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:
“So far as discipline is concerned, freedom means not its absence but the use of higher and more rational forms as contrasted with those that are lower or less rational.”
—Charles Horton Cooley (1864–1929)
“Under the dominion of an idea, which possesses the minds of multitudes, as civil freedom, or the religious sentiment, the power of persons are no longer subjects of calculation. A nation of men unanimously bent on freedom, or conquest, can easily confound the arithmetic of statists, and achieve extravagant actions, out of all proportion to their means; as, the Greeks, the Saracens, the Swiss, the Americans, and the French have done.”
—Ralph Waldo Emerson (1803–1882)