	20	10
17	10001	21	11
18	10010	22	12
19	10011	23	13
20	10100	24	14
21	10101	25	15
22	10110	26	16
23	10111	27	17