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Topic: NyaN fractions and partitioning of Naturals into other NyaN bases
then ternary.

Replies: 13   Last Post: Mar 16, 2013 5:36 AM

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JT

Posts: 1,150
Registered: 4/7/12
Re: NyaN fractions and partitioning of Naturals into other NyaN bases
then ternary.

Posted: Mar 15, 2013 12:17 PM
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On 15 mar, 17:04, JT <jonas.thornv...@gmail.com> wrote:
> Is there name for fractions when partitioned into other bases then
> decimal, in decimal base they are of course decimals but what do you
> call them in binary, octal, hexa and so on?
>
> Evidently transfer principle either did not understand how NyaN works
> or mocking me and i have no clue as to why.
> But below is fractions as written in NyaN bases it have some
> aestatichal symmetry that 0 based bases lacks.
>
> Binary         1=.2   1/2=.1     2/2=.2   1/4=.(1)1     2/4=. (1)2 ...
> ->...
> Ternary       1=.3    1/3=.1     2/3=.2   1/9=.(1)1     2/9=.(1)2
>  ->             1/27=.(2)1      2/27=.(2)2     1/81=.(3)1      2/81=.
> (3)2
> Quaternary  1=.4    1/4=.1     2/4=.2   1/16=.(1)1   2/16=.(1)2
> -> ...
> Quinary       1=.5    1/5=.1     2/5=.2   1/25=.(1)1   2/25=.(1)2
> -> ...
> Senary        1=.6    1/6=.1     2/6=.2   1/36=.(1)1   2/36=. 1)2
> -> ...
> Septenary   1=.7     1/7=.1     2/7=.2   1/49=.(1)1   2/49=.(1)2
> ->...
> Octal          1=.8     1/8=.1     2/8=.2   1/64=.(1)1   2/64=.(1)2
> ->...
> Nonary        1=.9     1/9=.1     2/9=.2   1/81=.(1)1   2/81=.(1)2
> ->...
> Decimal       1=.A    1/10=.1   2/10=.2  1/100=.(1)1  2/100=.(1)2
>
> Feel free to fill in the blanks it is alot easier then standard
> numbers systems.


Once one realise that each fraction with a denominator that are prime
can not be expressed in other bases then that prime or multiples of
it, you better stay out from using them in arithmetics and go for
fractions all the way to not be bothered with missing digitplaces and
precision. As to why digital circuits and programmers try to partition
into decimals i have really no good answer, is it because of realworld
standarisations?




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