# Why we need different number systems ?

string1037
why there are so many number systems when we can only use anyone of them ?
What's the need of octal and hexadecimal ?

Mensanator
why there are so many number systems when we can only use anyone of them ?
What's the need of octal and hexadecimal ?

They are easier to convert to binary.

why there are so many number systems when we can only use anyone of them ?
What's the need of octal and hexadecimal ?

Because some are more optimal than others for a specific purpose.

Here are few examples:

1. Time and Date

Time and date uses multiple bases to express time and date in relation to the amount of time it takes the Earth to revolve around the sun, and also with respect to the time it takes for the Earth to make a complete revolution on its own rotation (around its axis).

In terms of seconds up to days, we define a second to be a standard measure (something to do with the cesium atom, or in terms of the speed of light, roughly the amount of time it takes light to travel from here to the moon).

Now we use 60 seconds for minute, 60 minutes for an hour and 24 hours for a day.

On top of this we use 365 days for a standard year or an approximation of using 7 days for a week and 52 weeks for a year.

Notice that for measuring a year in terms of seconds we have a 365:24:60:60 representation: a mixture of different basis that are optimized for a specific purpose of relating time and date to the revolutions of our Earth and around our sun.

If we used base 10, then we would probably get some weird number and it wouldn't make as much sense as our current format.

2. Computers

If you ever do a computer degree (Computer Science, Computer Engineering, Electrical Engineering etc), you'll end up learning about logical gates. You'll also learn that using these gates you can do everything from arithmetic computations to logical computations and so on. The atomic version of information is the bit, and based on this we use any kind of analysis in the context of computer science and engineering to refer to bits or collections of bits.

Octal and hexadecimal representations just make it easier to deal with collections of bits. Instead of reading a sequence of 32 1's and 0's, it's a lot easier to read 8 hexadecimal digits.

These are just two examples, and I'm sure that there are more out there.

string1037
Thank you sir. Its very helpful for me.