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Concept# Mechanical calculator

Summary

A mechanical calculator, or calculating machine, is a mechanical device used to perform the basic operations of arithmetic automatically, or (historically) a simulation such as an analog computer or a slide rule. Most mechanical calculators were comparable in size to small desktop computers and have been rendered obsolete by the advent of the electronic calculator and the digital computer.
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, it had a dialed pedometer to perform additions and subtractions. A study of the surviving notes shows a machine that would have jammed after a few entries on the same dial, and that it could be damaged if a carry had to be propagated over a few digits (like adding 1 to 999). Schickard abandoned his project in 1624 and never mentioned it again until his death 11 years later in 1635.
Two decades after Schickard's supposedly failed attempt, in 1642, Blaise Pascal decisively solved these particular problems with his invention of the mechanical calculator. Co-opted into his father's labour as tax collector in Rouen, Pascal designed the calculator to help in the large amount of tedious arithmetic required; it was called Pascal's Calculator or Pascaline.
In 1672, Gottfried Leibniz started designing an entirely new machine called the Stepped Reckoner. It used a stepped drum, built by and named after him, the Leibniz wheel, was the first two-motion calculator, the first to use cursors (creating a memory of the first operand) and the first to have a movable carriage. Leibniz built two Stepped Reckoners, one in 1694 and one in 1706. The Leibniz wheel was used in many calculating machines for 200 years, and into the 1970s with the Curta hand calculator, until the advent of the electronic calculator in the mid-1970s.

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Pascal's calculator

Pascal's calculator (also known as the arithmetic machine or Pascaline) is a mechanical calculator invented by Blaise Pascal in 1642. Pascal was led to develop a calculator by the laborious arithmetical calculations required by his father's work as the 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.

Method of complements

In mathematics and computing, the method of complements is a technique to encode a symmetric range of positive and negative integers in a way that they can use the same algorithm (or mechanism) for addition throughout the whole range. For a given number of places half of the possible representations of numbers encode the positive numbers, the other half represents their respective additive inverses. The pairs of mutually additive inverse numbers are called complements. Thus subtraction of any number is implemented by adding its complement.

Comptometer

The Comptometer was the first commercially successful key-driven mechanical calculator, patented in the United States by Dorr Felt in 1887. A key-driven calculator is extremely fast because each key adds or subtracts its value to the accumulator as soon as it is pressed and a skilled operator can enter all of the digits of a number simultaneously, using as many fingers as required, making them sometimes faster to use than electronic calculators.

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