On Saturday, April 24, 2021 at 10:35:03 PM UTC+2 Glauco wrote:

> Hi Kunhao,
>
> in addition to the answers you already got about the representation, in 
> case you don't already know about
>
> http://us.metamath.org/mpegif/df-dig.html
>
> in Alexander's mathbox: "Definition of an operation to obtain the k_th 
> digit of a nonnegative real number in the positional system with 
> base b.  k=-1   corresponds to the first digit of the fractional part"
>
> I don't know if Alexander has also done some work on an "efficient" way 
> for generic base representations. 
>

 No, I haven't done anything more for generic base representations. I just 
needed a generalization of http://us2.metamath.org:88/mpeuni/df-bits.html 
which is applicable also for reals instead of integers only, the 
generalization from base two to arbitrary bases was just a by-product.

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