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T.R.N. Rao, A.K. Trehan, "Binary Logic for Residue Arithmetic Using Magnitude Index," IEEE Transactions on Computers, vol. 19, no. 8, pp. 752757, August, 1970.  
BibTex  x  
@article{ 10.1109/TC.1970.223026, author = {T.R.N. Rao and A.K. Trehan}, title = {Binary Logic for Residue Arithmetic Using Magnitude Index}, journal ={IEEE Transactions on Computers}, volume = {19}, number = {8}, issn = {00189340}, year = {1970}, pages = {752757}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.1970.223026}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Binary Logic for Residue Arithmetic Using Magnitude Index IS  8 SN  00189340 SP752 EP757 EPD  752757 A1  T.R.N. Rao, A1  A.K. Trehan, PY  1970 KW  Base extension KW  index generation logic KW  magnitude index KW  modular adders KW  naturalized form KW  overflow detection KW  residue multiplication KW  residue number system KW  scale by 2 KW  sign determination. VL  19 JA  IEEE Transactions on Computers ER   
We consider a residue number system using n pairwise relatively prime moduli m1 ,?,mn to represent any integer X in the range M/ 2=X>M/2, when M = ?mi. The moduli mi are chosen to be of the 21 type, in order that the residue arithmetic can be implemented by means of binary registers and binary logic. Further, for each residue number X, a magnitude index Px is maintained for all arithmetic operations. We investigate the properties of such a system and derive the addition, subtraction, multiplication, sign determination, and overflow detection algorithms. The proposed organization is found to improve the operation times for sign detection and overflow detection operations, while rendering multiplication to be a difficult operation.
Index Terms:
Base extension, index generation logic, magnitude index, modular adders, naturalized form, overflow detection, residue multiplication, residue number system, scale by 2, sign determination.
Citation:
T.R.N. Rao, A.K. Trehan, "Binary Logic for Residue Arithmetic Using Magnitude Index," IEEE Transactions on Computers, vol. 19, no. 8, pp. 752757, Aug. 1970, doi:10.1109/TC.1970.223026
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