New Numbering System Proposal

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New Numbering System Proposal

Post by Goatboy on Mon Jan 31, 2011 10:10 am
([msg=53037]see New Numbering System Proposal[/msg])

We all know about Binary: using two states - (on|off), (true|false), (1|0) - to represent values. This is called a base-2 number system since it uses two states. In a single Binary bit, we can hold two values, and in a byte we can hold 256. This is a pretty impressive, effective way of representing any number.

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.
I'm proud to announce that I have submitted this proposal to both the Mathematical Association of America and the Institute of Electrical and Electronics Engineers, and I am eagerly awaiting their replies. In the mean time, feel free to post any comments, questions, and concerns regarding this groundbreaking new system.

Sincerely,
Goatboy
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Re: New Numbering System Proposal

Post by neuromanta on Mon Jan 31, 2011 10:17 am
([msg=53038]see Re: New Numbering System Proposal[/msg])

Maybe I missed something, but I don't get why is it better to change decimal digits to letters... or is it some kind of sarcasm? Sorry I don't get it.
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Re: New Numbering System Proposal

Post by Goatboy on Mon Jan 31, 2011 10:19 am
([msg=53039]see Re: New Numbering System Proposal[/msg])

I believe it's more satire than anything, but yes.
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Re: New Numbering System Proposal

Post by insomaniacal on Mon Jan 31, 2011 6:02 pm
([msg=53046]see Re: New Numbering System Proposal[/msg])

I've seen people argue that we should be using Hexadecimal in everyday life, so I approached this with an open mind.

WTFs ensued.
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Re: New Numbering System Proposal

Post by pretentious on Mon Jan 31, 2011 8:14 pm
([msg=53049]see Re: New Numbering System Proposal[/msg])

I'm tempted to write a long winded article exploring how a Trinary system would not take up less space to store information, but i see it's not called for
Goatboy wrote:Oh, that's simple. All you need to do is dedicate many years of your life to studying security.

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Re: New Numbering System Proposal

Post by Goatboy on Mon Jan 31, 2011 11:28 pm
([msg=53059]see Re: New Numbering System Proposal[/msg])

I see my humor has been lost. Perhaps a move to the LULZ section will help punctuate the joke.
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Re: New Numbering System Proposal

Post by sanddbox on Tue Feb 01, 2011 2:49 am
([msg=53072]see Re: New Numbering System Proposal[/msg])

neuromanta wrote:Maybe I missed something, but I don't get why is it better to change decimal digits to letters... or is it some kind of sarcasm? Sorry I don't get it.


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