Why are there floating point bases?

1 answer

The author may have made an exaggeration, but given that bases 2 and 10 (binary and decimal) are the most common to use, this is the worst case philosophical faux pas. Per http://www.eecs.berkeley.edu/~wkahan/ieee754status/why-ieee.pdf: "Almost every machine that provides floating point arithmetic does this in binary (radix 2), octal (8), decimal (10) or hexadecimal (16). Biological and historical accidents make 10 the preferred basis for machines whose arithmetic will be subjected to frequent checks by people. Otherwise, binary ones are better. A radius greater than 2 can provide a minimal speed advantage during normalization, since the leading several significant bits can sometimes remain zeros, but this is an advantage its what is compensated by fines in the range / limit of accuracy and "unstable accuracy".

- , . . http://mentalfloss.com/article/31879/12-mind-blowing-number-systems-other-languages, . http://www.math.wichita.edu/history/topics/num-sys.html.

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IEEE (IEEE 754) : http://en.wikipedia.org/wiki/IEEE_floating_point. , , http://www.mrob.com/pub/math/floatformats.html.

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