"Luke-Jr" <[email protected]> > A : [email protected] > Copie à : "John Dlugosz" <[email protected]>, "Otto Stolz" > <[email protected]> > Objet : Re: Hexadecimal digits > > On Friday 04 June 2010 11:55:55 am John Dlugosz wrote: > > Those things really happen when writing in assembly language. I recall > > having to write "numbers" that only begin with a decimal digit, so "a > > fish" is a word, and "0ah fish" is a number. In C and C++, "a" is a word > > and "0xa" is a number. > > But I'm not talking about programming languages, just common everyday uses by > people who have it as their primary (not secondary) system of numbers.
It's true that we don't need new digits for hexadecimal numbers for programming, given that for such technical use, we already have unambiguous notations using prefixes like "0x" or "$" or suffixes like "H". The real need would be is we started to count, in our natural life, in a binary system like hexadecimal: there would still be the need to use it unambiguously with decimal numbers, so that numbers written like "10" would still remain unambiguosuly interpreted as ten and not sixteen: to avoid this problem, we would also need another set of digits for 0-9. Or we would have to use another additonal notation such as some diacritic (or prefix/suffix like for programming : but how are we supposed to ponounce them?). The other major problem will be linguistic : to make the hexadecimal convenient, we would also need to have other names than "ten", "twenty", unless we keep their meaning but forbid combining them in sequences like "twenty one" which would still be interpreted in a decimal system. So we would need new names for powers of 16, even if we keep the names we have for 0..9 and possibly more (ten, eleven, twelve are possible in English, thirteen would prebably be disqualified as a unit name; in French we could keep dix, onze, douze, treize, quatorze, quinze for the hexadecimal units; all other names for powers of 10 and their multiples would be disqualified in the new naming as they would not translate easily in the hexadecimal system). But then people would have to remember at least the order of magnitude between numbers named in the decimal system and number with the same numeric value in the hexadecimal system (converting numbers from the decimal to the hexadecimal system is not trivial after som small range, it is even a complex algorithm to implement on computers for high precision numbers... But let's imagine that such a new naming system exists, it will come with its own digits ; so they would all be encoded as a complete separate set of the 16 digits (in 0..15 inclusively), and they would certinaly have their own distinctive glyphs. There won't be any need to change the technical notation used in computers using the existing decimal digits 0..9, letters A..F, and prefixes/suffixes using another letter or symbol. So my opinion is then that, if digits were added for hexadecimal notations, they should all be encoded for the full range 0..15, not just the range 10..15, and in an unbroken sequence. In this system, the least significant unit digit (in numbers with multiple hexadecimal digits) may be freely replaceable by a decimal digit if it's in 0..9, without creating confusion, for practical reasons (0 and 1 are too commonly used every day and should not require any conversion between the two numeric systems). Implementers could then imagine the distinctive glyphs associated with those digits, but the glyphs should remain simple, and as narrow as existing decimal digits, and clearly distinct from existing digits, or letters in all major scripts already using the existing digits (otherwise this system will fail immediately and will be even less convenient than using the technical notations like "0x..." using in programming. The glyphs should also be mnemonic according to their value (that's why I suggested a glyph shape near from the shape of decimal digits, possibly by using some diacritic like a top bar (which could connect with the bar of the surrounding digits, so that it is drawn really fast, but this may create confusion with some existing notations used in maths or engineering). Another solution would be to borrow for use in Latin the 16 first glyphs of some other alphabets in other very different script (but in this script to borrow the glyphs of the Latin alphabet), but this would require two sets of hexadecimal digits, that would have to be encoded separately, and it is unlikely that scripts other than Latin will borrow Latin letters for that usage, given that they frequently borrow words written in the Latin script (notably trademarks, and on offocial documents like passports, or when transliterating people names and postal addresses). The glyphs would also need to be as fast to draw and easy to read as existing digits and letters (using a single stroke, or two very simple strokes). For now, there's no such coherent set of distinct glyphs for hexadecimal numbers. The learning curve for using the hexadecimal system in everyday use is still very far from reaching an international agreement (imagine the tremendous consequences and problems for pricing, and measures...). It will be extremely costly to change our everyday worldwide use of the positional decimal system (much more difficult than changing currencies). But there is anyway a limited but growing use of the hexadecimal system, for which new digit shapes could be more convenient than using desambiguating prefixes/suffixes. But before that, we would still first need to invent and use new names for powers of sixteen, and a rational way to name reasonnably large numbers in this system (at least up to 64-bit), including for fractions of unity ; this has already started in the metric units used in the computing industry, by the adoption of binary-based prefixes for measure names (kibi, mebi, gibi, ...) instead of the 10-based prefixes (kilo, mega, giga...), and the new recommendation of abbreviated symbols for these prefixes for multiples/submultiples (appending a lowercase "i" after the initial : "Ki, "Mi, Gi..." instead of just "k, M, G...") Note that these binary-based metric prefixes have been documented now since long, and are wellknown now by a growing population. But their adoption is still far from completion, and we still hear "kilobytes" instead of "kibibytes" : this is a clear sign that the need is not urgent, and that adopting new glyphs and digits after adopting new quantity names for powers of 16, is still very prematured, because this usage is still perceived as technical and limited in scope of application. And for such technical use, most often in computer technologies, the existing computer language notation (with prefixes like "0x") is just enough and does not require any new set of digits.
