A ``Binary'' System for Complex Numbers
Journal of the ACM (JACM)
Basic digit sets for radix representation
Journal of the ACM (JACM)
Communications of the ACM
On the Implementation of Arithmetic Support Functions for Generalized Signed-Digit Number Systems
IEEE Transactions on Computers
Digit-Set Conversions: Generalizations and Applications
IEEE Transactions on Computers
A complex-number multiplier using radix-4 digits
ARITH '95 Proceedings of the 12th Symposium on Computer Arithmetic
On Radix Representation of Rings
ARITH '97 Proceedings of the 13th Symposium on Computer Arithmetic (ARITH '97)
Real/Complex Reconfigurable Arithmetic Using Redundant Complex Number Systems
ARITH '97 Proceedings of the 13th Symposium on Computer Arithmetic (ARITH '97)
Constant-Time Addition and Simultaneous Format Conversion Based on Redundant Binary Representations
IEEE Transactions on Computers
Further Reducing the Redundancy of a Notation Over a Minimally Redundant Digit Set
Journal of VLSI Signal Processing Systems
| Hi-index | 14.98 |
This paper presents an analysis of radix representations of elements from general rings; in particular, we study the questions of redundancy and completeness in such representations. Mappings into radix representations, as well as conversions between such, are discussed, in particular where the target system is redundant. Results are shown valid for normed rings containing only a finite number of elements with a bounded distance from zero, essentially assuring that the ring is 驴discrete.驴 With only brief references to the more usual representations of integers, the emphasis is on various complex number systems, including the 驴classical驴 complex number systems for the Gaussian integers, as well as the Eisenstein integers, concluding with a summary on properties of some low-radix representations of such systems.