Editing Signed-digit representation (section)

==History==
Challenges in [[calculation]] stimulated early authors Colson (1726) and Cauchy (1840) to use signed-digit representation. The further step of replacing negated digits with new ones was suggested by Selling (1887) and Cajori (1928).

In 1928, [[Florian Cajori]] noted the recurring theme of signed digits, starting with [[John Colson|Colson]] (1726) and [[Augustin-Louis Cauchy|Cauchy]] (1840).<ref>[[Augustin-Louis Cauchy]] (16 November 1840) "Sur les moyens d'eviter les erreurs dans les calculs numerique", [[Comptes rendus]] 11:789. Also found in ''Oevres completes'' Ser. 1, vol. 5, pp.&nbsp;434&ndash;42.</ref> In his book ''History of Mathematical Notations'', Cajori titled the section "Negative numerals".<ref>{{cite book |last= Cajori |first=Florian |author-link=Florian Cajori|title= A History of Mathematical Notations |page= [https://archive.org/details/historyofmathema00cajo_0/page/57 57] |publisher= [[Dover Publications]] |year= 1993 |orig-year= 1928-1929 |isbn= 978-0486677668 | url = https://archive.org/details/historyofmathema00cajo_0|url-access= registration }}</ref> For completeness, Colson<ref>{{Cite journal |last=Colson |first=John |date=1726 |title=A Short Account of Negativo-Affirmative Arithmetick, by Mr. John Colson, F. R. S. |url=https://www.jstor.org/stable/103469 |journal=Philosophical Transactions |volume=34 |pages=161–173 |jstor=103469 |bibcode=1726RSPT...34..161C |issn=0260-7085}}</ref> uses examples and describes [[addition]] (pp.&nbsp;163–4), [[multiplication]] (pp.&nbsp;165–6) and [[division (mathematics)|division]] (pp.&nbsp;170–1) using a table of multiples of the divisor. He explains the convenience of approximation by truncation in multiplication. Colson also devised an instrument (Counting Table) that calculated using signed digits.

[[Eduard Selling]]<ref>Eduard Selling (1887) ''Eine neue Rechenmachine'', pp.&nbsp;15&ndash;18, Berlin</ref> advocated inverting the digits 1, 2, 3, 4, and 5 to indicate the negative sign. He also suggested ''snie'', ''jes'', ''jerd'', ''reff'', and ''niff'' as names to use vocally. Most of the other early sources used a bar over a digit to indicate a negative sign for it. Another German usage of signed-digits was described in 1902 in [[Klein's encyclopedia]].<ref>Rudolf Mehmke (1902) "Numerisches Rechen", §4 Beschränkung in den verwendeten Ziffern, [[Klein's encyclopedia]], I-2, p.&nbsp;944.</ref>