MSB-First Digit Serial Arithmetic

We develop a formal account of digit serial number representations by describing them as strings from a language. A pre x of a string represents an interval approximating a number by enclosure. Standard on-line representations are shown to be a special case of the general digit serial representations. Matrices are introduced as representations of intervals and a nite-state transducer is used for mapping strings into intervals. Homographic and bi-homographic functions are used for representing basic arithmetic operations on digit serial numbers, and nally a digit serial representation of oating point numbers is introduced.