Understanding The Different Number Systems
There are 4 main types of number systems, Binary, Octal, Decimal and Hexadecimal. In this blog, we will have a look at those different number systems.
Before learning about the other number systems, let's first try to represent numbers in a different way, using what we all have learnt.
let's consider a number 3561 (randomly chosen), its expanded form will be
this can also be written as
or
did you observe the same thing which I did? while going from right to left (←) the power of 10 is increasing, interesting. Also, the number which is raised to different powers (10⁰, 10¹, 10², 10³… in this case) is the base.
The Decimal Number System
This is the system with which we all are familiar. The Decimal Number system has a range of 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) using those digits any number can be formed, the base for the Decimal number system is 10.
The Binary Number system
The Binary Number system has a range of 2 digits (0, 1), this is the system that computer uses as it can be represented digitally, 0 as a low signal and 1 as a high signal, let's have a look at an example, decimal 13
The RHS is equal to 1 × 8 + 1 × 4 + 0 × 2 + 1 × 1, which is 8 + 4 + 1 = 13.
The Octal Number System
The Octal Number system has a range of 8 digits (0, 1, 2, 3, 4, 5, 6, 7), this system has a base of 8. For example decimal number 89
The RHS is equal to 1 × 64 + 3 × 8 + 1 × 1, which is 64 + 24 + 1 = 89.
The Hexadecimal Number System
The hexadecimal number system has a range of 16 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F), you will find yourself using this system when working with colours, white in hex (hexadecimal) is FFFFFF (first 2 places for the value of red which is 255, next 2 for blue which is 255, and the last 2 values for green which is also 255). Let’s try to convert decimal 209 to Hexadecimal, we can write 209 as (13 × 16 + 1 × 1), rewriting this will give us (D = 13, in hex):-
here is a table that has values from 0–15 written in all 4 Number systems discussed in this blog, as an exercise try to understand it and convert the value from one system to another.
That’s all for This blog, Have a great day Ahead!
Yash
