We develop a formal account of digit serial number representations by describing them as strings from a language. A prefix of a string represents an int erval approximating a number by enclosure. Standard on-line representations are shown to be a special case of the general digit serial representations. Matrices are introd uced as representations of intervals and a finite-state transducer is used for mapping str ings into intervals. Homographic and bi-homographic functions are used for representing basi c arithmetic operations on digit serial numbers, and finally a digit serial represen tation of floating point numbers is introduced. 1.) This work has been supported by The Danish Research Councils under the grant no.5.21.08.02.

Computer Arithmetic, On-line Computation, Number Representations, Redundant Digit sets, Continued Fractions, Intervals