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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.
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
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