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:
“What is rational is actual and what is actual is rational. On this conviction the plain man like the philosopher takes his stand, and from it philosophy starts in its study of the universe of mind as well as the universe of nature.”
—Georg Wilhelm Friedrich Hegel (1770–1831)
“O! O! another stroke! that makes the third.
He stabs me to the heart against my wish.
If that be so, thy state of health is poor;
But thine arithmetic is quite correct.”
—A.E. (Alfred Edward)