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Erschienen in:
What Is a Computer? Kapitel lesen Erstes Kapitel lesen

2021 | OriginalPaper | Buchkapitel

3. Foundations of Computing

verfasst von : Gerard O’Regan

Erschienen in: A Brief History of Computing

Verlag: Springer International Publishing

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Abstract

This chapter discusses the foundations of computing, including the binary number system and the Step Reckoner calculating machine, which were invented by Leibniz. The difference engine was designed by Babbage to evaluate polynomials and to produce accurate mathematical tables. Babbage’s design of the analytic engine provided the vision of a modern computer, and Boole’s symbolic logic provides the foundation for digital computing.

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Vorheriges Kapitel Computing in Early Civilizations
Nächstes Kapitel The First Digital Computers
Fußnoten
1
The segadecimal (or base-60) system was employed by the Babylonians c. 2000 BC. Indian and Arabic mathematicians developed the decimal system between 800 and 900 AD.
 
2
The power series expansion of the sine function is given by Sin(x) = x − x3/3! + x5/5! − x7/7! + ... The power series expansion for the cosine function is given by Cos(x) = 1 − x2/2! + x4/4! − x6/6! + ... Functions may be approximated by interpolation and the approximation of a function by a polynomial of degree n requires n + 1 points on the curve for the interpolation. That is, the curve formed by the polynomial of degree n that passes through the n + 1 points of the function to be approximated is an approximation to the function. The error function also needs to be considered.
 
3
The Jacquard loom was invented by Joseph Jacquard in 1801. It is a mechanical loom which used the holes in punch cards to control the weaving of patterns in a fabric. The use of punched cards allowed complex designs to be woven from the pattern defined on the punched cards. Each punched card corresponds to one row of the design and the cards were appropriately ordered. It was very easy to change the pattern of the fabric being weaved on the loom, as this simply involved changing cards.
 
4
Lady Ada Lovelace was the daughter of the poet Lord Byron.
 
5
There is some controversy as to whether this was entirely her own work or a joint effort by Lovelace and Babbage.
 
6
De-Morgan was a nineteenth-century British mathematician based at University College London. De-Morgan’s laws in Set Theory and Logic state that: (A ∪ B)c = Ac ∩ Bc and ¬ (A ∨ B) ≡ ¬A ∧ ¬B.
 
7
Finite Differences are a numerical method used in solving differential equations.
 
8
Victor Shestakov at Moscow State University also proposed a theory of electric switches based on Boolean algebra (published in Russian in 1941 whereas Shannon’s were published in 1937).
 
Literatur
Boo:48.
The Calculus of Logic. George Boole. Cambridge and Dublin Mathematical Journal. Vol. III (1848), pp. 183–98.
Boo:58.
An Investigation into the Laws of Thought. George Boole. Dover Publications. 1958. (First published in 1854)
Lei:03.
Explication de l’Arithmétique Binaire Wilhelm Gottfried Leibniz. Memoires de l’Academie Royale des Sciences. 1703.
Lov:42.
Sketch of the Analytic Engine invented by Charles Babbage. L.F. Menabrea, Bibliothèque Universelle de Genève, October, 1842, No. 82 Translated by Ada, Augusta, Countess of Lovelace.
McH:85.
Boole. Des McHale. Cork University Press. 1985.
ORg:13.
Giants of Computing. Gerard O’ Regan. Springer Verlag. 2013.
Sha:37.
A Symbolic Analysis of Relay and Switching Circuits. Claude Shannon. Masters Thesis. Massachusetts Institute of Technology. 1937.
Metadaten
Titel
Foundations of Computing
verfasst von
Gerard O’Regan
Copyright-Jahr
2021
Buch
A Brief History of Computing

Print ISBN: 978-3-030-66598-2

Electronic ISBN: 978-3-030-66599-9

Copyright-Jahr: 2021

DOI
https://doi.org/10.1007/978-3-030-66599-9_3