Hello everyone,

In this post, I will be talking about Number Systems. Yes, Even after researching and discussing on such advance topics like Speech Recognition, Image processing etc. I’m still posting this basic but very important thing for hackers, Wait! Chill, I’m using first term for hackers. Those who are into Computing.

Being honest, I have worked hundreds of times on Number Systems but I never tried to explore things behind them and used to just convert from one number system to other and Simply make them work for me.

So in this post, I’m not going to tell you how to convert from Binary ( A Number System ) to Hexadecimal ( Another one) or anyother. This one is going to be about advantages and disadvantages of each Number System. Also, Why and where do we need use these Number Systems.

From the invention ( 5th and 6th Century ) of Numbers by Aryabhata and revised by Brahmagupta, We have many Number Systems in this world, But obviously i’m not going to talk about all of them. So here’s the list of Number Systems that i have researched ( Little bit only ) on : Decimal, Binary, Hexadecimal and Octal.


Has a base of power 10, Uses “1234567890” to represent numbers. Easily readable. Used by humans. Easily manipulated. When it comes to computing, Can not work on its own, Uses other number system according to the situation. No benefits on Computing aspect.


Has a base of power 2, Uses “1” or “0” to represent numbers. Always works on core, But hard to read because of confusing “1” n “0” representation as well as representations can be really huge sometimes. *Very important point* Used when representation needs finite width like 8, 16, 32 and 64 bits (Example : Memory Cells, Registers etc.) and processors understands binary only.


Has a base of power 16, Uses “0123456789ABCDEF” to represent numbers. Fastest at manipulation work than any other number system. So common used for Encryption, Image Processing and other processes, Where date is huge but needs to be manipulated very quickly. Used when short and human friendly representation is required. Each character in Hexadecimal representation 4 binary digits (Nibble).


Has a base of power 8, Uses “01234567” to represent numbers. The actual invention of motives that we use to describe Hexadecimal. Used when representation needs to be short and in numbers only ( Example: CHMOD – File permissions in Unix ). Second most used by humans after Decimals. Each character in Octal representation 3 binary digits.

** Most important, Usage of these number systems varies on terms like Signed and Unsigned values, Magnitudes and Specially when it comes to embedded systems.

I will be posting more advantages, disadvantages and specific examples of Usage of these number systems in comments 🙂

That’s it for today,

Puneet Kalra