Talk:Binary prefix/Hexadecimal Billion


 * This is an archived discussion of Talk:Binary prefix. Please do not make any edits to this page. If you wish to continue this discussion, please use User talk:Michael Chuquet/Hexadecimal billion or the main article talk page.

'''History of this closed talk section of "Binary prefix":

14:01, 13 Aug 2004  81.57.112.41 (table formating) 22:51, 13 Aug 2004  Icairns (Remove milliard, billion, billiard, etc. as these are ambiguous terms) 21:51, 17 Aug 2004  81.57.112.41 (Replace milliard, billion, billiard, etc., (see discussion)) '''

Hexadecimal billion
No, that's not "ambiguous terms". It shows only, that the "short scale" is an erroneous system.

The hexadecimal million =  1 048 576 1   (&#8805; 1 000 000  1) the hexadecimal billion  =  1 048 576 2   (&#8805; 1 000 000  2) the hexadecimal trillion  =  1 048 576 3   (&#8805; 1 000 000  3),   and so on...

Nothing clearer than this ! Or, how do you want to name the real existing number 1 048 576 power two ?


 * What is your criterion for saying that the 'short scale' is erroneous? Are you quoting the Littré dictionary from the billion article? The word 'billion' in English has two definitions - each is correct in their respective contexts, but would be ambiguous outside that context. The 'short scale' may be 'erroneous' according to the French Government.  Ian Cairns 00:46, 18 Aug 2004 (UTC)

Thank you, Icairns, for your answer.

Firstly :  In cultural evolution, there can be changes – even great changes – but always for good reasons. The grouping by three digits was a positive and a practical progress, because it's easier to read numbers in groups shorter than six. But it is not a valuable reason to want to change the meaning (the signification ! ) of words, such as they were practiced since of the centuries. The proof : This has introduced a confusion which continues until our days.

Secondly :  By examining the two systems, the original "long scale" and the reformed "short scale", one must objectively say, that the long scale is more logical and easier to use for evaluation of orders of magnitude, because the prefix always expresses the power of the million. (cf. [])


 * As pointed out in Fowler's Modern English Usage, a frequently cited and influential work, the "short scale" is equally logical. Fowler notes that "for Americans it means a thousand multiplied by itself twice, or a thousand millions (1,000,000,000)." Similarly, a trillion is a thousand multiplied by itself three times, a quadrillion is a thousand multiplied by itself four times, etc. The real problem is a fundamental conflict that arose with the word "million." Powers of 1000 are more convenient. Unfortunately, instead of calling 1,000,000 a "mille-mille" or "bi-mille" or "bille," it was called a "million," an intensified version of "mille." And the origins of this word are apparently lost; it was in use long before Chuquet. Incidentally, note that in English a "great gross" is 12&times;144, not 144&times;144. What are the analogies to "gross" and "great gross" in other languages? [[User:Dpbsmith|Dpbsmith (talk)]] 19:54, 1 Sep 2004 (UTC)

Thirdly :  If by the “whims” of the history, the short scale was not used by the greatest power of the world, cultural and economic one, nobody would speak about the short scale, even if it would be used, suppose, by some small countries. Or rather, that would make a long time that they would have returned above. But there, under American influence, much of English-speaken countries, during the twentieth century, were tempted to align itself on the use of the United States. But it is far from being played.

In no other English-speaking country than the U.S.A., the short scale is legally recognized, on the contrary...  In spite of the current use of the British government, all the British scientists continue to use the long scale (see the contribuation of Jed aus Talk:Billion), like the population largely does it. (Does not suspect me of “primary  anti-Americanism”, far from there. I admire them for many technological and scientific exploits and especially for their intellectual opening for “the new one”. A capacity which we miss some times a little in our old Europe. But this European retention preserves us also – some times – of some errors and of several dead ends. At least, let's hope it.)

Fourthly :  In the light of present and future systems of numbers – I mean in particular the binary and the base sixteen systems – the long scale clearly shows its superiority and its accuracy. I am not worried about, really. I want to say, I am certain that – early or late – everyone will understand it. If I intervened since a few months on some entries of Wikipedia, (French pages, some German pages and also now in English) is only to accelerate this process of comprehension, which will intervene anywhere.

Fifthly :  Currently, if anyone reads an American (or most of English) newspaper, it is necessary to know that billion means thousand billion or milliard, trillion means billion, quadrillion... etc. I understand, you understand, everyone understand. It is not a problem. The journalists can continue still a little.

But in science, there cannot be two systems competitor, parallel. There is no place for two. It is necessary to be understood without ambiguity in science ! There will be a system correct, recognized and another one, considered erroneous which will be classified soon. The Europeans of the continent will never abound the long scale. Not only because it is the original system and much more logical, but also because future applications support the exactitude of the long scale (cf. the “hexadecimal billion”) Even the Americans will understand it – I am sure – and the American scientists firstly.

Finally :  The international institutions (International Conference for Weights and Measures, the BIPM etc.) recommend also explicitly to use the long scale.

For conclusion :  As like in science, currently, the SI decimal system is in use all over the world, employed even by US-American scientists, as like the system of "long scale" is the system of reference in number names. Those who don't like Pelletier terms, uses original Chuquet terms. (I read that would be to ambiguous: "I order two billiard tables."  But I wonder how much of railroad vans it would be necessary to fill, to store 10^15 tables, even small ones and in kit. Many languages preserve the same orthography for the "play" and the "number", and pronounce differently according to. Other languages vary slightly the orthography. In Spanish, I think so, "milliard" wants to say also "thousands". This is more doubtful.) The long scale is standard.  If there are still scientists in the United-States who did not have understood till now, it is high time. A billion in science is a billion all over the world, even in the U.S.A., Brazil and Puerto Rico. This in any language.

P.S. In the context of differences between American or English use and the use of many other countries, that is the "decimal point" and the "decimal comma", the best solution – always in science, journalism will follow, as always, with a few decades or years of delay – should be, that countries using the comma respect the English point. In English, on the other hand, scientists give up the comma between the thousands for profit of "non breaking spaces". Because “1,234 m”, for example, is visually to ambiguous. Much better is 1 234 m (against 1.234 m). – But I think, it should exist, even and especially in non-proportional fonts, a "half space", but half one exactly. – This is also the official recommendation of the international institutions.

So long, Ian. I saw a little your Wikipedia contribuations, good. Michael 19 Aug 2004, 09:45 (UTC)

Hello Michael I have no problem with the history of how we arrived at the (de facto) situation where we are today, except that I do not recognise either of the scales to be superior or erroneous. Each scale is consistent (i.e. not erroneous) of and within itself - the only problem is in the existence of two scales and the ambiguity / conflict between these two definitions.

I'm suggesting that the English-speaking world is at a slightly different place than you may think it is. I know of no current legal standard in the English-speaking world that mandates (de jure) the long scale. My experience of Americans / American English is that they use the short scale (almost?) exclusively - perhaps an American wikipedian can confirm / refute this? I suspect this has been debated extensively in Talk:Billion. For the UK, the short scale has been taught in UK schools for a long time, together with an explanation about the historical situation / existence of the long scale. A quick look at www.open.gov.uk (and searching in Google) shows that the UK Government uses the short scale exclusively in all aspects (financial, demographic, etc) of their numerate announcements. Yes, there are some people in the UK who still use long scale. Yes, there are schoolchildren who were confused by their teaching. For this reason, both sides of the 'confusion' in the UK are given in the billion article. I cannot remember how long ago I last saw a long scale billion in a newspaper - it was many years.

I would describe the current UK situation as one of transition from the long scale to the short scale.

Regarding BIPM - look at their own web domain:

Using Google, I came across where a Director of the BIPM is using short scale billions in a financial context. and where scientists are using short scale billion in a scientific context. Where is the mandate for long scale? Do you have the reference for this?

Conclusion: The current 'de facto' situation will not change because one side admits any 'error' or comprehends differently - there never was any error, except that written in the Littre dictionary. The usage of short scale continues to increase in the English-speaking world and will soon become ubiquitous in the English-speaking world.

PS: I look forward to the day when the world (including Wikipedia) standardises on the 'decimal space' and SI units - this is one place where an international consensus / compromise is possible (unlike billion).

Ian Cairns 13:12, 19 Aug 2004 (UTC)

Hello Ian,


 * I confirm you, even the short "scale is consistent of and within itself", because prefix is 3n + 3.  Ok.
 * I wrote: "much of English-speaken countries, during the twentieth century, were tempted to align itself on the use of the United States". And the result of this alignment is, what you describe by "the current UK situation as one of transition from the long scale to the short scale." This transition is – as you confirms it to me – far from being achieved and also not final. (I rather hold that for a fashion of second half of the twentieth century which will not last. But you have the right to think the opposite.) But let us suppose, the short scale would achieve the English unanimity – it is far from being the case – it remains that everyone knows that the German, French, Spanish, ... word : "billion" is the same one as the English one. Thus the problem remains entire.
 * I note that you do not make all the distictions which I make me: governments, population, public oppinon (journalism)  and scientific world.  But I believe, it is necessary.
 * – The governments decide which are the systems having legal tender and which are taught at the school.
 * – The population largely follows what they learned at school and and everyone is not able to change "opinion" afterwards throughout their life. I want to believe you that after a few twenty years of teaching the short scale in UK  seems to become "ubiquitous". But I had echoes that even young Britannics pull in doubts and and do not follow which their teachers them learned. But it is surely still a minority. If I understood well, you are a follower of the short scale (Me, before, I did not have an opinion on the subject. But my researches in connection with the hexadecimal system opened my eyes. Now I have a "sliced judgement" on top, but always argued and with respect for all those which do not think like me.)
 * – The journalists do not always follow the official instructions. They often obey their own "modes". I know that English newspapers, currently, widely gave up the the long scale. But this should be a "pyrric victory" for the short scale.
 * – The scientists finally, although they must also observe the legislation, but in last authority, they must defend what there is of truth and they considered the best. In this context, I want to quote Jed of the Discussion page "Billion". He wrote: "I am British and Australian, a scientist, engineer and teacher. Reading the current article I am surprised to find that it suggests that British and Australian usage of the word billion now follows the American usage of the word! Sorry, not so. In both the UK and Australia (and many other English speaking countries I have worked in) the American billion 10^9 is only used when referring to money values - all other usage including science, maths, engineering, construction, surveying, mapping, teaching.... etc, uses the correct value of 10^12."  –  That's clearly sayed !  But I know also, that the American scientists do not all understand hitherto, that the long scale is the scientific standard and that much of them, perhaps even the great majority, still use – by ignorence – their local scale. But soon, they also will understand.


 * I do not agree with you, to believe, that the two scales can coexist eternally. It must be one day a decision for a common use. (Besides, the SI units are already standard in the scientific world. Or you know serious contemporary scientists whom still use the British or American pints in their research ? Not me. No need for a recognition by Wikipedia.)
 * The short "scale is consistent of and within itself". But – except to be less elegant – it is historically erroneous. Because against the opinion of the majority of the scientists of the world, they changed, without need absolut, the significance of the terms. It will never convince the majority. In our time of the progressive globalisation, it will be dedicated to disappear. (Dead end, a temporary historical employment ! )   "You set on the wrong horse, Ian. But it is always time for change."
 * Future employment will confirm it. In what follows, I wants to show it a little to you.

Let's take the original Chuquet example number and convert them into hexadecimal :  745324 trillion 804300 billion  700023 million  654321 units    = =   9DD42 trillion   37B63 billion   6E67B million   207B1 units. The original Chuquet decimal exemple number : 745324  seven hundred   forty-five     thousand    three  hundred    twenty-fore   trillion, 804300  eight hundred         fore     thousand    three  hundred                  billion, 700023  seven hundred                  thousand                      twenty-three  million, 654321    six hundred   fifty-fore     thousand    three  hundred    twenty-one    units. The Chuquet number expressed in hexadecimal : 9DD42                 ninety-thirteen thousand  thirteen hundred     forty-two    trillion, 37B63                 thirty-seven    thousand   eleven  hundred     sixty-three  billion, 6E67B                  sixty-fifteen  thousand     six   hundred   seventy-eleven million, 207B1                twone ty          thousand    seven  hundred  eleventy -one    units. It is obviously the same magnitude because :   ~ 10 × 65536 × 1.0485763   =   ~ 750 000. 0x10 (sixteen) is called "onety ". It's easy, it's clear, it's praticable. hexadecimal million  is   decimal  million × 1.048576 hexadecimal billion  is   decimal  billion × 1.099511627776 hexadecimal trillion is   decimal trillion × 1.152921504606846976  etc. But this concordance exists only with the original Chuquet system, not with the reformed one. The modern internal 64 bits bus, that's 2 power 64 or F FFFFF FFFFF FFFFF units and the zero. Sixteen trillion hexadecimal units.

You will answer me that, firstly, one was not accustomed to pronouncing the hexadecimal numbers and, secondly, the hexadecimal numbers are too ambiguous, because, if there are no letters, one do not know, if it's about decimal or of hexadecimal. Either it is always necessary to prefix "0x" or "dec".

And you would be in right twice. Hitherto the pronociation of the hexadecimal numbers did not exist, but that will come, I am sure. For the second point, it is completely clear that in its current form, the hexadecimal system does not have any chance for generalization. It would be necessary to have other digits, coherent, signs already known by everyone, present in the existing fonts and elegant...

For concluding today : The moity of the circumference of the Earth (~ 20 037.5 km) divided twice per 1024 gives a chain (of 1024 digits) of exactly 19 109 257 µm. You see...

And surely we have ten fingers, but let's consider modernly : Two thumbs and eight other fingers. Eight twice makes sixteen.

Michael,  20 Aug 2004,  ~ 22 H (UTC)

Hello Michael

I notice that you do not give any response as to where the long-scale is mandated in the English-speaking world or where it is mandated in BIPM. Do you acknowledge that the BIPM do use short-scale in their English documentation, as I presented? Do you have any evidence to the contrary?

I understand that you, Jed and Ken Moore (in the Billion article, which I have read) have a common understanding (long-scale) of billion. I disagree with the prominence that you, Jed and Ken Moore give to the long-scale in the modern English-speaking world. The change from long-scale to short-scale in the English-speaking world is inevitable and is happening today - the only argument is how long it will take to complete. I am not aware of any American today who continues to use the long-scale. I have no idea how the world will progress on common naming after the English-speaking world unites on the short-scale - maybe it will be English-speaking versus the remainder? Who knows? In my opinion, there is no chance (0%) that the English-speaking world will acknowledge any 'error' in the existence, or its use, of short-scale, or that they will make any further change towards the long-scale, in the interests of world unaminity. This simply will not happen.

I gave evidence that the short-scale is being taught in UK schools, and has been taught ever since Harold Wilson declared the UK Government's usage of short-scale in the House of Commons in 1974 - the nearest thing the UK has to a legal position. I showed that today the UK Government websites all use short-scale. What evidence do you have that long-scale is being actively promoted today anywhere in the English-speaking world?

(When the UK moved from non-decimal money to decimal money in 1971 (Decimal day), they were many old people who continued to convert new money to old money, hanging on to old ideas. You will continue to find occasional Jeds and Kens - but you will miss the sea-change)

In all my 28 years in the IT industry, working in octal, decimal and hexadecimal, I never heard anyone ever try to pronounce hexadecimal numbers in the way you describe. I see no need to do this, and I find it ambiguous. Where / Why do you think there is a need to do this? There is enough trouble over the acceptance of Mebi- and Kibi-, with many people continuing to use the decimal Mega- and Kilo- when they mean a binary prefix. What does a thousand mean? Well, either 1000 or 1024 since it depends on whether you are speaking decimal or hexadecimal. How will this improve anything or remove ambiguity? Why would the English-speaking world adopt an ambiguous definition of thousand when there is already enough ambiguity in the terms: billion, trillion, etc (etc. = &c = et cetera = usw).

In the English-speaking world, because the word 'billion' (and larger numbers) causes ambiguity, various dictionaries and Wikipedia, amongst others, recommend not using this and other long-scale or short-scale specific terms, but using either 10^9 or 10^12 (or whatever) instead (as is appropriate in the context). This is the reason why I suggested removing all words over one million in the table. I still think this suggestion is better in the English-speaking Wikipedia, and I have heard no hard evidence to the contrary. I have no opinion on non-English-language Wikipedia pages. Regards, Ian Cairns 00:03, 23 Aug 2004 (UTC)

PS: I remember Tom Lehrer describing the New Math during the 1960s as

'Octal is like Decimal - if you are missing two thumbs'.

Hello Ian,

You was in right to modify. It's ok. I delayed too much with my answer. (I adapted now for XVGA.) Nevertheless I will answer you even at greater length.

Three points only in short:
 * Me also, after having recorded the other answer, I realized that I had nothing said concerning your research in connection with the use of the BIMP, excuses. I always have much respect for people like you, who make good researches ! More another time.
 * Besides, I can reassure you, fortunately, I still have my two thumbs. It is for that, I largely prefer the hexadecimal one against the octal one.
 * Your promoting of the display of the two values at the Billion page is really very good. Chapeau !

Michael,  30 Aug 2004,  16:10 H (UTC)

P.S. Do you read French texts, if I will show you pages in another answer ?


 * Hello Michael. Thank you for your points. I've now changed my talk page to mention my languages. Yes, I too have worked in Paris... among many other cities around the world. You will remember that I have not queried the position on billion, other than in the English-speaking world. Ian Cairns 18:49, 30 Aug 2004 (UTC)

Hello Ian,

I still thank you for your sympatic "Hello" on my user-page.


 * "Nicolas Chuquet" :  If one holds in his hands the clean copies of all the 197 pages of the original publication of  "Le Triparty en la Science des Nombres", Nicolas Chuquet, 1484 (of the "Bulletino di Bibliographia e di Storia delle Scienze matematiche e fisische. - Bologna volumes XIII, 1880, ISSN 9012-9458", which is consultable in good university libraries like that of the Institute Henry Poincaré in Paris) one knows that Nicolas Chuquet used the long scale exclusively.  This was obvious of entry, because N. Chuquet was a serious mathematician, who will not define a system in the first (Numeration named) chapter of his "Triparty", for then using himself a contradictory employment. But, a falsified quotation, taken again by hundreds of Web site and a pseudo-scientist "lucky find" (A double use of Chuquet himself !) let believe the opposite. An integral publication of the original writings apropos, (on another site that Wikipedia) soon will put an end to its rumours unfounded. I will keep you informed.


 * "BIPM English short scale use" :  As I already wrote you in my preceding answer your research on top is a good research and I thank you much for having held  me informed. In this precise case they confirmed a standard NIST and are aligned indeed on the short scale. But, although – at present – the SI standard is incontestably the reference in the scientific world, it is not sure, if these "capitulards" of the BIPM will keep this prevalence for a very long time still. (see lower)


 * "To resume long/short scale and hexadecimal billion" :  Myself, I will not have the least problem to adopt the short scale quickly, even in French or other languages, if that proved to be necessary.  (Although – as already I said – I consider that it is less elegant and less logical.  It misses also a reference of a historical theoretician, but this last fact is of less importance.)  But, the fact that the hexadecimal billion is certainly equal 16^5 x 16^5, definitely prevents me.


 * "Hexadecimal numeration" :  You wrote: "In all my 28 years in the IT industry, working in octal, decimal and hexadecimal, I never heard anyone ever try to pronounce hexadecimal numbers in the way you describe." That does not astonish me at all. If, somebody whom I know very well, (you can be sure for it ;-) developed "the hexadecimal metric system" already in 1989, this new proposed system has only started to be known and discussed since several months. If, with oral employment, it can lend indeed to ambiguity, (All the intelligent speakers expresse nevertheless so that there is not so.) with the writing, the new hexadecimal digits, so-called "omni-litteral digits", excluded any ambiguity. This new proposed system has the ambition to become the further universal system of reference.

If you want to go – by turnings with fr.Wikipedia – to the site of the author Michael Florencetime, ("Tiens", which coincidence. Still another name cousin of me !) you must know that his site is optimized for a platform PC : xVGA or better, rather a fast speed Internet connection and a powerful processing unit – at some pages, much of real time JavaScript calculations – and a modern browser like IE 5, better IE 6, Netscape 6 or 7 or the quite good new Firefox. On a Linux platform, Konqueror is uncapable, but Firefox functions. The IE5-Mac displays totally erroneous, but Safari for example rather correctly.

So long, Michael,  01 Sep 2004,  15:40 H (UTC)

P.S. ''I refer to your penultimate answer :   I never said that thousand hexadecimal is 1024. Never! That's four times more, as you can confirm to me instantaneously. "The numeral thousand refer to thousands of different numbers," as our college Michael Hardy would say, while distinguishing judiciously between numeral and numbers. That depends on your base. Thousand binary is 8. Thousand base four is 64. Thousand octal 512. Thousand decimal is 1000. (Thousand base 13 is 2197, for example.) Thousand hexadecimal 4096. But 1024 are exactly thousand octal base three radix two, of course.''


 * Hello Michael - Yes, you are right - Your newly-invented meaning for 'thousand' (hexadecimal) is in fact 4096 decimal. I am perfectly happy that the word 'thousand' means a triple power of ten. Why should I also wish to use the same word for a hexadecimal number to mean 4096 decimal? This is confusing. If I wanted a word for '1000 hexadecimal' (NOT the same as 'thousand hexadecimal' - as the 1 represents 4096) then I would certainly wish to employ a different word. I already suffer with the ambiguity of billion, etc. Why should I make this worse by making 'thousand' ambiguous too? Also, did you spot the new article 'long scale' that Dpbsmith has created? I think this will help rationalise the many articles in this area. Regards, Ian Cairns 20:49, 1 Sep 2004 (UTC)

Hello Ian,

Since the mathematicians handle the concept of bases, one always called thousand n power 3. Eight decimal is and was always thousand base two. You can wish another word for the numeral thousand in all the different bases. But is it realistic? I think it is not necessary either. It is necessary to know in which base one speaks, supposing for example, in binary. Then, it is clear and normal that "the numeral thousand one hundred" means "the number twelve decimal". Where is the problem?

But like it was agreed, we do not continue more this discussion here, because we actually moved away too much from the theme of this talk page: "Binary Prefix". The last, that I will still add, tomorrow or the day after tomorrow, it is a short response to Dpbsmith for its intervention here of before yesterday.

If you, or someone else, wants to deepen, he is invited to do this on User talk:Michael Chuquet/Hexadecimal billion and to not add any more here. This "archieved" page, weighs already 30 KB !

Thanks Ian for this talk, have a good day. So long. Michael Chuquet 01:40, 3 Sep 2004 (UTC)