{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T08:01:30Z","timestamp":1771488090767,"version":"3.50.1"},"reference-count":72,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"1","license":[{"start":{"date-parts":[[2011,2,1]],"date-time":"2011-02-01T00:00:00Z","timestamp":1296518400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Educ."],"published-print":{"date-parts":[[2011,2]]},"DOI":"10.1109\/te.2010.2048329","type":"journal-article","created":{"date-parts":[[2010,5,12]],"date-time":"2010-05-12T19:47:39Z","timestamp":1273693659000},"page":"156-163","source":"Crossref","is-referenced-by-count":52,"title":["How to Teach Residue Number System to Computer Scientists and Engineers"],"prefix":"10.1109","volume":"54","author":[{"given":"Keivan","family":"Navi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Amir Sabbagh","family":"Molahosseini","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammad","family":"Esmaeildoust","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"263","reference":[{"key":"ref72","author":"mcclellan","year":"1979","journal-title":"Number Theory in Digital Signal Processing"},{"key":"ref71","doi-asserted-by":"publisher","DOI":"10.1109\/ACSSC.1985.671430"},{"key":"ref70","first-page":"70","article-title":"application of residue number systems to complex digital filters","author":"leung","year":"1981","journal-title":"Proc IEEE Asilmar Conf Circuits Syst Comput"},{"key":"ref39","doi-asserted-by":"crossref","first-page":"3729","DOI":"10.3923\/jas.2007.3729.3735","article-title":"a new moduli set for residue number system in ternary valued logic","volume":"7","author":"hosseinzadeh","year":"2007","journal-title":"J Appl Sci"},{"key":"ref38","first-page":"1","article-title":"a new moduli set for residue number system: <formula formulatype=\"inline\"><tex notation=\"tex\">$\\{r^{n}-2, r^{n}-1, r^{n}\\}$<\/tex> <\/formula>","author":"hosseinzadeh","year":"2007","journal-title":"Proc IEEE Int Conf Electr Electron Eng"},{"key":"ref33","doi-asserted-by":"crossref","first-page":"929","DOI":"10.1016\/j.sysarc.2008.03.006","article-title":"an efficient architecture for designing reverse converters based on a general three-moduli set","volume":"54","author":"molahosseini","year":"2008","journal-title":"J Syst Archit"},{"key":"ref32","doi-asserted-by":"crossref","first-page":"1628","DOI":"10.1587\/transinf.E92.D.1628","article-title":"efficient mrc-based residue to binary converters for the new moduli sets <formula formulatype=\"inline\"><tex notation=\"tex\">$\\{2^{2{\\rm n}}, 2^{\\rm n} - 1, 2^{{\\rm n} + 1} - 1\\}$<\/tex><\/formula> and <formula formulatype=\"inline\"> <tex notation=\"tex\">$\\{2^{2{\\rm n}}, 2^{\\rm n} - 1, 2^{{\\rm n} - 1} - 1\\}$<\/tex> <\/formula>","volume":"e92 d","author":"molahosseini","year":"2009","journal-title":"IEICE Trans Inf Syst"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2007.04.028"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2002.808191"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2005.851388"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1986.1085824"},{"key":"ref35","first-page":"340","article-title":"multiple-valued logic in vlsi: challenges and opportunities","author":"dubrova","year":"1999","journal-title":"Proc Norchip Conf"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1109\/ISMVL.1996.508341"},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2005.849143"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.1109\/TIM.2009.2016793"},{"key":"ref61","doi-asserted-by":"publisher","DOI":"10.1049\/iet-cdt:20060026"},{"key":"ref63","doi-asserted-by":"publisher","DOI":"10.1109\/TC.1980.1675473"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1587\/elex.6.1006"},{"key":"ref64","doi-asserted-by":"publisher","DOI":"10.1109\/82.204109"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2007.890623"},{"key":"ref65","doi-asserted-by":"publisher","DOI":"10.1587\/elex.5.672"},{"key":"ref66","first-page":"183","article-title":"a fully parallel reverse converter","volume":"1","author":"hosseinzadeh","year":"2007","journal-title":"Int J Comput Elect Eng"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1109\/ICTTA.2008.4530266"},{"key":"ref67","doi-asserted-by":"publisher","DOI":"10.1109\/ISPA.2003.1296391"},{"key":"ref68","doi-asserted-by":"publisher","DOI":"10.1109\/82.826745"},{"key":"ref69","doi-asserted-by":"publisher","DOI":"10.1109\/GLSV.1999.757457"},{"key":"ref2","author":"parhami","year":"2000","journal-title":"Computer Arithmetic Algorithms and Hardware Design"},{"key":"ref1","author":"koren","year":"1993","journal-title":"Computer Arithmetic Algorithms"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1109\/TCSII.2007.900844"},{"key":"ref22","doi-asserted-by":"crossref","first-page":"1245","DOI":"10.1109\/TCSI.2007.895515","article-title":"rns-to-binary converters for two four-moduli set <formula formulatype=\"inline\"><tex notation=\"tex\">$\\{2^{n} -1, 2^{n}, 2^{n} + 1, 2^{n + 1} - 1\\}$<\/tex><\/formula> and <formula formulatype=\"inline\"> <tex notation=\"tex\">$\\{2^{n} -1, 2^{n}, 2^{n} + 1, 2^{n + 1} + 1\\}$<\/tex> <\/formula>","volume":"54","author":"mohan","year":"2007","journal-title":"IEEE Trans Circuits Syst I Reg Papers"},{"key":"ref21","first-page":"643","article-title":"new reverse converters for the moduli set <formula formulatype=\"inline\"><tex notation=\"tex\">$\\{2^{n} - 3, 2^{n} - 1, 2^{n} + 1, 2^{n}+3\\}$<\/tex><\/formula>","volume":"62","author":"mohan","year":"2008","journal-title":"J Electron Commun"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2007.05.040"},{"key":"ref23","doi-asserted-by":"crossref","first-page":"1296","DOI":"10.1109\/TCSI.2003.817789","article-title":"an efficient reverse converter for the 4-moduli set <formula formulatype=\"inline\"><tex notation=\"tex\">$\\{2^{n} -1, 2^{n}, 2^{n} + 1, 2^{2n} + 1\\}$<\/tex><\/formula> based on the new chinese remainder theorem","volume":"50","author":"cao","year":"2003","journal-title":"IEEE Trans Circuits Syst I Reg Papers"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1109\/TVLSI.2004.840400"},{"key":"ref25","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1109\/TCSI.2009.2026681","article-title":"efficient reverse converter designs for the new 4-moduli sets <formula formulatype=\"inline\"><tex notation=\"tex\">$\\{2^{\\rm n} -1, 2^{\\rm n}, 2^{\\rm n} + 1, 2^{2{\\rm n} + 1} -1\\}$<\/tex><\/formula> and <formula formulatype=\"inline\"><tex notation=\"tex\">$\\{2^{\\rm n} -1, 2^{\\rm n} + 1, 2^{2{\\rm n}}, 2^{2{\\rm n}} + 1\\}$<\/tex><\/formula> based on new crts","volume":"57","author":"molahosseini","year":"2010","journal-title":"IEEE Trans Circuits Syst I Reg Papers"},{"key":"ref50","doi-asserted-by":"crossref","first-page":"1211","DOI":"10.1109\/TC.2004.60","article-title":"fast parallel-prefix modulo <formula formulatype=\"inline\"><tex notation=\"tex\">$2^{\\rm n} +1$<\/tex><\/formula> adder","volume":"53","author":"efstathiou","year":"2004","journal-title":"IEEE Trans Comput"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2007.895369"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.1109\/TC.2004.1261842"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1109\/MWSCAS.1996.593165"},{"key":"ref57","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/BF00929618","article-title":"an efficient tree architecture for modulo <formula formulatype=\"inline\"><tex notation=\"tex\">$2^{n} +1$<\/tex> <\/formula> multiplication","volume":"14","author":"wang","year":"1996","journal-title":"J VLSI Signal Process"},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.1109\/12.709376"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.2307\/2007970"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1109\/MWSCAS.1994.519272"},{"key":"ref53","first-page":"111","article-title":"a review of modular multiplication methods and respective hardware implementations","volume":"30","author":"nedjah","year":"2006","journal-title":"Informatica"},{"key":"ref52","first-page":"312","article-title":"low powe modulo <formula formulatype=\"inline\"> <tex notation=\"tex\">$2^{n} +1$<\/tex><\/formula> adder based on carry save diminshed-one number system","volume":"5","author":"timarchi","year":"2007","journal-title":"Amer J Appl Sci"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1109\/TCSII.2003.821524"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1142\/S0218126605002131"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1109\/ITSIM.2008.4631946"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1109\/IWSOC.2004.1319854"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1109\/NRSC.2001.929397"},{"key":"ref14","first-page":"1472","article-title":"redundant residue number system based error correction codes","volume":"3","author":"yang","year":"2001","journal-title":"Proc IEEE Veh Technol Conf"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1109\/WISP.2007.4447506"},{"key":"ref16","first-page":"iv-512","article-title":"moduli selection in rns for efficient vlsi implementation","volume":"4","author":"wang","year":"2003","journal-title":"Proc IEEE Int Symp Circuits Syst"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1109\/SSST.1995.390542"},{"key":"ref18","doi-asserted-by":"crossref","first-page":"1772","DOI":"10.1109\/TSP.2002.1011216","article-title":"adder based residue to binary numbers converters for <formula formulatype=\"inline\"><tex notation=\"tex\">$(2^{n}-1, 2^{n}, 2^{n} +1)$<\/tex> <\/formula>","volume":"50","author":"wang","year":"2002","journal-title":"IEEE Trans Signal Process"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1109\/82.899659"},{"key":"ref4","doi-asserted-by":"crossref","first-page":"775","DOI":"10.1080\/00207160410001708805","article-title":"a high-speed division algorithm in residue number system using parity-checking technique","volume":"81","author":"ysng","year":"2004","journal-title":"Int J Comput Math"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1109\/MC.1984.1659138"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1109\/ARITH.2007.16"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2008.917994"},{"key":"ref8","first-page":"1412","article-title":"residue number system for low-power dsp applications","author":"cardarilli","year":"2007","journal-title":"Proc IEEE Asilomar Conf Signals Syst Comput"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1109\/101.950050"},{"key":"ref49","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1109\/12.863036","article-title":"high-speed parallel-prefix modulo <formula formulatype=\"inline\"><tex notation=\"tex\">$2^{n} -1$<\/tex> <\/formula> adders","volume":"49","author":"kalampoukas","year":"2000","journal-title":"IEEE Trans Comput"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1977.1084321"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1987.1086130"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1142\/S0218126605002726"},{"key":"ref48","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1109\/ARITH.1999.762841","article-title":"efficient vlsi implementation of modulo <formula formulatype=\"inline\"><tex notation=\"tex\">$(2^{n}\\pm 1)$<\/tex> <\/formula> addition and multiplication","author":"zimmermann","year":"1999","journal-title":"Proc 14th IEEE Symp Comput Arithmetic"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1109\/82.471401"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1109\/12.250610"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1049\/el:19880812"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1109\/12.833113"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1109\/DSD.2003.1231911"}],"container-title":["IEEE Transactions on Education"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx5\/13\/5705620\/05457965.pdf?arnumber=5457965","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,11]],"date-time":"2021-10-11T00:43:46Z","timestamp":1633913026000},"score":1,"resource":{"primary":{"URL":"http:\/\/ieeexplore.ieee.org\/document\/5457965\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,2]]},"references-count":72,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.1109\/te.2010.2048329","relation":{},"ISSN":["0018-9359","1557-9638"],"issn-type":[{"value":"0018-9359","type":"print"},{"value":"1557-9638","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,2]]}}}