Scaling of signed residue numbers with mixed-radix conversion in FPGA with extended scaling factor selection

• Autorzy: Smyk R. , Czyżak M. , Ulman Z.
• Języki publikacji: EN

Abstrakty

EN

A scaling technique of signed residue numbers in FPGA is proposed. The technique is based on conversion of residue numbers to the Mixed-Radix System (MRS). The scaling factor is assumed to be a moduli product from the Residue Number System (RNS) base. Scaling is performed by scaling of MRS terms, the subsequent generation of residue representations of scaled terms, binary addition of these representations and generation of residues for all moduli. The sign of the residue number is detected by using the most significant digit of the MRS representation. Basic blocks of the scaler are realized in the form of modified two-operand modulo adders with included additional multiply and modulo reduction operations. An exemplary pipelined realization of the scaler in the Xilinx FPGA environment is shown. The design is based on Look-Up Tables (LUT)(2,sup>6 x 1) that simulate small RAMs which serve as main components for the look-up realization. Also a method is shown that allows for flexible selection of scaling factors from a set of moduli products of the RNS base. This is made by forming auxiliary MRSs by permutation of moduli of the base. All formed MRSs are associated with the given RNS with respect to the base but each MRS has different set of weights. Thus for the required scaling factor, the suitable MRS can be chosen that provides for the scaling error smaller than 1.

Słowa kluczowe

EN

residue number system; RNS; scaling; scaling algorithms; mixed-radix system; MRS; FPGA

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Computer Applications in Electrical Engineering
• Rocznik: 2013
• Tom: Vol. 11
• Strony: 465--477
• Opis fizyczny: Bibliogr. 18 poz., rys.

Twórcy

autor

Smyk R.

• University of Technology, 80-233 Gdańsk, ul. Narutowicza 11/12

autor

Czyżak M.

• University of Technology, 80-233 Gdańsk, ul. Narutowicza 11/12

autor

Ulman Z.

• University of Technology, 80-233 Gdańsk, ul. Narutowicza 11/12

Bibliografia

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