Re: OT: Need help with numeric bases

On Mon, 24 Feb 2003 21:55:04 -0800 Apollo Hogan
<apollo@...> writes:
> One can also do it with Multiplication:  to convert x to base b,
> just
> iteratively apply the following steps:  (Assuming 0<=x<1 already)
> 1) multiply by b
> 2) the result will have an integer part between 0 and b-1
> (inclusive);
>    that is the next digit of your base-b rep
> 3) replace x with its fractional part
>
> For example, to convert 0.125 to base 7, we get:
>         rep     x       x*7
>         0.      0.125   0.875
>         0.0..   0.875   6.125
>         0.06..  0.125   0.875
> etc.  Here we get a repeat already, so we see that 0.125 (base 10)
> is
> written as 0.0606060606... in base 7.
>
> A more interesting example, write PI in base 12:  (We first strip
> off the
> integer part 3)
>         rep     x               x*12
>         3.      0.1415926..     1.69911184..
>         3.1     0.69911184..    8.38934211..
>         3.18    0.38934211..    4.67210540..
>         3.184   0.67210540..    8.06526483..
>         3.1848
> etc. ad nauseum; hence PI = 3.1848... in base 12.
hmm... what about non-integer bases?

> --Apollo
Robert Wilson
han_solo55@juno.com
http://kuvazokad.free.fr
fanai kabl dala ninl.

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