Download A History of Algorithms: From the Pebble to the Microchip by Jean-Luc Chabert, C. Weeks, Evelyne Barbin, J. Borowczyk, M. PDF

By Jean-Luc Chabert, C. Weeks, Evelyne Barbin, J. Borowczyk, M. Guillemot, A. Michel-Pajus, A. Djebbar, Jean-Claude Martzloff

ISBN-10: 3540633693

ISBN-13: 9783540633693

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The improvement of computing has reawakened curiosity in algorithms. frequently missed by means of historians and glossy scientists, algorithmic approaches were instrumental within the improvement of primary rules: perform ended in concept simply up to the opposite direction around. the aim of this booklet is to provide a ancient heritage to modern algorithmic perform.

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The extent to which the divisibility characteristics of a number are evident or not depends upon the numeration system being used. 9 Binary Arithmetic 41 deduced from the way they were written. It also has the advantage of only requiring a small number of signs for representing a number. We also know about the interest that Leibniz had for Chinese hieroglyphics, it being moreover one of the topics dealt with in his 1703 memoir. Leibniz relates that, according to Chinese legend, king Fohy (Fu Xi) introduced 'the figure of eight Cova' consisting of diagrams of the form: The meaning of this figure had remained mysterious up till then, but Leibniz provided an explanation by appealing to the binary numeration system.

5 Optimising Calculations 29 Ibn al-MajdI From Qiiwf l-lubiib Ms. British Museum, W Add. 7469, ff. 41 b-42a. From the French translation of the Arabic by A. Djebbar. You need, in [problems) like this to carry out a number of multiplications [equal) to the number of the square [of the number of digits) of the number [you wish to square) [... ). To summarise, we can say: take away from the number of multiplications half of what remains of the square of the number of places of [the number) raised to a square, after having taken [from it) half the number of [the digits of] that number.

We can also represent a rational number as a binary word, by including in the word a marker to show the beginning of the fractional part. The position of this marker, designated by a point, can be moved, which is why it is called floating point representation. Thus an ... fif,. 1m with aj =0 or 1, andjj =0 or 1 stands for the rational number an2n + ... + al2 + ao + jj2- l +/22- 2 + ... +Im 2-m. 1001 represents the number 8 + 2 + 1 + 112 + 1116 = 11 + 9/16. Using this system, just as with the denary system, rational numbers do not all have an exact finite representation.

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