Decision for the glyphs to represent binary numbers

Mikhail Vasilev

Task: represent binary numbers using existing and widely accessible glyphs.

Requirements :
1.  Maximize legibility.
2.  Consistent with the lowercase flow.
3.  Use more or less established glyphs present in popular fonts.
4.  Avoid parsing ambiguity, that means should use "rare" or non-alphabetic glyphs.
5.  Should be equal width characters.

For now it is for my personal use but there are some projects that will make use of it. E.g. I am developing a new programming language and want to include such numeric literals in its syntax.

Future goals among others is to popularize binary number usage in general and to set stakes for particular glyphs.  Still, to narrow down the problem for now, let's imagine that it is only for a programming language that uses modern latin system as a base. I've approached this task several times past years and here is what I currently have and think.

Firstly, I already made my decision for the glyph to represent the zero and it will be En dash.
Dash and letter structure showed the best legibilty and reading efficiency in general, so this principle clearly won over other variants.
For example I can present numbers like this:
 
----  -s-s  ssss    (0000  0101  1111)

Of course if I'd simply define my own characters, that would be the best, but obviously that will not allow real digital application that can be used now or in any near future.
 
The big question is - which glyph for the "one"? There is a dilemma: if I use some commonly used letter (there are nice fits), but this would  create potential problems like ambiguity with spoken words and what is even worse, digital parsing of text elements.  
Ideally numbers in the text stream should not confuse the parser or search functionality (tat means don't need to be surrounded or prefixed by additional separators).
So I am left with some "non-letter" glyphs or letters that are rarely used. But this again raises question, what can be considered as rarely used and by whom?

Fonts that I have used for viewing:
Arial
Cambria
Consolas
Courier New
EB Garamond
Liberation Sans
Liberation Serif
Tahoma
Times New Roman


So here is my top 3 list, selected from sevral dozens of glyphs.
5 digit grouping is used here.

1
028f - LATIN LETTER SMALL CAPITAL Y

num1 =  ʏʏ–ʏ–  ʏ–ʏʏ–  –ʏʏ––  
num2 =  –––––  –ʏ–ʏ–  ʏ–ʏ––  
num3 =  ʏʏʏʏʏ  ʏ–ʏ––  –ʏ–ʏʏ  

2
03ed - COPTIC SMALL LETTER SHIMA

num1 =  ϭϭ–ϭ–  ϭ–ϭϭ–  –ϭϭ––  
num2 =  –––––  –ϭ–ϭ–  ϭ–ϭ––  
num3 =  ϭϭϭϭϭ  ϭ–ϭ––  –ϭ–ϭϭ  

3
1d0b - LATIN LETTER SMALL CAPITAL K

num1 =  ᴋᴋ–ᴋ–  ᴋ–ᴋᴋ–  –ᴋᴋ––  
num2 =  –––––  –ᴋ–ᴋ–  ᴋ–ᴋ––  
num3 =  ᴋᴋᴋᴋᴋ  ᴋ–ᴋ––  –ᴋ–ᴋᴋ  


Few others that did not make it to the top:

0473 - CYRILLIC SMALL LETTER FITA

num1 =  ѳѳ–ѳ–  ѳ–ѳѳ–  –ѳѳ––  
num2 =  –––––  –ѳ–ѳ–  ѳ–ѳ––  
num3 =  ѳѳѳѳѳ  ѳ–ѳ––  –ѳ–ѳѳ  

028a - LATIN SMALL LETTER UPSILON

num1 =  ʊʊ–ʊ–  ʊ–ʊʊ–  –ʊʊ––  
num2 =  –––––  –ʊ–ʊ–  ʊ–ʊ––  
num3 =  ʊʊʊʊʊ  ʊ–ʊ––  –ʊ–ʊʊ  

04ff - CYRILLIC SMALL LETTER HA WITH STROKE

num1 =  ӿӿ–ӿ–  ӿ–ӿӿ–  –ӿӿ––  
num2 =  –––––  –ӿ–ӿ–  ӿ–ӿ––  
num3 =  ӿӿӿӿӿ  ӿ–ӿ––  –ӿ–ӿӿ  

1d24 - LATIN LETTER VOICED LARYNGEAL SPIRANT

num1 =  ᴤᴤ–ᴤ–  ᴤ–ᴤᴤ–  –ᴤᴤ––  
num2 =  –––––  –ᴤ–ᴤ–  ᴤ–ᴤ––  
num3 =  ᴤᴤᴤᴤᴤ  ᴤ–ᴤ––  –ᴤ–ᴤᴤ  



Main doubts are about non-equal width of these characters in some fonts, but I assume that can be fixed by choosing different
font if an editor allows multiple fonts rendering. Unfortunately not many code editors allow for that but let's ignore this
issue for now.



Possible topics for discussion:

Which one do you find most legible combination?
(that would need to be tested in various fonts of course)
Any comments on such solution in general?
Which digit grouping you'd prefer (3, 4, 5 ...)?

Florian Pircher

What about +−++−−−+−++−−−+−+−++−++?

Mikhail Vasilev

Florian Pircher said:

What about +−++−−−+−++−−−+−+−++−++?

This was one of the candidates.
Cons are: it is not very consistenet with the lowercase flow (for most fonts). Plus and minus chars are quite wide in most fonts (wider than an average letter and En dash) and most of the time not vertically aligned with the lowercase.

Also in general, slightly less legible to my eye than the "winners" especially in regular weight fonts like Times New roman.
Some semibold fonts give much better look for this combination.
So could be good if assume rich text format, i.e. setting different font family and size on the same line.
But I am still on the fence whether I make this assumption or not while judging.