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

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

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The improvement of computing has reawakened curiosity in algorithms. usually missed through historians and smooth scientists, algorithmic methods were instrumental within the improvement of primary rules: perform resulted in thought simply up to the wrong way around. the aim of this publication is to provide a ancient heritage to modern algorithmic perform.

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Magic squares have not, however, always been thought of in this way.

This is repeated n times. This technique of adding a number to the previous result (shifting in this special case) is called accumulation. In practice, if the multiplier bit is zero, the addition can be simply skipped, but not the shift of course. This method of binary multiplication is referred to as shift-and-add. The result of multiplying two n bit numbers may be a 2n bit number, so a double register is needed to accommodate it. The multiplication can be carried out using five registers: register A stays constant and contains the multiplicand, register B contains the multiplier initially, register BM holds the bit multiplier and the double register P I -P 2 holds accumulated results.

In fact, it is found contemporaneously, and at different times, in China, India, the Arab world and in Europe. The use of this technique in all civilisations rests on the same basic mathematical principle, but with many variations in the way it is presented and the names given to it: it is known variously as multiplication using a 'tableau', a 'grid', a 'net', or 'the jalousie'. This last was so called because it referred to a type of Venetian blind in the form of a grating, common in Venice, through which nuns or ladies could see out from the inside without being observed from the outside.

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