In the literature several methods to achieve exact computation on real numbers has been investigated. In some of these methods real numbers are represented by infinite (lazy) strings of digits. It is a well known fact that, when this approach is taken, the standard digit notation cannot be used. New forms of digit notations for the reals are necessary. The standard solution to this representation problem consists in adding negative digits to the notation. In this article we present an alternative solution. It consists in using non natural numbers as ``base''. That is to use positional digit notation where the ratio between the weight of two consecutive digits it is not necessarily a natural number, as in the standard case, but it can be a rational or even an irrational number. We discuss in full one particular example for this form of notation: namely the one having two digits (0 and 1) and the golden ratio as base. This choice is motivated by the pleasing properties enjoyed by the golden ratio notation. In particular the algorithms for the arithmetic operations are quite simple when this notation is used.