Editing History of computing hardware (section)

===Mechanical calculators===
In 1609, [[Guidobaldo del Monte]] made a mechanical multiplier to calculate fractions of a degree. Based on a system of four gears, the rotation of an index on one quadrant corresponds to 60 rotations of another index on an opposite quadrant.<ref>{{cite journal |first=Domenico Bertolini|last=Meli|date=1992|doi=10.1163/182539192x00019 |title=Guidobaldo Dal Monte and the Archimedean Revival |journal=Nuncius|number=1|pages=3–34|volume=7}}</ref> Thanks to this machine, errors in the calculation of first, second, third and quarter degrees can be avoided. Guidobaldo is the first to document the use of gears for mechanical calculation.

[[Wilhelm Schickard]], a German [[polymath]], designed a calculating machine in 1623 which combined a mechanized form of Napier's rods with the world's first mechanical adding machine built into the base. Because it made use of a single-tooth gear there were circumstances in which its carry mechanism would jam.<ref>{{harvnb|Williams|1997|p=128}} "...the single-tooth gear, like that used by Schickard, would not do for a general carry mechanism. The single-tooth gear works fine if the carry is only going to be propagated a few places but, if the carry has to be propagated several places along the accumulator, the force needed to operate the machine would be of such magnitude that it would do damage to the delicate gear works."</ref> A fire destroyed at least one of the machines in 1624 and it is believed Schickard was too disheartened to build another.

[[File:Pascaline calculator.jpg|thumb|View through the back of [[Pascal's calculator]]. [[Blaise Pascal|Pascal]] invented his machine in 1642.]]
In 1642, while still a teenager, [[Blaise Pascal]] started some pioneering work on calculating machines and after three years of effort and 50 prototypes<ref>{{Cite book |url=https://fr.wikisource.org/wiki/La_Machine_d%E2%80%99arithm%C3%A9tique |last=Pascal |first=Blaise |title=La Machine d'arithmétique |date=1645 |language=fr}}</ref> he invented a [[mechanical calculator]].{{sfn|Marguin|1994|p=48}}{{sfn|Ocagne|1893|p=245}} He built twenty of these machines (called [[Pascal's calculator]] or Pascaline) in the following ten years.{{sfn|Mourlevat|1988|p=12}} Nine Pascalines have survived, most of which are on display in European museums.{{efn|All nine machines are described in {{harvnb|Vidal|Vogt|2011}}.}} A continuing debate exists over whether Schickard or Pascal should be regarded as the "inventor of the mechanical calculator" and the range of issues to be considered is discussed elsewhere.<ref>{{cite web|first=Jim|last=Falk|title=Schickard versus Pascal - an empty debate?|url=https://metastudies.net/pmwiki/pmwiki.php?n=Site.SchicardvsPascal|access-date=2014-05-15 |archive-url=https://web.archive.org/web/20140408215848/http://metastudies.net/pmwiki/pmwiki.php?n=Site.SchicardvsPascal|archive-date=2014-04-08 |url-status=dead}}</ref>

[[File:Napier's calculating tables.JPG|thumb|left|A set of [[John Napier]]'s calculating tables from around 1680]]
[[Gottfried Wilhelm Leibniz|Gottfried Wilhelm von Leibniz]] invented the [[stepped reckoner]] and his [[Leibniz wheel|famous stepped drum mechanism]] around 1672. He attempted to create a machine that could be used not only for addition and subtraction but would use a moveable carriage to enable multiplication and division. Leibniz once said "It is unworthy of excellent men to lose hours like slaves in the labour of calculation which could safely be relegated to anyone else if machines were used."{{sfn|Smith|1929|pp=180–181}} However, Leibniz did not incorporate a fully successful carry mechanism. Leibniz also described the [[binary numeral system]],{{sfn|Leibniz|1703}} a central ingredient of all modern computers. However, up to the 1940s, many subsequent designs (including [[Charles Babbage]]'s machines of 1822 and even [[ENIAC]] of 1945) were based on the decimal system.{{efn|[[Binary-coded decimal]] (BCD) is a numeric representation, or [[character encoding]], which is still widely used.}}

[[File:Arithmometer - Detail of Multiplier pre 1851.jpg|thumb|Detail of an arithmometer built before 1851. The one-digit multiplier cursor (ivory top) is the leftmost cursor.]]

Around 1820, [[Charles Xavier Thomas|Charles Xavier Thomas de Colmar]] created what would over the rest of the century become the first successful, mass-produced mechanical calculator, the Thomas [[Arithmometer]]. It could be used to add and subtract, and with a moveable carriage the operator could also multiply, and divide by a process of long multiplication and long division.<ref>{{Cite web |date=2005 |title=Discovering the Arithmometer |url=https://www.cis.cornell.edu/boom/2005/ProjectArchive/arithometer/ |archive-url=https://web.archive.org/web/20060913173424/http://www.cis.cornell.edu/boom/2005/ProjectArchive/arithometer/index.html |archive-date=2006-09-13 |access-date=2023-08-26 |website=[[Cornell University]]}}</ref> It utilised a stepped drum similar in conception to that invented by Leibniz. Mechanical calculators remained in use until the 1970s.