This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
On the Design of Modulo Arithmetic Units Based on Cyclic Groups
November 1976 (vol. 25 no. 11)
pp. 1057-1067
S.S. Yau, Departments of Computer Sciences and Electrical Engineering, Northwestern University
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.
Index Terms:
Binary encoding, cyclic groups, design, modulo arithmetics, modulo arithmetic units, residue number system.
Citation:
S.S. Yau, J. Chung, "On the Design of Modulo Arithmetic Units Based on Cyclic Groups," IEEE Transactions on Computers, vol. 25, no. 11, pp. 1057-1067, Nov. 1976, doi:10.1109/TC.1976.1674555
Usage of this product signifies your acceptance of the Terms of Use.