DocumentCode

82512

Title

Design of Reverse Converters for General RNS Moduli Sets ${ 2^{k}, 2^{n}-1, 2^{n}+1, 2^{n+1}-1 }$ and ${ 2^</h1></div></div> </li> <li class='list-group-item border-0 py-3 px-0'> <div class='row g-0 align-items-center mb-2'><div class='col-12 col-md-3 fullRecLabelEnglish fw-bold mb-2 mb-md-0'><span class='text-muted small'>Author</span></div><div class='col-12 col-md-9 leftDirection leftAlign'><h2 class='mb-0 fw-semibold'>Patronik, Piotr ; Piestrak, Stanislaw J.</h2></div></div> </li> <li class='list-group-item border-0 py-3 px-0'> <div class='row g-0 align-items-center mb-2'><div class='col-12 col-md-3 fullRecLabelEnglish fw-bold mb-2 mb-md-0'><span class='text-muted small'>Author_Institution</span></div><div class='col-12 col-md-9 leftDirection leftAlign'>Inst. of Comput. Eng., Wroclaw Univ. of Technol., Wrocław, Poland</div></div> </li> <li class='list-group-item border-0 py-3 px-0'> <div class='row g-0 align-items-center mb-2'><div class='col-12 col-md-3 fullRecLabelEnglish fw-bold mb-2 mb-md-0'><span class='text-muted small'>Volume</span></div><div class='col-12 col-md-9 leftDirection leftAlign'>61</div></div> </li> <li class='list-group-item border-0 py-3 px-0'> <div class='row g-0 align-items-center mb-2'><div class='col-12 col-md-3 fullRecLabelEnglish fw-bold mb-2 mb-md-0'><span class='text-muted small'>Issue</span></div><div class='col-12 col-md-9 leftDirection leftAlign'>6</div></div> </li> <li class='list-group-item border-0 py-3 px-0'> <div class='row g-0 align-items-center mb-2'><div class='col-12 col-md-3 fullRecLabelEnglish fw-bold mb-2 mb-md-0'><span class='text-muted small'>fYear</span></div><div class='col-12 col-md-9 leftDirection leftAlign'>2014</div></div> </li> <li class='list-group-item border-0 py-3 px-0'> <div class='row g-0 align-items-center mb-2'><div class='col-12 col-md-3 fullRecLabelEnglish fw-bold mb-2 mb-md-0'><span class='text-muted small'>fDate</span></div><div class='col-12 col-md-9 leftDirection leftAlign'>Jun-14</div></div> </li> <li class='list-group-item border-0 py-3 px-0'> <div class='row g-0 align-items-center mb-2'><div class='col-12 col-md-3 fullRecLabelEnglish fw-bold mb-2 mb-md-0'><span class='text-muted small'>Firstpage</span></div><div class='col-12 col-md-9 leftDirection leftAlign'>1687</div></div> </li> <li class='list-group-item border-0 py-3 px-0'> <div class='row g-0 align-items-center mb-2'><div class='col-12 col-md-3 fullRecLabelEnglish fw-bold mb-2 mb-md-0'><span class='text-muted small'>Lastpage</span></div><div class='col-12 col-md-9 leftDirection leftAlign'>1700</div></div> </li> <li class='list-group-item border-0 py-3 px-0'> <div class='row g-0 align-items-center mb-2'><div class='col-12 col-md-3 fullRecLabelEnglish fw-bold mb-2 mb-md-0'><span class='text-muted small'>Abstract</span></div><div class='col-12 col-md-9 leftDirection leftAlign'>This paper presents the design methods of residue-to-binary (reverse) converters for two 4-moduli sets {2<sup>k</sup>, 2<sup>n</sup>-1, 2<sup>n</sup>+1, 2<sup>n+1</sup>-1} and {2<sup>k</sup>, 2<sup>n</sup>-1, 2<sup>n</sup>+1, 2<sup>n-1</sup>-1} for the pairs of positive integers n (n even) and arbitrary k > 0, which provide flexible dynamic ranges for the residue number system (RNS). These two moduli sets are generalizations of the 4-moduli sets {2<sup>n</sup>, 2<sup>n</sup>-1, 2<sup>n</sup>+1, 2<sup>n+1</sup>-1} and {2<sup>n</sup>, 2<sup>n</sup>-1, 2<sup>n</sup>+1, 2<sup>n-1</sup>-1} ( n even) with only a single parameter n. They facilitate selecting a moduli set which not only suits exactly the required dynamic range but also allows to balance delay disparity and hardware complexity between an even modulus and the odd moduli datapath channels. The new reverse converter for the moduli set {2<sup>k</sup>, 2<sup>n</sup>-1, 2<sup>n</sup>+1, 2<sup>n+1</sup>-1} not only enjoys slightly better performance than its known counterpart but also applies to arbitrary k. The reverse converter for the new moduli set {2<sup>k</sup>, 2<sup>n</sup>-1, 2<sup>n</sup>+1, 2<sup>n-1</sup>-1} is the first ever proposed. Synthesis results obtained for the 65 nm technology show that at least one of two versions of our converters is superior w.r.t. delay, power consumption, and area than its counterpart for the 4-moduli set {2<sup>k</sup>, 2<sup>n</sup>-1, 2<sup>n</sup>+1, 2<sup>n+1</sup>-1}, for all dynamic ranges from 14 to 64 bits.</div></div> </li> <li class='list-group-item border-0 py-3 px-0'> <div class='row g-0 align-items-center mb-2'><div class='col-12 col-md-3 fullRecLabelEnglish fw-bold mb-2 mb-md-0'><span class='text-muted small'>Keywords</span></div><div class='col-12 col-md-9 leftDirection leftAlign'>application specific integrated circuits; convertors; residue number systems; 4-moduli sets; delay disparity; even modulus; flexible dynamic ranges; general RNS moduli sets; hardware complexity; odd moduli datapath channels; power consumption; residue number system; residue-to-binary converters; reverse converters; size 65 nm; storage capacity 14 bit to 64 bit; superior w.r.t. delay; Complexity theory; Delays; Design methodology; Digital signal processing; Dynamic range; Hardware; Vectors; Application-specific integrated circuit (ASIC); Chinese remainder theorem (CRT); computer arithmetic; digital signal processing (DSP); residue arithmetic; residue number system (RNS); residue-to-binary converter; reverse converter;</div></div> </li> <li class='list-group-item border-0 py-3 px-0'> <div class='row g-0 align-items-center mb-2'><div class='col-12 col-md-3 fullRecLabelEnglish fw-bold mb-2 mb-md-0'><span class='text-muted small'>fLanguage</span></div><div class='col-12 col-md-9 leftDirection leftAlign'>English</div></div> </li> <li class='list-group-item border-0 py-3 px-0'> <div class='row g-0 align-items-center mb-2'><div class='col-12 col-md-3 fullRecLabelEnglish fw-bold mb-2 mb-md-0'><span class='text-muted small'>Journal_Title</span></div><div class='col-12 col-md-9 leftDirection leftAlign'>Circuits and Systems I: Regular Papers, IEEE Transactions on</div></div> </li> <li class='list-group-item border-0 py-3 px-0'> <div class='row g-0 align-items-center mb-2'><div class='col-12 col-md-3 fullRecLabelEnglish fw-bold mb-2 mb-md-0'><span class='text-muted small'>Publisher</span></div><div class='col-12 col-md-9 leftDirection leftAlign'>ieee</div></div> </li> <li class='list-group-item border-0 py-3 px-0'> <div class='row g-0 align-items-center mb-2'><div class='col-12 col-md-3 fullRecLabelEnglish fw-bold mb-2 mb-md-0'><span class='text-muted small'>ISSN</span></div><div class='col-12 col-md-9 leftDirection leftAlign'>1549-8328</div></div> </li> <li class='list-group-item border-0 py-3 px-0'> <div class='row g-0 align-items-center mb-2'><div class='col-12 col-md-3 fullRecLabelEnglish fw-bold mb-2 mb-md-0'><span class='text-muted small'>Type</span></div><div class='col-12 col-md-9 leftDirection leftAlign'><h2 class='mb-0 fw-semibold'>jour</h2></div></div> </li> <li class='list-group-item border-0 py-3 px-0'> <div class='row g-0 align-items-center mb-2'><div class='col-12 col-md-3 fullRecLabelEnglish fw-bold mb-2 mb-md-0'><span class='text-muted small'>DOI</span></div><div class='col-12 col-md-9 leftDirection leftAlign'>10.1109/TCSI.2013.2290843</div></div> </li> <li class='list-group-item border-0 py-3 px-0'> <div class='row g-0 align-items-center mb-2'><div class='col-12 col-md-3 fullRecLabelEnglish fw-bold mb-2 mb-md-0'><span class='text-muted small'>Filename</span></div><div class='col-12 col-md-9 leftDirection leftAlign'>6728709</div></div> </li> <div class='list-group-item border-0 py-3 px-0'> <div class='row g-0 align-items-center'><div class='col-12 col-md-3 fw-bold mb-2 mb-md-0'><span class='text-muted small'>Link To Document</span></div><div class='col-12 col-md-9 leftDirection leftAlign'><a class='text-break' href='https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=82512' target='_blank' rel=$ https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=82512