"digital computers, where the efficiency of addition, in particular the carry mechanism, is an important limitation to overall performance. The abacus, also called a counting frame, is a calculating tool that was in use centuries before the adoption of the written modern numeral system and is still widely used by merchants, traders and clerks in Asia, Africa, and elsewhere; it dates back to at least 2700–2300 BC, when it was used in Sumer. Blaise Pascal invented the mechanical calculator in 1642; it was the first operational adding machine. It made use of a gravity-assisted carry mechanism. It was the only"
"Mechanical calculator A mechanical calculator, or calculating machine, is a mechanical device used to perform automatically the basic operations of arithmetic. Most mechanical calculators were comparable in size to small desktop computers and have been rendered obsolete by the advent of the electronic calculator. Surviving notes from Wilhelm Schickard in 1623 reveal that he designed and had built the earliest of the modern attempts at mechanizing calculation. His machine was composed of two sets of technologies: first an abacus made of Napier's bones, to simplify multiplications and divisions first described six years earlier in 1617, and for the mechanical part,"
"1639 had been appointed the king's commissioner of taxes in the city of Rouen—a city whose tax records, thanks to uprisings, were in utter chaos. In 1642, in an effort to ease his father's endless, exhausting calculations, and recalculations, of taxes owed and paid (into which work the young Pascal had been recruited), Pascal, not yet 19, constructed a mechanical calculator capable of addition and subtraction, called ""Pascal's calculator"" or the ""Pascaline"". Of the eight Pascalines known to have survived, four are held by the Musée des Arts et Métiers in Paris and one more by the Zwinger museum in"
"process. The notion of a mechanical calculator for mathematical functions can be traced back to the Antikythera mechanism of the 2nd century BC, while early modern examples are attributed to Pascal and Leibniz in the 17th century. In 1784 J. H. Müller, an engineer in the Hessian army, devised and built an adding machine and described the basic principles of a difference machine in a book published in 1786 (the first written reference to a difference machine is dated to 1784), but he was unable to obtain funding to progress with the idea. Charles Babbage began to construct a small"
"Stepped reckoner The step reckoner (or stepped reckoner) was a digital mechanical calculator invented by the German mathematician Gottfried Wilhelm Leibniz around 1672 and completed in 1694. The name comes from the translation of the German term for its operating mechanism, ""Staffelwalze"", meaning 'stepped drum'. It was the first calculator that could perform all four arithmetic operations. Its intricate precision gearwork, however, was somewhat beyond the fabrication technology of the time; mechanical problems, in addition to a design flaw in the carry mechanism, prevented the machines from working reliably. Two prototypes were built; today only one survives in the National"
"Pascal's calculator Pascal's calculator (also known as the arithmetic machine or Pascaline) is a mechanical calculator invented by Blaise Pascal in the early 17th century. Pascal was led to develop a calculator by the laborious arithmetical calculations required by his father's work as supervisor of taxes in Rouen. He designed the machine to add and subtract two numbers directly and to perform multiplication and division through repeated addition or subtraction. Pascal's calculator was especially successful in the design of its carry mechanism, which adds 1 to 9 on one dial, and when it changes from 9 to 0, carries 1"
"operational mechanical calculator in the 17th century and the earliest automatic, digital computer. Pascal's calculator was limited by its carry mechanism, which forced its wheels to only turn one way so it could add. To subtract, the operator had to use the Pascal's calculator's complement, which required as many steps as an addition. Giovanni Poleni followed Pascal, building the second functional mechanical calculator in 1709, a calculating clock made of wood that, once setup, could multiply two numbers automatically. Adders execute integer addition in electronic digital computers, usually using binary arithmetic. The simplest architecture is the ripple carry adder, which"
"an office environment. The Arithmometer was designed around Leibniz wheels and initially used Pascal's 9's complement method for subtractions. Pascal's calculator Pascal's calculator (also known as the arithmetic machine or Pascaline) is a mechanical calculator invented by Blaise Pascal in the early 17th century. Pascal was led to develop a calculator by the laborious arithmetical calculations required by his father's work as supervisor of taxes in Rouen. He designed the machine to add and subtract two numbers directly and to perform multiplication and division through repeated addition or subtraction. Pascal's calculator was especially successful in the design of its carry"
"not realized. Johann Helfrich von Müller Johann Helfrich von Müller (January 16, 1746 – 1830) was an engineer in the Hessian army who conceived the difference engine in 1786 (first written reference to the basic principles of a difference machine is dated to 1784), an idea that later evolved into modern computers. In 1784, he was responsible for an improved adding machine based on principles of Leibniz's stepped reckoner. Müller was demonstrably the first who came up with the idea of calculating mathematical tables automatically by a machine. To achieve this, he planned building a printing differential engine. However, this"
"Arithmometer The Arithmometer or Arithmomètre was the first digital mechanical calculator strong enough and reliable enough to be used daily in an office environment. This calculator could add and subtract two numbers directly and could perform long multiplications and divisions effectively by using a movable accumulator for the result. Patented in France by Thomas de Colmar in 1820 and manufactured from 1851 to 1915, it became the first commercially successful mechanical calculator. Its sturdy design gave it a strong reputation for reliability and accuracy and made it a key player in the move from to calculating machines that took place"
"development of sophisticated computing equipment. Wilhelm Schickard designed and constructed the first working mechanical calculator in 1623. In 1673, Gottfried Leibniz demonstrated a digital mechanical calculator, called the Stepped Reckoner. He may be considered the first computer scientist and information theorist, for, among other reasons, documenting the binary number system. In 1820, Thomas de Colmar launched the mechanical calculator industry when he released his simplified arithmometer, which was the first calculating machine strong enough and reliable enough to be used daily in an office environment. Charles Babbage started the design of the first ""automatic mechanical calculator"", his Difference Engine, in"
"the capacity of the accumulator. To divide by a multidigit divisor, this process is used: It can be seen that these procedures are just mechanized versions of long division and multiplication. Stepped reckoner The step reckoner (or stepped reckoner) was a digital mechanical calculator invented by the German mathematician Gottfried Wilhelm Leibniz around 1672 and completed in 1694. The name comes from the translation of the German term for its operating mechanism, ""Staffelwalze"", meaning 'stepped drum'. It was the first calculator that could perform all four arithmetic operations. Its intricate precision gearwork, however, was somewhat beyond the fabrication technology of"
"Johann Helfrich von Müller Johann Helfrich von Müller (January 16, 1746 – 1830) was an engineer in the Hessian army who conceived the difference engine in 1786 (first written reference to the basic principles of a difference machine is dated to 1784), an idea that later evolved into modern computers. In 1784, he was responsible for an improved adding machine based on principles of Leibniz's stepped reckoner. Müller was demonstrably the first who came up with the idea of calculating mathematical tables automatically by a machine. To achieve this, he planned building a printing differential engine. However, this plan was"
"additions and subtractions directly and multiplication and divisions by repetitions, whilst Schickard's machine, invented several decades earlier was less functionally efficient but was supported by a mechanised form of multiplication tables. These two were followed by a string of inventors and inventions leading to those of Thomas de Colmar who launched the mechanical calculator industry in 1851 when he released his simplified arithmometer (it took him thirty years to refine his machine, patented in 1820, into a simpler and more reliable form). However, they did not gain widespread use until Dorr E. Felt started manufacturing his comptometer (1887) and Burroughs"
"additional innovation with the technological capabilities of the 17th century. because their gears would jam when a carry had to be moved several places along the accumulator. The only 17th century calculating clocks that have survived to this day do not have a machine wide carry mechanism and therefore cannot be called fully effective mechanical calculators. A much more successful calculating clock was built by the Italian Giovanni Poleni in the 18th century and was a two-motion calculating clock (the numbers are inscribed first and then they are processed). The 18th century saw the first mechanical calculator that could perform"
"Gottfried Leibniz (1646–1716), building on Pascal's work, became one of the most prolific inventors in the field of mechanical calculators; he was the first to describe a pinwheel calculator, in 1685, and invented the Leibniz wheel, used in the arithmometer, the first mass-produced mechanical calculator. He also refined the binary number system, foundation of virtually all modern computer architectures. John Hadley (1682–1744) was the inventor of the octant, the precursor to the sextant (invented by John Bird), which greatly improved the science of navigation. Denis Papin (1647–1712) was best known for his pioneering invention of the steam digester, the forerunner"
"aims a debate about whether Pascal or Schickard should be credited as the ""inventor"" of the adding machine (or calculating machine) is probably pointless.) Schickard and Pascal were followed by Gottfried Leibniz who spent forty years designing a four-operation mechanical calculator, the stepped reckoner, inventing in the process his leibniz wheel, but who couldn't design a fully operational machine. There were also five unsuccessful attempts to design a calculating clock in the 17th century. The 18th century saw the arrival of some notable improvements, first by Poleni with the first fully functional calculating clock and four-operation machine, but these machines"
"of effort and 50 prototypes he invented a mechanical calculator. He built twenty of these machines (called Pascal's calculator or Pascaline) in the following ten years. Nine Pascalines have survived, most of which are on display in European museums. 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. Gottfried Wilhelm von Leibniz invented the stepped reckoner and his famous stepped drum mechanism around 1672. He attempted to create a machine that could be used not only for addition and"
"machine in 1818 while serving in the French Army where he had to do a great deal of calculations. He made use of principles from previous mechanical calculators like the stepped reckoner of Leibniz and Pascal's calculator. He patented it on November 18, 1820. This machine implements a true multiplication where, by just pulling on a ribbon, the multiplicand entered on the input sliders is multiplied by a one-digit multiplier number and it uses the method for subtracting. Both of these features will be dropped in later designs. The first machine was built by Devrine, a Parisian clockmaker, and took"
"in Butzbach and had some astronomical instruments made. In 1618, he appointed Daniel Mögling (alias Theophilus Schweighart), who was a Rosicrucian and medical doctor and a member of a family of professors from Tübingen, as a court mathematician and court astronomer. Mogling, who also translated Philip Sidney's ""Arcadia"" brought him into contact with Wilhelm Schickard (1592–1635), who had invented a calculating machine in 1623. Philip III also corresponded with the astronomers Kepler and Galileo. He had met the 17 years older Galileo during his two trips to Italy in 1602 and 1607. Kepler visited Butzabch twice, in July 1621 and"
"multiplier or divisor digits, in a procedure equivalent to the familiar long multiplication and long division procedures taught in school. Sequences of these operations can be performed on the number in the accumulator; for example it can calculate roots by a series of divisions and additions. Leibniz got the idea for a calculating machine in 1672 in Paris, from a pedometer. Later he learned about Blaise Pascal's machine when he read Pascal's ""Pensees"". He concentrated on expanding Pascal's mechanism so it could multiply and divide. He presented a wooden model to the Royal Society of London on 1 February 1673"
"of the calculus ratiocinator (ca 1680): ""The clock"": Bolter credits the invention of the weight-driven clock as ""The key invention [of Europe in the Middle Ages]"", in particular, the verge escapement that provides us with the tick and tock of a mechanical clock. ""The accurate automatic machine"" led immediately to ""mechanical automata"" beginning in the 13th century and finally to ""computational machines""—the difference engine and analytical engines of Charles Babbage and Countess Ada Lovelace, mid-19th century. Lovelace is credited with the first creation of an algorithm intended for processing on a computer – Babbage's analytical engine, the first device considered"
"Jean-Baptiste Schwilgué Jean-Baptiste Schwilgué (born in Strasbourg in 1776, died in the same place in 1856) was the author of the third astronomical clock of Strasbourg Cathedral, built between 1838 and 1843 (not 1842, as it is written on the clock itself). In 1844 Schwilgué, together with his son Charles, patented a key-driven calculating machine (see the link in the External Links section), which seems to be the third key-driven machine in the world, after that of Luigi Torchi (1834) and James White (1822). He produced a number of clocks for church towers, of which the only one still functioning"
"Blaise Pascal Blaise Pascal (; ; 19 June 1623 – 19 August 1662) was a French mathematician, physicist, inventor, writer and Catholic theologian. He was a child prodigy who was educated by his father, a tax collector in Rouen. Pascal's earliest work was in the natural and applied sciences where he made important contributions to the study of fluids, and clarified the concepts of pressure and vacuum by generalising the work of Evangelista Torricelli. Pascal also wrote in defence of the scientific method. In 1642, while still a teenager, he started some pioneering work on calculating machines. After three years"
"Percy Ludgate Percy Edwin Ludgate (2 August 1883 – 16 October 1922) was an accountant in Dublin and designer of an analytical engine. Working alone, Ludgate designed an analytical engine while unaware of Charles Babbage's designs, although he later went on to write about Babbage's machine. Ludgate's engine used multiplication as its base mechanism unlike Babbage's which used addition, Ludgate's engine used rods similar to slide rules. Its precise mechanism is unknown as the only written accounts of the engine which survive do not detail its workings. Ludgate also helped advance calculators by expanding Charles Babbage's design for the first"
"along with instructions on how to use the tables to simplify the types of calculations he needed to perform. In 1840 Fowler produced a mechanical calculating machine which operated using balanced ternary arithmetic. This machine was designed to give mechanical form to the techniques described in his book, ""Tables for Facilitating Arithmetical Calculations"". The choice of balanced ternary allowed the mechanisms to be simple, though the values had to be converted to balanced ternary before processing and the results converted back to decimal at the end of the calculation. Apprehensive in case his ideas should again be stolen, he designed"
"mechanical calculator ever designed. Odhner thought of his machine in 1871 while repairing a Thomas' Arithmometer (which was the only mechanical calculator in production at the time) and decided to replace its heavy, bulky Leibniz cylinder by a lighter, smaller pinwheel disk. This is why the two machines share the same name but look completely different. Odhner developed the first version of his mechanical calculator in 1873. In 1876, he agreed to build 14 machines for Ludvig Nobel, his employer at the time, which he delivered in 1877. He patented his original machine in several countries in 1878–1879 and an"
"by Blaise Pascal's work with calculating machines to combine the Pascaline with Napier's bones, and build a machine that could perform both addition and multiplication. Grillet displayed his machine at fairs in France and the Netherlands between 1673 and 1681. He tried to establish a business of manufacturing and selling calculating machines, with unclear success. In addition to the calculating machine, in his career Grillet invented a hygrometer (for which he was accused of plagiarism by another inventor); graphometers; drawing instrument set; protractor, set square, with plumb-bob. In 1690, the first textile-printing factory in England was established by a Frenchman"
"Arithmaurel First patented in France by Timoleon Maurel, in 1842, the Arithmaurel was a mechanical calculator that had a very intuitive user interface, especially for multiplying and dividing numbers because the result was displayed as soon as the operands were entered. It received a gold medal at the French national show in Paris in 1849. Unfortunately its complexity and the fragility of its design prevented it from being manufactured. Its name came from the concatenation of Arithmometer, the machine that inspired its design and of Maurel, the name of its inventor. The heart of the machine uses one Leibniz stepped"
"Renaissance saw the invention of the mechanical calculator (by Wilhelm Schickard and several decades later Blaise Pascal), a device that was at times somewhat over-promoted as being able to perform all four arithmetic operations with minimal human intervention. Pascal's calculator could add and subtract two numbers directly and thus, if the tedium could be borne, multiply and divide by repetition. Schickard's machine, constructed several decades earlier, used a clever set of mechanised multiplication tables to ease the process of multiplication and division with the adding machine as a means of completing this operation. (Because they were different inventions with different"
"for mathematical practitioners; not only did he make and sell instruments, he also collaborated on their design and sold mathematical books. The Oxford Museum of the History of Science has acquired two of his quadrants along with a small amount of his prints, and cites him as ""perhaps the most talented and original mathematical instrument maker in London in the middle of the seventeenth century"". Henry Sutton (instrument maker) Henry Sutton (ca. 1637-1665) was an English instrument maker who operated out of London from 1650 to 1661. He is known for his high-quality engravings of scales and quadrants. His colleagues"
"designed his arithmometer, the first mechanical calculator strong enough and reliable enough to be used daily in an office environment. It is not clear whether he ever saw Leibniz's device, but he either re-invented it or utilised Leibniz's invention of the step drum. Pascal began to work on his calculator in 1642, when he was 19 years old. He had been assisting his father, who worked as a tax commissioner, and sought to produce a device which could reduce some of his workload. Pascal received a Royal Privilege in 1649 that granted him exclusive rights to make and sell calculating"
"Alfred Deacon of London in c. 1862 produced a small difference engine (20-digit numbers and third-order differences). American George B. Grant started working on his calculating machine in 1869, unaware of the works of Babbage and Scheutz (Schentz). One year later (1870) he learned about difference engines and proceed to design one himself, describing his construction in 1871. In 1874 the Boston Thursday Club raised a subscription for the construction of a large-scale model, which was built in 1876. It could be expanded to enhance precision, weighed about . Christel Hamann built one machine (16-digit numbers and second-order differences) in"