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Perspex machine XI: topology of the transreal numbers

Anderson, J.A.D.W. (2008) Perspex machine XI: topology of the transreal numbers. In: IMECS 2008: international multiconference of engineers and computer scientists. International Association of Engineers, Hong Kong, pp. 330-338. ISBN 9789889867188

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The transreal numbers are a total number system in which even, arithmetical operation is well defined even-where. This has many benefits over the real numbers as a basis for computation and, possibly, for physical theories. We define the topology of the transreal numbers and show that it gives a more coherent interpretation of two's complement arithmetic than the conventional integer model. Trans-two's-complement arithmetic handles the infinities and 0/0 more coherently, and with very much less circuitry, than floating-point arithmetic. This reduction in circuitry is especially beneficial in parallel computers, such as the Perspex machine, and the increase in functionality makes Digital Signal Processing chips better suited to general computation.

Item Type:Book or Report Section
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Computer Science
ID Code:14335
Uncontrolled Keywords:transmetric space, transreal number, two's complement
Additional Information:International Multiconference of Engineers and Computer Scientists Hong Kong, China 19-21 Mar 2008
Publisher:International Association of Engineers

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