Some of us have heard of Trinary, which - you guessed it - uses three states: (on|neutral|off), (-1|0|+1), (0|1|2) etc. This is called a base-3 number system because it uses three states, as opposed to base-2 which uses two. Because of this, a single "trit" (trinary bit) can hold up to three values, and a "tryte" (trinary byte, or 6 trits) can hold up to 729 values. That's way more than a byte can hold, and it occupies less space! You can count up to 242 on one hand in Trinary as opposed to a measly 31 in Binary!

Then of course there is Hexadecimal (base-16 using letters in addition to numbers) and plain old Base-64 (lower-case, UPPER-CASE, + and /), but I won't go into those in detail. You get the idea.

As we can see, as the number of states a number system can address increases, so does the efficiency of that system.

This got me thinking...

Binary is good. Trinary is great. Quaternary and Quinary (base-4 and base-5, respectively), while not widely adopted, would naturally be better. But what beats all of them?

Decimary

Think about it. We could use ten states - (A|B|C|D|E|F|G|H|I|J) - to represent values. A single "dit" (Decimary bit) could address up to 10 values. Similarly, a "dyte" (Decimary byte, 10 dits) could address a whopping TEN BILLION (10,000,000,000) values!

For example, counting would be from A to J, and then would proceed similarly to the other number systems:

- Code: Select all
`Decimary`

------------------------------------------------------------------------------------

A B C D E F G H I J BA BB BC .. BI BJ CA CB CC .. CI CJ DA DB .. BAA

0 1 2 3 4 5 6 7 8 9 10 11 12 .. 18 19 20 21 22 .. 28 29 30 31 .. 100

------------------------------------------------------------------------------------

Decimal

I think this base-10 system could be used extensively in today's world. The benefits and applications are endless:

- We have 10 fingers, and Decimary uses 10 (or should I say, "BA") values. It just naturally fits!
- Decimary has excellent value addressing capabilities.
- Conversions to and from other number systems would be simple.

Sincerely,

Goatboy