Number Systems (In Short)

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

SystemBase / RadixSymbols / Digits
Decimal100,1,2,3,4,5,6,7,8,9
Binary20, 1
Octal80, 1, 2, 3, 4, 5, 6,7
Hexadecimal160, 1, … 9,A, B, C, D, E, F

Quantities/Counting


Decimal

Binary

Octal
Hexa-
decimal
0000000
1000111
2001022
3001133
4010044
5010155
6011066
7011177
8 1000 10 8
9 1001119
10101012A
11101113B
12110014C
13110115D
14111016E
15111117F
16 10000 2010
17100012111
18100102212
19100112313
20101002414
21101012515
22101102616
23101112717