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:
“Since the Greeks, Western man has believed that Being, all Being, is intelligible, that there is a reason for everything ... and that the cosmos is, finally, intelligible. The Oriental, on the other hand, has accepted his existence within a universe that would appear to be meaningless, to the rational Western mind, and has lived with this meaninglessness. Hence the artistic form that seems natural to the Oriental is one that is just as formless or formal, as irrational, as life itself.”
—William Barrett (b. 1913)
“I hope I may claim in the present work to have made it probable that the laws of arithmetic are analytic judgments and consequently a priori. Arithmetic thus becomes simply a development of logic, and every proposition of arithmetic a law of logic, albeit a derivative one. To apply arithmetic in the physical sciences is to bring logic to bear on observed facts; calculation becomes deduction.”
—Gottlob Frege (1848–1925)