Contents

## Outline Introduction Background: Mod-(2 n 1) Addition

Koran, Jessica, Contributing Writer has reference to this Academic Journal, PHwiki organized this Journal Unified Approach to the Design of Modulo-(2n ± 1) Adders Based on Signed-LSB Representation of ResiduesGhassem JaberipurDept. Electrical & Computer Engr. Shahid Beheshti Univ., Tehran, Iranjaberipur@sbu.ac.irBehrooz Parhami Dept. Electrical & Computer Engr. Univ. of Cali as long as nia, Santa Barbara, USA parhami@ece.ucsb.edu19th IEEE International Symposium on Computer Arithmetic Portl in addition to , Oregon, USA, June 8-10, 2009 OutlineIntroductionBackgroundSigned-LSB RepresentationNew Modulo-(2n ± 1) AddersMod-(2n + 1) AdderMod-(2n 1) AdderConversion from/to BinaryComparisons & ApplicationsConclusion2IntroductionRenewed interest in RNS arithmeticSeparate designs as long as mod-(2n ± 1) in addition to mod-2nError-prone in addition to labor-intensive optimizationsNew signed-LSB representation of residuesSole use of st in addition to ard arithmetic building blocksGreater confidence in correctnessConfigurable RNS processor as long as fault tolerance3

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Background: Mod-(2n 1) AdditionMod-m:Mod-(2n1): 4Background: Symbols Used5Background: Mod-2n Adder6

Kalamboukas et al., 20057RPP modulo 255 adderTPP modulo 255 adderBackground: Mod-(2n 1) AddersBackground: Mod-(2n + 1) AdditionMod-(2n+1):W’ is difficult to compute, there as long as e, let 8Background: Mod-(2n + 1) AddersEfstathiou, et al., 20049Flaw:Sn is wrong

Background: Mod-(2n + 1) AddersThe corrected mod-257 TPP adder10Same Latency More areaBackground: Dim-1 RepresentationDiminshed-1 mod-(2n + 1)11Signed-LSB RepresentationFaithful representation of [1, 2n 1]Problem: Mixed posibits in addition to negabits: A + B12

Universal Full AddersFull adder can compress mixed posibits in addition to negabits13X1 + X2 + x3 = X1 1 + X2 1 + x3 = 2c + s 2 = 2C + sNew Modulo-(2n + 1) Adder14Mod-(2n + 1) Signed-LSB Addition15

New Mod-(2n 1) Adder16Mod-(2n + 1) vs. Mod-(2n 1) 17Conversion from/to Binary18Weighted representation Conversion of input to residue representation is very simpleFast residue-to-binary converters implement the Chinese remainder theorem via CSAsWeighted representationSigned-LSB representation

ApplicationsFault-tolerant RNS processor19Comparison: Gate-Level Analysis20Comparison: Synthesis Results21

ConclusionImplementing mod-(2n 1) in addition to mod-(2n + 1) addition using generic CSA in addition to binary addersEasier/faster exploration of the design spaceSimpler testing in addition to verificationGreater confidence in design correctnessConfigurable modular adders (fault tolerance)Potential as long as less complex modular subtractors in addition to modular multipliers22Questions The authors gratefully acknowledge the assistance of Mr. Saeed Nejati in addition to Ms. Hanieh Alavi. G. Jaberipur also acknowledges support from IPM School of Computer Science in addition to from Shahid Beheshti University. Supplement at: www.ece.ucsb.edu/~parhami/publications.htm23

## Koran, Jessica Contributing Writer

Koran, Jessica is from United States and they belong to Glam and they are from Brisbane, United States got related to this Particular Journal. and Koran, Jessica deal with the subjects like Health and Wellness

## Journal Ratings by Talmudical Yeshiva of Philadelphia

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