Dozenal, binary and hexadecimal numbers with new numerals only.
A few hours ago I suggested in an article here on Medium that binary might be written in unique numerals in order to distinguish it from decimal. I suggested that 101two might be written fgf and pronounced ‘ni si’ as a normal number and ‘eff jee eff’ as digits.
I’ve done some thinking since then and one thing I realized was that given the prevalence of hexadecimal and the associated use of ‘F’ as a numeral meaning fifteen, ‘f’ is not the best choice for a binary numeral, because when pronounced as digits, ‘F’ and ‘f’ sound the same.
Another thought was that it would be nice if hexadecimal could spoken and written proudly, by which I mean without acknowledging that it is in some way nonstandard, and to achieve that it needs to be by it’s written numerals distinct from base ten, and also by it’s pronunciation. Then it can stand next to decimal as an equal, if you like, and a hexadecimal speaker can stand next to a decimal speaker as an equal, if you like. This needs to be across the board, so that no hexadecimal number needs to bear a label to distinguish it from a decimal number. Likewise with binary numbers. Likewise with dozenal.
A Japanese person (or indeed anyone who can speak and write Japanese) in England is everywhere and at all times free to speak and/or write in Japanese without adding in English, “that’s Japanese”. The reason the Japanese person can do it (without causing confusion and therefore resentment) is that Japanese always sounds nothing like English and Japanese script always looks nothing like English.
Similarly the user of an alternative base would be free to use any base anywhere, without saying which base it was, or even saying that it was not base ten, without causing confusion, if the base were instantly identifiable, ideally as a specific base, or if not, at least as being not decimal or any other commonly spoken alternative base.
How about 101two is written ‘svstwo’ or just ‘svs’? ‘s’ and ‘v’ are both near the end of the alphabet and won’t conflict with hexadecimal. I was thinking that perhaps when speaking fast, ‘svs’ might change from ‘ess vee ess’ to “et fee et” or even to “ e’ fee e’ ” or “ e’ pee e’ ”, in other words with ‘s’ sounding like ‘et’ with a dropped ‘t’ and substitution of a glottal stop, and ‘v’ pronounced like ‘pee’ because it’s quicker and easier and clearer.
[Another idea would be to have 101two written ‘sps’, I suppose, but I like the idea of the left hand being able to type binary numbers alone while the right hand is free to use the mouse and the numeric keypad.]
In an extreme scenario ‘svs’ might shorten to “ e’ ee e’ ”, and sound a bit like Morse code’s ‘dit dit dit dah dah dah…’ spoken form. e’ might even change to a’ (‘at’ with the ‘t’ dropped) to make the sounds more distinct while not sounding so much like spoken Morse code that it could be mistaken for it.
Another way ‘svs’ might be pronounced as digits at high speed is ‘etty et’. Ten would be ‘svsv’ and ‘etty etty’, with ‘etty’ rhyming with ‘Betty’. Using a comma before each group of four digits, s,vsvs (1,0101two)might be pronounced as digits as ‘et ee-et ee-et’ of even ‘et yet yet’ or “ e’ ye’ ye’ ”. As normal number it would be pronounced, ‘mi ni si’ which has no ‘ee’ sound.
Hexadecimal numbers if you wanted to illustrate how they are binary numbers in other form, could have the numerals replaced with binary numbers pronounced either as digits or as normal numbers. Thus hexadecimal FE might be pronounced as digits as “mi ni ti si,(not sure about the comma) mi ni ti” or “et et et et, et et etty” and as a normal number as “mi ni ti si ri mi ni ti”.
You’d need nondecimal symbols for the fifteen numerals of hexadecimal. Zero can stay the same without causing ambiguity, although it might be a good idea to replace that too, because it looks too much like an upper case ‘o’.
A to F for ten to fifteen could be kept, while one to nine could be G,H,J,K,L,M,N,P, and R. If ‘L’ is considered to look too much like a one, another letter could be substituted. For extra clarity, if needed, one syllable words with the right initial letter could stand in for letters during pronunciation. ‘Ack’ for ‘A’ and ‘Golf’ for ‘G’ and so on (two syllable words could be used over a two way radio for an even greater clarity increase). G could be pronounced ‘jee’ or ‘one’ or ‘si’. M could be pronounced ‘em’ or ‘six’ or ‘ni ti’ or ‘four two’.
Having said that, how about using lower case letters? I’ve never understood why upper case letters were chosen to stand for the numerals ten to fifteen in hexadecimal. At a guess, I’d say it was because they are the same height as Arabic numerals, which seems like a terrible reason. By the way, I do wonder about the use of letters of the alphabet as numerals. I think Arabic numerals had the right idea, so to speak, when they competed against Roman numerals: they were distinct in appearance and sound from Roman Numerals and letters of the alphabet and all other symbols used in Europe at the time. Thus the numerals could not be accused, so to speak, of causing confusion, and could coexist with them at first.
Ideally, new symbols should be found for any ‘alternative base’ — to borrow a phrase from Erik Engheim. Unicode is there. Let’s search it for suitable symbols.