Quote notation

Quote notation is a number system for representing rational numbers which was designed to be attractive for use in computer architecture. In a typical computer architecture, the representation and manipulation of rational numbers is a complex topic. In quote notation, arithmetic operations take particularly simple, consistent forms, and can produce exact answers with no roundoff error.

Quote notation’s arithmetic algorithms work with a typical right-to-left direction, in which the addition, subtraction, and multiplication algorithms have the same complexity for natural numbers, and division is easier than a typical division algorithm.

The notation was invented by Eric Hehner of the University of Toronto and Nigel Horspool, then at McGill University, and published in the SIAM Journal on Computing, v.8, n.2, May 1979, pp. 124–134. The construction of this system follows the approach of Kurt Hensel's p-adic numbers.

A rational number is represented in quote notation as a sequence of digits with a quote mark and radix point. For example, 12'3.4 is in quote notation.

The radix point may come before the quote mark, as in 12.3'4, or at the same place, as in 12!3. When the radix point and the quote coincide, an exclamation point (!) is used.

The radix point has its usual function; moving it left divides by the base; moving it right multiplies by the base. When the radix point is at the right end, the multiplicative factor is 1, and the point can be omitted. Scientific notation may be used as an alternative to the radix point.

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