[Feature Request] Add alternate Binary Positional Numeral system.

[pie75]

A long time ago, i watched a video on binary number systems, called "the best way to count", which, among many things, presented a positional numeral style for binary, that seemed interesting and intuitive. (the description of it is timestamped here)

The basic idea is pretty simple, replace 0 with a short vertical bar, and 1 with a long vertical bar. So numbers could look like this:

Western-Arabic Decimal	Western-Arabic Binary	Simplified Binary
0	0	.
1	1	I
2	10	I.
3	11	II
4	100	I..
5	101	I.I
6	110	II.
7	111	III

i've played with handwriting it at times, but never had a practical use for better binary legibility -- until i started playing Gauguin. I primarily play Gauguin in binary.

i'm curious to see if really practically using system would make it easier to do binary arithmetic, as my main problem is constantly reading the numbers as decimal, which makes my regular associations with them more crosswired; and while i can still do the algorithms, it's harder to make associations between numbers that i already understand (such as 101 = 10 + 11. (aka I.I = I. + II ))

The simplest solution is an option to replace the numbers 0 and 1 with . and I.
Alternatively, a custom font that has just the 0 and 1 glyphs replaced with lines.
Though if possible, a more bespoke solution would be nice; to join short groups of vertical bars with a horizontal bar, to make legibility easier, as described in the video.

[meikpiep]

Sounds very promising. :)

I'm optimistic that the current font will fit for this and will look into details like grouping - the implementation should be a kind of straight forward.

We have to deal with "where to put the new option", avoiding to overwhelm the user. One of my existing ideas is to show sample values when choosing the number system. This could be great to put this notation with some explanation or link.

[meikpiep]

I just watched the part of the video - its hard to not get addicted to it. :)

I love the idea and now I actually get why simply exchanging the characters won't include grouping. I'm willing to implement this representation with a nice grouping.

The only question left for me is: What is a good fit for the number of digits to group? My intuition tells me 'at most five'...
@pie75 & others: Do you have an idea or a reference or any info? Implementation wise, it won't be a huge difference if I connect 3 or 5 lines with a horizontal line. The difficult part will be fitting the digits into the space, a la 'variable font size'.