Rational Arithmetic
Eric Hehner and Nigel Horspool proposed in 1979 the use of a p-adic representation for rational numbers on computers called Quote notation. The primary advantage of such a representation is that addition, subtraction, and multiplication can be done in a straightforward manner analogous to similar methods for binary integers; and division is even simpler, resembling multiplication. However, it has the disadvantage that representations can be much larger than simply storing the numerator and denominator in binary; for example, if 2n − 1 is a Mersenne prime, its reciprocal will require 2n − 1 bits to represent.
Read more about this topic: p-adic Number
Famous quotes containing the words rational and/or arithmetic:
“One rational voice is dumb: over a grave
The household of Impulse mourns one dearly loved.
Sad is Eros, builder of cities,
And weeping anarchic Aphrodite.”
—W.H. (Wystan Hugh)
“Your discovery of the contradiction caused me the greatest surprise and, I would almost say, consternation, since it has shaken the basis on which I intended to build my arithmetic.... It is all the more serious since, with the loss of my rule V, not only the foundations of my arithmetic, but also the sole possible foundations of arithmetic seem to vanish.”
—Gottlob Frege (1848–1925)