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On Binal Fractions

Published online by Cambridge University Press:  03 November 2016

Allan Cunningham
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Binal Fractions. The reciprocals (1/N) of any number (N) will be termed Binal Fractions, or shortly Binals, when expressed in the binary scale. The notation used is similar to that of ordinary decimals. Thus (see table at end):

1°. A point is used to mark the beginning of the fraction.

2°. The binal (1/N) consists of a certain sequence of ciphers and units (the only digits used) to the right of the point; partly non-recurrent and partly recurrent.

Type
Research Article
Information
The Mathematical Gazette , Volume 4 , Issue 71 , May 1908 , pp. 259 - 267
Copyright
Copyright © Mathematical Association 1908

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References

page 260 note * In the author’s Paper on Haupt-Exponents of 2, in the Quarterly Journal of Pure and Applied Mathematics, vol. 37, 1905, p. 142, a Table of the values of (p–1)÷ξ is given—for prime moduli (p)—up to p ≯ 10000; from which the value of ξ can be found by a trifling division.