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Topic: Question about Base
Replies: 12   Last Post: May 19, 2013 5:01 PM

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Posts: 5
Registered: 5/18/13
Re: Question about Base
Posted: May 19, 2013 5:01 PM
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On Sun, 19 May 2013 06:42:02 -0700 (PDT), JT
<> wrote:
>On 18 Maj, 10:02, Jymesion <> wrote:
>> I'm playing around with a science-fictional arithmetic, and I want to
>> explore any established concepts which intersect with what I'm doing.

>The principles of bijective zeroless base will of course work for
>anybase not just ternaries.

I used ternary only as an example (it's been decades since I used
mathematical terminology, and I was afraid I'd misuse/misremember it
-- I thought a simple example would avoid any misunderstanding).

If I were to attempt to put it into proper terms, the system I'm
playing with is:
A multibase system using position values with duplex digits sans zero.
(Is that anywhere near comprehensible?)

What it amounts to, in laymen's terms (my preferred method), is:

There are only two symbols: a stylized stroke for '1' and a stylized
two strokes for '2'.

Each digit contains two positions, upper and lower. Symbols in the
second position are inverted to distinguish them.

Digits are created using Base3. The digits are therefore:
1 = 1 over empty
2 = 2 over empty
3 = empty over 1
4 = 1 over 3
5 = 2 over 3
6 = empty over 2
7 = 1 over 6
8 = 2 over 6

The system is Base8 without a zero.

By this, the only things which must be learned by rote are:
The symbol '1'
The symbol '2'
1+2 invokes position value, a '1' in the second position in the digit.
Symbols in the second position are inverted.
1+8=11 because a digit must be added to create another position.

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