DocumentCode
1759151
Title
Radix- 
Arithmetic for Multiplication by a Constant
Author
Oudjida, A.K. ; Chaillet, N.
Author_Institution
Centre de Dev. des Technol. Av., Algiers, Algeria
Volume
61
Issue
5
fYear
2014
fDate
41760
Firstpage
349
Lastpage
353
Abstract
In this brief, radix-2r arithmetic is explored to minimize the number of additions in the multiplication by a constant. We provide the formal proof that, for an N-bit constant, the maximum number of additions using radix- 2ris lower than Dimitrov´s estimated upper bound 2. N/log(N) using the double-base number system (DBNS). In comparison with the canonical signed digit (CSD) and the DBNS, the new radix- 2rrecoding requires an average of 23.12% and 3.07% less additions for a 64-bit constant, respectively.
Keywords
computational complexity; digital arithmetic; DBNS; Dimitrov estimated upper bound; N-bit constant; double-base number system; multiplier-less mutiple constant multiplication; multiplier-less single constant multiplication; radix-2r arithmetic; Adders; Computational complexity; Hardware; Runtime; Signal processing algorithms; Upper bound; Double-base number system (DBNS); Radix-$2^{r}$ arithmetic; Radix-2r arithmetic; high-speed and low-power design; linear-time-invariant systems; multiplierless single/mutiple constant multiplication (SCM/MCM);
fLanguage
English
Journal_Title
Circuits and Systems II: Express Briefs, IEEE Transactions on
Publisher
ieee
ISSN
1549-7747
Type
jour
DOI
10.1109/TCSII.2014.2312799
Filename
6805622
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