Abstract
Many of the modulo arithmetics can be considered as cyclic groups. A generalized method for implementing the cyclic groups is established based on a decomposed mapping approach. In order to obtain efficient implementation of cyclic groups, certain mapping relations and a proper binary encoding method are investigated. Furthermore, a new class of code, called the circulative code, is developed, and two methods for generating such a code are presented. Various modulo arithmetic units can then be easily designed through a unique formula and can also be machine implemented. The modulo arithmetic units using this design approach are usually simpler than those conventional ones.
Original language | English (US) |
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Pages (from-to) | 1057-1067 |
Number of pages | 11 |
Journal | IEEE Transactions on Computers |
Volume | C-25 |
Issue number | 11 |
DOIs | |
State | Published - Nov 1976 |
Externally published | Yes |
Keywords
- Binary encoding
- arithmetics
- cyclic groups
- design
- modulo
- modulo arithmetic units
- residue number system
ASJC Scopus subject areas
- Software
- Theoretical Computer Science
- Hardware and Architecture
- Computational Theory and Mathematics