{"id":"https://openalex.org/W1608328750","doi":"https://doi.org/10.1109/arith.1999.762842","title":"A reverse converter for the 4-moduli superset {2/sup n/-1, 2/sup n/, 2/sup n/+1, 2/sup n+1/+1}","display_name":"A reverse converter for the 4-moduli superset {2/sup n/-1, 2/sup n/, 2/sup n/+1, 2/sup n+1/+1}","publication_year":2003,"publication_date":"2003-01-20","ids":{"openalex":"https://openalex.org/W1608328750","doi":"https://doi.org/10.1109/arith.1999.762842","mag":"1608328750"},"language":"en","primary_location":{"id":"doi:10.1109/arith.1999.762842","is_oa":false,"landing_page_url":"https://doi.org/10.1109/arith.1999.762842","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings 14th IEEE Symposium on Computer Arithmetic (Cat. No.99CB36336)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042917527","display_name":"Manish Bhardwaj","orcid":"https://orcid.org/0000-0001-7804-3658"},"institutions":[{"id":"https://openalex.org/I4210090209","display_name":"Institute of Microelectronics","ror":"https://ror.org/009rw8n36","country_code":"SG","type":"facility","lineage":["https://openalex.org/I115228651","https://openalex.org/I4210090209","https://openalex.org/I91275662"]},{"id":"https://openalex.org/I1325886976","display_name":"Siemens (Germany)","ror":"https://ror.org/059mq0909","country_code":"DE","type":"company","lineage":["https://openalex.org/I1325886976"]}],"countries":["DE","SG"],"is_corresponding":true,"raw_author_name":"M. Bhardwaj","raw_affiliation_strings":["Signal Processing and Control ICs, Microelectronics Design Center, Siemens Microelectronics, Inc., Singapore","Microelectron. Design Center, Siemens Microelectron. (Asia Pacific), Singapore"],"affiliations":[{"raw_affiliation_string":"Signal Processing and Control ICs, Microelectronics Design Center, Siemens Microelectronics, Inc., Singapore","institution_ids":["https://openalex.org/I4210090209"]},{"raw_affiliation_string":"Microelectron. Design Center, Siemens Microelectron. (Asia Pacific), Singapore","institution_ids":["https://openalex.org/I1325886976"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070475093","display_name":"Thambipillai Srikanthan","orcid":"https://orcid.org/0000-0003-3664-4345"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"T. Srikanthan","raw_affiliation_strings":["Center for High Performance, Embedded Systems (CHiPES), Nanyang Technological University, Singapore","[Center for High Performance, Embedded Systems (CHiPES), Nanyang Technological University, Singapore]"],"affiliations":[{"raw_affiliation_string":"Center for High Performance, Embedded Systems (CHiPES), Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"[Center for High Performance, Embedded Systems (CHiPES), Nanyang Technological University, Singapore]","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103390059","display_name":"Christopher T. Clarke","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"C.T. Clarke","raw_affiliation_strings":["Submetrics Limited, Bath, UK","Department of Electronic & Electrical Engineering"],"affiliations":[{"raw_affiliation_string":"Submetrics Limited, Bath, UK","institution_ids":[]},{"raw_affiliation_string":"Department of Electronic & Electrical Engineering","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5042917527"],"corresponding_institution_ids":["https://openalex.org/I1325886976","https://openalex.org/I4210090209"],"apc_list":null,"apc_paid":null,"fwci":4.5207,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.94444304,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"168","last_page":"175"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10363","display_name":"Low-power high-performance VLSI design","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10363","display_name":"Low-power high-performance VLSI design","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/adder","display_name":"Adder","score":0.7057762742042542},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5256367921829224},{"id":"https://openalex.org/keywords/moduli","display_name":"Moduli","score":0.49427103996276855},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4882402718067169},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.4800466299057007},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4750376045703888},{"id":"https://openalex.org/keywords/very-large-scale-integration","display_name":"Very-large-scale integration","score":0.4679265022277832},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4664473235607147},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.4393089711666107},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4286787509918213},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35002076625823975},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3333720266819},{"id":"https://openalex.org/keywords/embedded-system","display_name":"Embedded system","score":0.11912021040916443},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08970829844474792}],"concepts":[{"id":"https://openalex.org/C164620267","wikidata":"https://www.wikidata.org/wiki/Q376953","display_name":"Adder","level":3,"score":0.7057762742042542},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5256367921829224},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.49427103996276855},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4882402718067169},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.4800466299057007},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4750376045703888},{"id":"https://openalex.org/C14580979","wikidata":"https://www.wikidata.org/wiki/Q876049","display_name":"Very-large-scale integration","level":2,"score":0.4679265022277832},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4664473235607147},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.4393089711666107},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4286787509918213},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35002076625823975},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3333720266819},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.11912021040916443},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08970829844474792},{"id":"https://openalex.org/C82876162","wikidata":"https://www.wikidata.org/wiki/Q17096504","display_name":"Latency (audio)","level":2,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/arith.1999.762842","is_oa":false,"landing_page_url":"https://doi.org/10.1109/arith.1999.762842","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings 14th IEEE Symposium on Computer Arithmetic (Cat. No.99CB36336)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1489433220","https://openalex.org/W1932719017","https://openalex.org/W1971999288","https://openalex.org/W1986331843","https://openalex.org/W1997339082","https://openalex.org/W1998961262","https://openalex.org/W2004549991","https://openalex.org/W2016066384","https://openalex.org/W2043469410","https://openalex.org/W2053718477","https://openalex.org/W2084055884","https://openalex.org/W2091225468","https://openalex.org/W2118620301","https://openalex.org/W2132236349","https://openalex.org/W2149043711","https://openalex.org/W2153389984","https://openalex.org/W3145671615"],"related_works":["https://openalex.org/W4390550886","https://openalex.org/W3217463396","https://openalex.org/W2790557758","https://openalex.org/W2516396101","https://openalex.org/W3204929712","https://openalex.org/W4295102875","https://openalex.org/W2202197943","https://openalex.org/W2015155483","https://openalex.org/W2530574867","https://openalex.org/W2531233410"],"abstract_inverted_index":{"The":[0,39,178],"authors":[1],"propose":[2,117],"an":[3],"extension":[4,24],"to":[5,26,78,140,151],"the":[6,31,53,66,72,92,105,108,133,145,160,181,190],"popular":[7],"{2/sup":[8],"n/-1,":[9],"2/sup":[10,12],"n/,":[11],"n/+1}":[13],"moduli":[14,63],"set":[15],"by":[16,48,87],"adding":[17],"a":[18,124,155,172],"fourth":[19],"modulus":[20],"\"2/sup":[21],"n+1/+1.":[22],"This":[23],"leads":[25],"higher":[27],"parallelism":[28],"while":[29,144],"keeping":[30],"forward":[32],"conversion":[33,45],"and":[34,100,123,167,170,189],"modular":[35],"arithmetic":[36],"units":[37],"simple.":[38],"main":[40],"challenge":[41],"of":[42,62,68,107,157,180],"efficient":[43,113],"reverse":[44,58,162],"is":[46,83,130,183,193],"met":[47],"three":[49],"techniques":[50],"described":[51],"for":[52],"first":[54],"time.":[55],"Firstly,":[56],"we":[57,116],"convert":[59],"linear":[60,152],"combinations":[61],"hence":[64],"reducing":[65],"number":[67],"non-zero":[69],"bits":[70],"in":[71,102,195],"Booth":[73],"encoded":[74],"multiplicands":[75],"from":[76],"n":[77],"merely":[79],"2.":[80],"Secondly,":[81],"it":[82],"shown":[84,131],"that":[85,132],"division":[86,126],"3,":[88],"if":[89],"introduced":[90],"at":[91],"right":[93],"stage,":[94],"can":[95,135,147],"be":[96],"implemented":[97],"very":[98],"efficiently":[99],"can,":[101],"turn,":[103],"reduce":[104,136,148],"cost":[106,192],"converter.":[109],"To":[110],"implement":[111],"VLSI":[112],"modulo":[114],"reduction,":[115],"two":[118],"techniques-multiple":[119],"split":[120],"tables":[121],"(MST)":[122],"modified":[125],"algorithm":[127],"(MDA).":[128],"It":[129],"MST":[134],"exponential":[137],"ROM":[138,142],"requirements":[139,143],"quadratic":[141,194],"MDA":[146],"these":[149,158],"further":[150],"requirements.":[153],"As":[154],"result":[156],"innovations,":[159],"proposed":[161],"converter":[163,182],"uses":[164],"simple":[165],"shift":[166],"add":[168],"operations":[169],"needs":[171],"lookup":[173],"with":[174],"only":[175],"6":[176],"entries.":[177],"delay":[179],"approximately":[184],"10n+13":[185],"full":[186],"adder":[187],"delays":[188],"area":[191],"n.":[196]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
