Quote notation

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Quote notation is a represention of the rational numbers for which the addition, subtraction, and multiplication algorithms are the same as for the natural numbers, and division is easier than the usual division algorithm, and works in the same direction (right-to-left) as the other arithmetic algorithms. It was invented by Eric Hehner of the University of Toronto, and published in the SIAM Journal on Computation, v.8, n.2, May 1979, pp. 124–134.

The representation is based on Hensel's p-adic arithmetic. The basic idea is to represent the rational number $x - 10y/999\ldots$ as $\ldots0y'x$ , where there are as many decimal digits in $\ldots0y$ as in $999\ldots$ . Thus, 191/33 is 7-120/99 is 12'7, and $- 10$ is 0-90/9 is 9'0. (This representation of negative integers corresponds to the use of two's complement in binary representations.)

The extension of quote notation from the decimal system to the binary system, in which only two symbols are needed, is also explored in Hehner's paper.