A binary counting of rational numbers
Samuel C. Hsieh, Christopher Nelson · Journal of computing sciences in colleges · 2011
A one-to-one correspondence between positive binary numbers and positive rational numbers is defined and studied. Efficient algorithms to compute the rational number for a given binary ordinal number and to compute the binary ordinal number for a given rational number are presented and analyzed. This one-to-one correspondence and the related algorithms provide a link between the well-known problem of counting rational numbers and a key topic in computer science: binary numbers. The binary ordinal number of a rational and that of its reciprocal are shown to be related in a simple manner.