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On the Design of Modulo Arithmetic Units Based on Cyclic Groups
November 1976 (vol. 25 no. 11)
pp. 1057-1067
ASCII Text
x 
 
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, November, 1976.
 
 
BibTex
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@article{ 10.1109/TC.1976.1674555,
author = {S.S. Yau and J. Chung},
title = {On the Design of Modulo Arithmetic Units Based on Cyclic Groups},
journal ={IEEE Transactions on Computers},
volume = {25},
number = {11},
issn = {0018-9340},
year = {1976},
pages = {1057-1067},
doi = {http://doi.ieeecomputersociety.org/10.1109/TC.1976.1674555},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Computers
TI - On the Design of Modulo Arithmetic Units Based on Cyclic Groups
IS - 11
SN - 0018-9340
SP1057
EP1067
EPD - 1057-1067
A1 - S.S. Yau,
A1 - J. Chung,
PY - 1976
KW - Binary encoding
KW - cyclic groups
KW - design
KW - modulo arithmetics
KW - modulo arithmetic units
KW - residue number system.
VL - 25
JA - IEEE Transactions on Computers
ER -
 
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
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