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In Konrad Zuse's Plankalkül ZIA ID 0020 from 1972, in his patent submission Z23624 "Rechenmaschine" ZIA ID 0177 from 1936 and modern German Wikipedia article on the dyadic system, 2020-01-17 we see L for one and 0 for zero. In certain modern lecture materials I cannot cite here I saw a variant with O/L instead of 0/L.

Mr. Zuse wrote he chose 0, L as the binary digits (so as to distinguish them from the decimal digits 0 and 1) but did not explain why the binary one is L and not some other letter (say, A, B, C, D, ...).

What is the origin of the usage of 0/L and O/L as representations of no/yes and false/true?

Martin Schröder
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    I can't find the right references right now (I hope some else has better Google-fu), but best I know the notation is Zuse's, dating to about 1937, based on notebook entries. It then appears in one of his patent applications (~1940), where binary numbers are called "Sekundalzahlen", and it is explained that instead of '1', 'L' is used in these to prevent mix-ups. – njuffa Apr 08 '20 at 08:02
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    I seem to recall that Zuse used shorthand in his notebooks (which I cannot read), so what would be needed is a transcription. Zuse reproduced some of his notebook entries in his book "Der Computer -- Mein Lebenswerk", you might want to check there. Raúl Rojas has published fairly extensively about Zuse; you might want to check his publications, too. Also, see whether you can get a hold of Zuse's patent applications from the Deutsches Patentamt. – njuffa Apr 08 '20 at 09:00
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    Some things go in circles. I'm old enough to remember TTYs, where "zero" was printed with a "phi" (slash thru an "O") to make it clear what was letter "O" and what was zero. Then came GUIs and WYSIWYGs and fancy fonts and pain for software devs; and now we have fonts specifically designed for software devs with 'zero' having a slash and lower-case "L" having serifs so nobody confuses it with a "one." – Carl Witthoft Apr 08 '20 at 13:01
  • @njuffa Please convert your comments into an answer. They essentially answer the question and give more than enough pointers to the references. – Conifold Apr 09 '20 at 21:26
  • @Just_A_Man [Speculation] It may have something to do with the typewriting conventions of the time. Having looked at historical models before, some 1930s typewriters lacked a '1', expecting typists to substitute lowercase 'L' (see also this online post). That would straightforwardly motivate use of uppercase 'L'. [Conifold:] I don't think an answer without references is much of an answer. I don't have access to either Zuse's own book nor Rojas's publications at the moment, whether online or offline. – njuffa Apr 10 '20 at 00:52
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    @Just_A_Man I am in the process of trawling the internet to find out whether the lack of a '1'-key applied to German typewriters of the 1930s as well. – njuffa Apr 10 '20 at 01:28
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    @Just_A_Man I found pictures of many old typewriters at a site facilitating trade in old typewriters, and I have found various German models from the relevant time period that did not have a '1'-key including models by Adler, Olympia, and AEG. So yes, my hypothesis seems plausible. Pondering answer now. – njuffa Apr 10 '20 at 01:48
  • @njuffa I agree about the importance of references, but I easily found both Zuse's Der Computer - Mein Lebenswerk and Rojas's Die Rechenmaschinen von Konrad Zuse on googlebooks after reading your original comments. – Conifold Apr 10 '20 at 06:18

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Likely relevant resources are Konrad Zuse, "Der Computer ― Mein Lebenswerk" (Springer, Berlin 1984) and Raúl Rojas (ed.), "Die Rechenmachinen Konrad Zuses" (Springer, Berlin 1998). F.L. Bauer, H. Wössner, The "Plankalkül" of Konrad Zuse: A Forerunner of Today’s Programming Languages. Communications of the ACM, Vol. 15, No. 7, July 1972, pp. 678-685 references an earlier edition of the former book as Z70 in a footnote:

From a remark in [Z70, p. 157], one can infer that Zuse already during his Berlin period, that is before 1944, used L and 0, which he called Sekundalziffern (see also [Z70, p. 68] in his diary entry of June 20, 1937).

Based on the Google Books preview of the latter book it includes the full text of Zuse's German patent application Z391 from 1941, which contains (p. 116 of the book; document 005/011 in the online Zuse archive) the following sentence:

Um Verwechslungen zu vermeiden, wird bei Sekundalzahlen die Ziffer 1 als L geschrieben.

"Sekundalzahlen" is Zuse's term for binary numbers. The sentence states that 'L' is used instead of '1' to prevent mixups. A plausible hypothesis as to the nature of the mixup in question is that typewriters in the 1930s and 1940s often lacked a dedicated '1'-key, requiring typists to use the lowercase letter 'l' instead. A perusal of a site dealing with trade in old typewriters that includes pictures of typewriters available for sale shows that this restriction also applied to at least some models of the German brands Adler, Olympia, and AEG. The use of the uppercase letter 'L' would therefore have been motivated by a desire to distinguish the binary digit from an ordinary decimal '1' and the lowercase letter 'l'.

I am not aware of any sources that suggest an origin of the 0/L notation in works preceding Zuse's, but cannot with certainty eliminate the possibility that he adapted it from some other, pre-existing work.

njuffa
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