DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE                
                               ODENSE UNIVERSITY                               

                       MSB-first Digit Serial Arithmetic                       

                                Asger M. Nielsen                               
                 Department of Mathematics and Computer Science                
                               Odense University                               

                     Tuesday, February 14, 1995, at 2:15 PM                    
                                The Seminar Room                               


  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  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 finite-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 finally a  digit serial
  representation of floating point numbers is introduced.


                                                               Kim Skak Larsen