1733:"Most books" are ignorant of modern scholarship, which points to the work of Harriot and Caramel as providing complete descriptions of modern binary notation before Leibniz. Leibniz was certainly important, as his contributions are the ones that stuck, but it is inaccurate and wrong to write the summary paragraph of the history section in a way that assigns him all the credit and completely snubs the other pioneers of the subject. To put it another way: that paragraph is supposed to be a summary of the whole history section. Your change rewrites it to completely omit any mention of one of the main subsections in the section. That is not an improvement. —
1125:), because the way non-binary rhythms like triplets, quintuplets, and septuplets are represented (by writing "3", "5", or "7") is really an extension, akin to writing vulgar fractions instead of non-terminating decimals. But the groupings are not always binary, and by the time you get to the phrasing-level, there's nothing that forces you to have eight-bar units instead of, say, seven-bar units, save an already long-eroded tradition, that one does not
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demonstrate how a computer would do it, as this would be different from doing it from the decimal way. There is a page on "Division (digital)", but that's not very clear either. Perhaps an external link would be useful. I've looked at the link that the poster 'should' have posted his comments to, but that takes you to a page entitled "Editing
Knowledge:Reference desk/Mathematics (new section)", which doesn't seem very appropriate.
1448:, because you don't so much have "binary numbers" as real numbers that happen to be expressed in base 2. You could just as well express the reals in base 3 or base 4 or base 10 or base 720720 if you invented enough symbols, but that doesn't mean that we somehow have "base-3 numbers" or "base-720720 numbers", as those would be exactly the same set; only "numbers expressed in base 3" and "numbers expressed in base 720720".
1354:(It's in the Archive programmes section, so won't vanish any time soon). An analogue binary clock is featured at 36:56, measuring in hours on the inner dial, and half-minutes on the outer dial. Having been in trouble for just going ahead and doing my own thing on Knowledge before (well, we all try to learn from our mistakes...) I thought I should bring it up on the Talk page for discussion first.
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1718:. Hence, the common theory considered Leibniz as the start of modern binary. If we defined all European scholar who studied this area before Leibniz as the modern binary, why don't we define the development in Egypt, China and India as the real start of modern binary number so that we can become more neutral for each region. —
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or not these symbols can be put together to form an eye is particularly important for binary numbers. So we should probably avoid mentioning this question. That may mean removing the image as you suggest, since even if we don't say that the image was used historically in that way, just having the image there implies it. —
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mathematics". So my impression (with no more knowledge than you beyond what we have both read from the same source) is that there is a disagreement between scholars, or at least between that source's author and other scholars. I think this article is not the right place for describing this controversy (
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mentioned. His contributions are described in great detail in the fourth paragraph. As per David
Eppstein's edit summary, there's just no reason for him to appear at the very beginning of the article when other binary systems clearly predate Pingala's work. For example, one of the binary-like systems
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It is helpful to distinguish numerical/mathematical systems from specific applications such as a data encoding scheme. Base 32 is not notable as a numerical system, it amounts to a compact notation for 5 binary bits, a section of the binary article could fully cover the content of this stub and link
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The problem with that is the scope of the article would be restricted to numbers like 1010 and 1000010101011, and would not properly include how they are used or what they are used for. Addition is an operation. Leopardus pardalis is a species. The field of real numbers is covered in the article real
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Can someone cite a reference for 1679 as a date of release of
Explication de l'Arithmétique Binaire... the document is dated on 1703.... and one more thing... I came across a book ISBN: 978-84-323-1667-8 (p. 30-32) that suggest that Leibniz created the binary system before 1673 marked by the date of
1292:
seems most likely) but that we should describe both sides there rather than trying to take sides ourselves. As for what we put in this article, although we should mention the
Egyptian numbering system (that part seems to be uncontroversial and highly relevant), I don't think the question of whether
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I have found a fantastic example of a binary analogue clock in a programme on BBC iPlayer. However, I am unsure of the copyright implications of posting a still image of it. I mean, there's fair use and all that, but I don't know where to start. It is such a brilliant example of such a rare thing,
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is a means of representing a number. So the title with the word "numeral" as opposed to "number" is more precise and correct, since the actual numbers that are described by binary numerals are precisely the same numbers that are described by any other system of numerals. I'm open to debate about
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Rather than removing referense to eyes alltogether, I'd recommend (in general terms) to (1) cut it down, (2) qualify it ("allegedly", "possibly", "according to some scholars"), and (3) link it to a discussion elsewhere on
Knowledge. One reason for this is that it is likely to creep back into this
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The article regarding the eye of horus states that the idea that it was used for mathematical purposes is false. If that is the case the picture regarding it should removed and the relevant section edited. Personally I have no knowledge in this area I was merely jumping from link to link, I just
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Further to the above, I've tried to add a wiki link for the word 'dividend' but it comes up with the wrong definition. I've read the editing tutorial and it doesn't really explain how to correct this, so I'll leave it to someone more knowledgeable.. hopefully they'll change the tutorial as well!
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I know where you coming from. As a C/S teacher it is hard to forget the past and explain current affairs moving history lessens to where they belong. But, however binary numbers where at the cradle of electronic computing this was not always the case and binary was invented outside the realm of
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I agree with the comments above - the article doesn't really explain how you do binary division. For purposes of clarity, the quotient should be different from the divisor and it's also confusing that the dividend is shown as 110111 instead of 11011. It would be useful if the article could
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Just to clarify: the source clearly states that these symbols were used for binary fractions. The disputed part is whether they also depict pieces of an eye or are just abstract symbols. And it also says that the idea that these symbols form an eye has "become standard among historians of
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For binary arithmetic, I understood addition, subtraction and multiplication fine; but I felt division was poorly explained. It is only explained in one paragraph (which is too condensed) and it would be helpful if the provided example was displayed at different stages of the process.
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It should also discuss theories of how human brain evolved that made it use binary to make music or even why it didn't instead have make disorderly music that plays only on whole number beats but there's no distinguishing feature between an odd number beat and an even number beat.
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That would be correct if the article was about the two numerals used, and did not go on to add system, and include the mathematics of the binary numbering system. There is a difference between the symbol used to describe a number, the numeral 1, and the number one, which is unary.
1233:
As the comment you responded to clearly states, Pingala's contribution are already there, in the history section. They do not need to be added anywhere, because they are already there. But, the history section is also missing any mention of binary systems in
Ancient Egypt, both
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electronic computing. Having said that, I do agree that currently binary numbers exclusively bear a meaning in electronic computing and the history is a fringe show. It should be move to a section history of binary theory and not be at the core of the article.
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explaining how music relates to an amount of time expressed in binary based on the way its sections are divided up. I know music also sometimes uses a mixed base where the last digit is expressed in base 3 and the other digits are expressed in base 2.
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717:, etc — the excess verbiage just makes the title look more technical and intimidating without adding any useful meaning. Additionally the Google scholar hit count argument applies even more strongly for this as it does for the proposed move. —
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Why are people using numeral for things like that? We're not here to correct the world, we're here to say what's said in reliable sources. Just check out google ngrams for positional number system compared to positional numeral systems.
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which is a policy I fully agree with. I also agree with David
Eppstein that the 'system' part should just be dropped to leave 'Binary number'. System doesn't add anything useful and doesn't disambiguuate with some other common term.
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and it was reverted by others. Most books divide the history of binary to before and after
Leibniz. Every development before Leibniz was claimed as the predecessors. For example, See "History of Binary and Other Nondecimal
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says 'The lead, ideally the introductory sentence or at least introductory paragraph, of an article, should make clear what the scope of the article is.' The scope of an article is not narrowly determined by the title.
693:. But I would prefer "binary number" (i.e. for the title to refer to the individual pieces of notation described by the system, rather than to the system as a whole) for the same reason that we have articles titled
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429:– A numeral is a symbol for a number. A numbering system is the mathematics of using a particular number as a base. By over 40 to 1 books written choose "binary number system", not numbering, and not numeral.
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Yeah, I didn't mean that the question was settled always and forever, just that it has been discussed before. (I do not personally have a strong feeling one way or the other about what the title should be.)
216:(binary digits), which in turn may be represented by any mechanism capable of being in two mutually exclusive states. The following sequence of symbols could all be interpreted as the binary numeric value of
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I think that the binary system used here is different from the binary of computer science. May I request to add a section in this article or computer binary is already included in another page?
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the dead of the
Maguncia Bishop, employer or main source of income for Leibniz, event that urge him to create a device (or first calculator) to sell it, obtaining a steady source of income .
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If first division yields 0 as remainder that is, it is fully divisible, add 1 to the remaining number and divide by 2. If divisible, register 1, otherwise register 0 to the right of first 0.
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Could someone who knows about it work on
Section 5.5, Square root? The opening sentence and equation are very unclear to me, and the subsequent algorithm needs some commentary. Thanks.
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I see no reason why this would be an improvement. I would also oppose merging to Base32 - its use as a real, if obscure, counting system has no overlap with the encoding scheme.
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There is no mention of Pingala in this section. His work is an important ancient contribution to the concept. Here's a summary of the information missing from this article:
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says 'Precision – Titles usually use names and terms that are precise enough to unambiguously identify the topical scope of the article, but not overly precise.'
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1121:? (・・? I guess in a sense traditional Western music notation is binary (at least, for note values below a half; from half notes upward the notation is more
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in connection with the systematic enumeration of meters with fixed patterns of short and long syllables. The procedure of Pingala's system is as follows:
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stub to binary number as it is essentially a notation for five binary bits. It would best be covered as a section of the binary number article.
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If first division yields 1 as remainder, add 1 and divide again by 2. If fully divisible, register 1, otherwise write 0 to the right of first 1.
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Ah, OK, I just noticed that. Still, since that one was conducted just over four years ago, it may be reasonable to open another one now.
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I'd like to know how to create a ternary clock using LEDs to express ternary values, so that I can add it to the ternary wikipedia page.
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I agree - Base-32 is a real counting system which is in use. However, why not mention it in this article (if it hasn't already been?).
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which says that the title should agree with the most common use in reliable sources. A Google Scholar search turns up 4150 results for
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1416:, something that is fine on other sites but not here. I doubt you will find much sourcing for ternary-coded-decimal digital clocks. —
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When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
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Two complements is mentioned but I do believe it should have at least a section explaining the basics and eventually referring to
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I don't think it's strictly necessary, but actually I think the lead reads nicely with it and I would support keeping it. --
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The current order Decimal - Binary misgui is misleading, leading to believe that 1/1 is 0.9999... is the norm. --
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I think the addition is neutral-bordering-useful. In any case, the language and disposition of edit summaries by
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Why does the sentence say "almost" all modern computers? Are there some that don't use binary? What are they? -
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article anyway as other editors come by, so why not do it right in a way that is likely to be stable.--
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until a consensus is reached, and readers of this page are welcome to contribute to the discussion. –
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Multiplying the binary numbers its soo hard to understand i am struggling with it
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Pingala? It makes most sense to structure the history section chronologically.--
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described in the article dates back to the 9th century BC. Why should it appear
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You mean you never heard anything in 3/4? Or 6/8? Or something like Musorgsky's
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1 0 1 0 0 1 1 0 1 1 | − | − − | | − | | x o x o o x x o x x y n y n n y y n y y
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If you wish to start a new discussion or revive an old one, please do so on the
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Computer implementations treat negative values in various ways - is that what
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that it would be sad if we could not find a way to allow a still image of it.
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You should only add that sort of thing to Knowledge articles when it can be
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Are you volunteering or is this something that we should work on together?
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Using singular rather than plural makes a difference to your comparison
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Divide the number by 2. If divisible register 1, otherwise register 0.
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No, it does equal 667. 663 would be 1010010111. This is binary, not
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is a system of numbers (real, rational, integer, hyperreal, etc). A
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Is this recent addition to the lead topical? IMHO it is not enough.
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This procedure is continued until 0 as final remainder is obtained.
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I'm going to tweak it myself. Further edits would be appreciated.
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colums order: Fraction, Binary, Decimal, Fractional approximation
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An editor has identified a potential problem with the redirect
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Sorry, it had an equals sign in it and the script rejected it.
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There's no comparison and numeral just sounds awkward there.
1156:(2nd century BC) developed the binary system for describing
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number. We do not need to add explanatory words like that.
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and "Gottfried Wilhelm Leibniz invents the Binary System"
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for additional information. I made the following changes:
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Those of you who have access to iPlayer, please check out
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Good idea. I've taken a stab at it; feel free to reword. —
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where would you suggest we put the section noted above?
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811:- it might be wise to consider the other articles in
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955:I think the best resolution would be to redirect "
212:Any number can be represented by any sequence of
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1628:This message was posted before February 2018.
268:"computer-based devices such as mobile phones"
1342:Fantastic example of an analogue binary clock
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864:but I think it still makes the same point. —
1620:http://www.invent.org/hall_of_fame/140.html
1598:I have just modified one external link on
1174:presents the first known description of a
611:be a separate article and not redirect to
525:polling is not a substitute for discussion
226:This does not equal 667. It equals 663.
1078:I think there should be a section titled
981:to its application for data encoding.
549:whether the word "system" is needed.
360:Discussion of the name of this article
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529:Knowledge's policy on article titles
411:The following discussion is closed.
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1440:(as I think it used to be) or just
878:I tried numbering and number wins.
813:Category:Positional numeral systems
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1602:. Please take a moment to review
1883:. This discussion will occur at
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1705:This is the my previous edition
1436:IMHO the title should really be
1352:"How They Dug The Victoria Line"
1272:thought I ought to mention it.
897:The discussion above is closed.
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1267:Eye of Horus in History section
1242:. Those should be added, too. —
1236:Ancient Egyptian multiplication
1701:About the lead of history part
1432:Title seems a little misguided
1369:Date of binary system creation
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629:Yes, it should be. And until
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1595:Hello fellow Wikipedians,
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607:- in that case, shouldn't
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1749:Leading with the history?
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1463:Have you looked above at
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1119:Pictures at an Exhibition
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910:Propose a merge from the
825:Quaternary numeral system
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1865:Redirects for discussion
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899:Please do not modify it.
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1879:and has thus listed it
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674:"binary numeral system"
447:- reason for request?--
670:"binary number system"
666:policy on common names
664:- Consistent with the
394:, with no objections.
192:Deleted per request. -
1844:Technical mathematics
1438:binary numeral system
1176:binary numeral system
421:Binary numeral system
42:of past discussions.
1640:regular verification
1446:binary (mathematics)
426:Binary number system
250:binary coded decimal
1630:After February 2018
1207:Rurik the Varangian
1129:to follow anymore.
1037:Square root section
1684:InternetArchiveBot
1635:InternetArchiveBot
1567:That's handled at
1412:— otherwise it is
1240:Egyptian fractions
1152:An Indian scholar
906:merge from base 32
707:addition operation
695:Leopardus pardalis
414:
18:Talk:Binary number
1660:
1414:original research
715:real number field
412:
342:quantum computers
232:comment added by
154:comment added by
132:comment added by
86:comment added by
72:
71:
54:
53:
48:current talk page
1918:
1908:
1903:
1874:
1828:Two's_complement
1694:
1685:
1658:
1657:
1636:
1569:Two's complement
1410:reliably sourced
1173:
1166:
641:
592:
580:No, binary is a
553:
521:
515:
509:
428:
338:analog computers
244:
166:
144:
98:
68:
56:
55:
33:
32:
26:
1926:
1925:
1921:
1920:
1919:
1917:
1916:
1915:
1906:
1901:
1868:
1846:
1824:
1822:Negativ numbers
1786:
1751:
1703:
1688:
1683:
1651:
1644:have permission
1634:
1608:this simple FaQ
1593:
1518:
1516:Computer Binary
1465:#Requested move
1434:
1391:
1371:
1356:Meaning of Fife
1344:
1269:
1147:
1076:
1039:
939:jjbernardiscool
908:
903:
902:
798:
639:
590:
551:
519:
513:
507:
501:
424:
417:
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385:
362:
270:
227:
224:
210:
172:
149:
127:
81:
77:
64:
30:
22:
21:
20:
12:
11:
5:
1924:
1922:
1881:for discussion
1867:
1861:
1845:
1842:
1823:
1820:
1819:
1818:
1790:Backinstadiums
1785:
1782:
1767:
1750:
1747:
1746:
1745:
1735:David Eppstein
1702:
1699:
1678:
1677:
1670:
1623:
1622:
1614:Added archive
1592:
1589:
1588:
1587:
1586:
1585:
1584:
1583:
1573:David Eppstein
1553:has in mind?--
1517:
1514:
1513:
1512:
1511:
1510:
1509:
1508:
1433:
1430:
1429:
1428:
1418:David Eppstein
1395:Backinstadiums
1390:
1387:
1370:
1367:
1343:
1340:
1339:
1338:
1337:
1336:
1335:
1334:
1324:David Eppstein
1295:David Eppstein
1268:
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1263:
1262:
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1260:
1259:
1258:
1257:
1244:David Eppstein
1193:
1192:
1189:
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1183:
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1143:
1142:
1141:
1075:
1070:
1069:
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1038:
1035:
1034:
1033:
1023:Digitalhamster
1015:
1014:
996:
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994:
993:
975:
974:
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972:
950:
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907:
904:
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892:
891:
890:
866:David Eppstein
840:
839:
805:
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797:
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792:
791:
790:
789:
788:
729:
719:David Eppstein
688:
659:
658:
657:
656:
655:
654:
653:
652:
651:
640:Sławomir Biały
613:numeral system
591:Sławomir Biały
582:numeral system
552:Sławomir Biały
534:
533:
508:*'''Support'''
500:
497:
496:
495:
477:
476:
475:
418:
409:
389:
388:
387:
386:
384:
383:Requested move
381:
361:
358:
357:
356:
320:
319:
318:
317:
269:
266:
265:
264:
234:208.92.108.117
222:
209:
208:Representation
206:
205:
204:
171:
168:
156:94.192.160.171
134:94.192.160.171
123:
122:
88:131.251.142.91
76:
73:
70:
69:
62:
52:
51:
34:
23:
15:
14:
13:
10:
9:
6:
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1808:Adam majewski
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1755:24.107.121.66
1748:
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1721:
1720:Miracle dream
1717:
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1600:Binary number
1596:
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1537:Deacon Vorbis
1534:
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1172:
1171:Chandaḥśāstra
1167:
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1164:Chandaḥśāstra
1159:
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1144:
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1132:
1128:
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1120:
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1101:
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1067:
1063:
1059:
1058:208.50.124.65
1055:
1054:
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1052:
1048:
1044:
1043:208.50.124.65
1036:
1032:
1028:
1024:
1020:
1017:
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1013:
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998:
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984:
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976:
971:" is handled.
970:
966:
965:binary number
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829:RockMagnetist
826:
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736:WP:COMMONNAME
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678:RockMagnetist
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609:number system
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586:number system
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542:number system
539:
536:
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514:*'''Oppose'''
512:
506:
503:
502:
498:
494:
490:
486:
485:Michael Hardy
482:
478:
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392:Binary number
382:
380:
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371:
370:Michael Hardy
367:
359:
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347:
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49:
45:
41:
40:
35:
28:
27:
19:
1895:
1892:
1889:
1869:
1850:41.115.106.9
1847:
1825:
1787:
1766:
1752:
1704:
1682:
1679:
1654:source check
1633:
1627:
1624:
1597:
1594:
1519:
1483:Double sharp
1450:Double sharp
1445:
1441:
1437:
1435:
1392:
1376:Ayala.canela
1372:
1349:
1345:
1290:Eye of Horus
1270:
1202:
1197:
1161:
1151:
1148:
1131:Double sharp
1126:
1122:
1118:
1114:
1100:Blackbombchu
1096:
1085:Blackbombchu
1077:
1040:
1018:
1004:Andy Dingley
999:
909:
898:
808:
801:
731:
690:
672:and 391 for
661:
631:this morning
604:
537:
522:
516:
510:
504:
444:
419:
410:
363:
321:
271:
228:— Preceding
225:
211:
179:71.146.20.62
173:
150:— Preceding
146:
128:— Preceding
124:
112:71.146.20.62
106:, not here.
82:— Preceding
78:
65:
43:
37:
1709:Numeration"
711:real number
538:Weak oppose
274:Incnis Mrsi
36:This is an
1691:Report bug
1274:Sonzaisuru
929:why merge
796:Discussion
344:binary? --
254:R. S. Shaw
194:R. S. Shaw
1674:this tool
1667:this tool
1115:Promenade
303:User:EEng
66:Archive 2
60:Archive 1
1831:Theking2
1771:Theking2
1680:Cheers.—
1551:Redpo888
1522:Redpo888
1196:Pingala
1080:In music
1073:In music
983:Bcharles
916:Bcharles
773:WP:SCOPE
769:WP:TITLE
713:and not
705:and not
703:addition
697:and not
605:Question
584:, not a
523:. Since
445:Question
324:GroveGuy
307:Rschwieb
230:unsigned
170:See also
152:unsigned
130:unsigned
108:See also
84:unsigned
1890:Laundry
1604:my edit
1160:in his
1158:prosody
1154:Pingala
969:base 64
957:base 32
931:base 32
912:base 32
821:Decimal
817:Base 13
809:Comment
732:Support
691:Support
662:Support
617:ukexpat
546:numeral
449:ukexpat
340:? Are
39:archive
1442:binary
1168:. The
1123:ad hoc
1019:oppose
1000:oppose
961:base32
959:" to "
935:binary
880:Apteva
756:Apteva
635:number
568:Apteva
499:Survey
465:Apteva
431:Apteva
396:Drmies
1893:Pizza
1203:after
1117:from
933:into
540:. A
16:<
1854:talk
1835:talk
1812:talk
1806:. --
1794:talk
1775:talk
1759:talk
1739:talk
1724:talk
1577:talk
1559:talk
1541:talk
1526:talk
1502:talk
1487:talk
1473:talk
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1422:talk
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1380:talk
1360:talk
1328:talk
1314:talk
1299:talk
1278:talk
1248:talk
1225:talk
1211:talk
1135:talk
1127:need
1104:talk
1089:talk
1062:talk
1047:talk
1027:talk
1008:talk
987:talk
943:talk
920:talk
884:talk
870:talk
853:talk
849:Dmcq
833:talk
782:talk
778:Dmcq
760:talk
745:talk
741:Dmcq
734:per
723:talk
682:talk
645:talk
621:talk
596:talk
572:talk
557:talk
520:~~~~
489:talk
469:talk
453:talk
435:talk
400:talk
374:talk
350:talk
328:talk
311:talk
293:talk
278:talk
258:talk
238:talk
214:bits
198:talk
183:talk
160:talk
138:talk
116:talk
104:here
102:Ask
92:talk
1648:RfC
1618:to
1571:. —
1498:JBL
1469:JBL
1444:or
1221:-JG
937:?
615:?--
588:.
346:JBL
289:JBL
252:. -
218:667
1910:)
1907:c̄
1896:03
1856:)
1837:)
1814:)
1796:)
1777:)
1761:)
1741:)
1726:)
1661:.
1656:}}
1652:{{
1579:)
1561:)
1555:Nø
1543:)
1528:)
1504:)
1496:--
1489:)
1475:)
1467:?
1456:)
1424:)
1401:)
1382:)
1362:)
1330:)
1316:)
1310:Nø
1301:)
1280:)
1250:)
1227:)
1213:)
1198:is
1137:)
1106:)
1091:)
1064:)
1049:)
1029:)
1010:)
989:)
945:)
922:)
886:)
872:)
855:)
835:)
827:.
823:,
819:,
784:)
762:)
747:)
725:)
709:,
701:,
684:)
647:)
623:)
598:)
574:)
559:)
511:or
491:)
483:.
471:)
455:)
437:)
423:→
402:)
376:)
368:.
352:)
330:)
313:)
295:)
280:)
260:)
240:)
220::
200:)
185:)
162:)
140:)
118:)
110:.
94:)
1902:d
1899:(
1852:(
1833:(
1810:(
1792:(
1773:(
1757:(
1737:(
1722:(
1693:)
1689:(
1676:.
1669:.
1575:(
1557:(
1539:(
1524:(
1500:(
1485:(
1471:(
1452:(
1420:(
1397:(
1378:(
1358:(
1326:(
1312:(
1297:(
1276:(
1246:(
1223:(
1209:(
1133:(
1102:(
1087:(
1060:(
1045:(
1025:(
1006:(
985:(
941:(
918:(
882:(
868:(
851:(
831:(
780:(
758:(
743:(
721:(
680:(
643:(
619:(
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555:(
531:.
487:(
467:(
451:(
433:(
398:(
372:(
348:(
326:(
309:(
291:(
276:(
256:(
236:(
196:(
181:(
177:—
158:(
136:(
114:(
90:(
50:.
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