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 |
Categories: Education
You must be logged in to post a comment.