Number Systems

          I would like to introduce, in this

post, the concept of  NUMBER SYSTEMS.

Many of you know it by other names but 

please, read on.
          Number systems are just different but
perfectly accurate ways of representing numbers.

          The every day number system which 

is used nearly everywhere is base ten of

course. Not many people wonder why we use

only ten digits (0-9. *Ten is formed by 1 and 0) in 

our base system. The truth is that it is not necessary

to use base ten, the only reason being we have ten 

fingers on our hands. There are several other number 

systems existing :

• Vigesimal (Base 20, used in France where the word 80 is used as four-20's)
• Quinary (Base 5, based on 5 fingers on each hand)
• Quaternary (Base 4, for 4 limbs)
• Duo-decimal (Base 12, on various parts of the body- eyes, ears, etc.)

            Bases 3 - 5 are used by tribes in Brazil. Base

12 is also useful because many numbers divide into 12.

Let's take the numbers 34 and 3 in both bases- Duodecimal

and decimal :

   34/3 = 11.111111....                 *2A / 3 = B.4

*duodecimal equivalent of 34.

             

             In decimal, we arrived at a continuous decimal

but in duodecimal, we just had a simple decimal

[B.4]. This converts into decimal as 11.11111....

This is the advantage of using different bases.
            If your'e wondering, "why not use base 12 for
everything ?", the reason mathematicians do not force
people to use on base is because no base is perfect.
I will explain how this works.
            Take bases 10 and 12, again.
Now most continuous decimals caused by division by
3 in base 10 are rendered innocuous in base 12.
            But because there are an infinite number of primes,
there will always be a prime which doesn't divide into 12,
causing a continuous fraction in base 12.
            But no base will ever be divisible by all the primes
because there are an infinite number of them