{"id":"https://openalex.org/W2031715633","doi":"https://doi.org/10.1109/tcsi.2013.2252642","title":"Radix-4 and Radix-8 Booth Encoded Multi-Modulus Multipliers","display_name":"Radix-4 and Radix-8 Booth Encoded Multi-Modulus Multipliers","publication_year":2013,"publication_date":"2013-04-12","ids":{"openalex":"https://openalex.org/W2031715633","doi":"https://doi.org/10.1109/tcsi.2013.2252642","mag":"2031715633"},"language":"en","primary_location":{"id":"doi:10.1109/tcsi.2013.2252642","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2013.2252642","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Circuits and Systems I: Regular Papers","raw_type":"journal-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/A5057613858","display_name":"Ramya Muralidharan","orcid":null},"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":true,"raw_author_name":"Ramya Muralidharan","raw_affiliation_strings":["School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore","Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore, , Singapore"],"affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore, , Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029335324","display_name":"Chip-Hong Chang","orcid":"https://orcid.org/0000-0002-8897-6176"},"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":"Chip-Hong Chang","raw_affiliation_strings":["School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore","Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore, , Singapore"],"affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore, , Singapore","institution_ids":["https://openalex.org/I172675005"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5057613858"],"corresponding_institution_ids":["https://openalex.org/I172675005"],"apc_list":null,"apc_paid":null,"fwci":5.6626,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.95657985,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"60","issue":"11","first_page":"2940","last_page":"2952"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9994999766349792,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9957000017166138,"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"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9915000200271606,"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/modulo","display_name":"Modulo","score":0.7417100071907043},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4637271761894226},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4527653455734253},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4015415906906128},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34947723150253296},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.31607234477996826}],"concepts":[{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.7417100071907043},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4637271761894226},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4527653455734253},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4015415906906128},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34947723150253296},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31607234477996826}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcsi.2013.2252642","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2013.2252642","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Circuits and Systems I: Regular Papers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W208970040","https://openalex.org/W1483115357","https://openalex.org/W1601793793","https://openalex.org/W1971928471","https://openalex.org/W1990458563","https://openalex.org/W1991602527","https://openalex.org/W1996975125","https://openalex.org/W1997999036","https://openalex.org/W2024821731","https://openalex.org/W2027170045","https://openalex.org/W2052865078","https://openalex.org/W2075158086","https://openalex.org/W2075738377","https://openalex.org/W2080580079","https://openalex.org/W2091526179","https://openalex.org/W2097883101","https://openalex.org/W2099512056","https://openalex.org/W2106224035","https://openalex.org/W2110979084","https://openalex.org/W2112940205","https://openalex.org/W2117651800","https://openalex.org/W2119693293","https://openalex.org/W2120088694","https://openalex.org/W2126522734","https://openalex.org/W2126996784","https://openalex.org/W2127106974","https://openalex.org/W2132341963","https://openalex.org/W2133169993","https://openalex.org/W2141245660","https://openalex.org/W2143437590","https://openalex.org/W2148042619","https://openalex.org/W2150083471","https://openalex.org/W2161034909","https://openalex.org/W2338651015"],"related_works":["https://openalex.org/W2117548279","https://openalex.org/W2807449856","https://openalex.org/W238211858","https://openalex.org/W2070252991","https://openalex.org/W2025727968","https://openalex.org/W2941201715","https://openalex.org/W1979597421","https://openalex.org/W2803761277","https://openalex.org/W4297742300","https://openalex.org/W2070522125"],"abstract_inverted_index":{"Novel":[0],"multi-modulus":[1,34,113,199,238,265,291],"designs":[2],"capable":[3],"of":[4,30,64,142,243,270,299],"performing":[5],"the":[6,27,38,42,75,85,88,98,115,119,140,143,194,198,223,246,268,271,281,286,289],"desired":[7],"modulo":[8,43,49,55,151,165,172,183],"operation":[9],"for":[10,118],"more":[11],"than":[12],"one":[13],"modulus":[14],"in":[15,22,197,280],"Residue":[16],"Number":[17],"System":[18],"(RNS)":[19],"are":[20,70,136,189],"explored":[21],"this":[23],"paper":[24],"to":[25,191,285],"lower":[26],"hardware":[28,39,195],"overhead":[29],"residue":[31],"multiplication.":[32],"Two":[33],"multipliers":[35,61,188,239,266,274,292],"that":[36,222],"reuse":[37],"resources":[40,196],"amongst":[41],"2":[44,50,56,77,90,101,107,121,126,131,145,152,159,166,173,184,226,232,253,259],"<sup":[45,51,57,78,91,102,108,122,127,132,146,153,160,167,174,185,206,210,214,227,233,254,260],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[46,52,58,79,92,103,109,123,128,133,147,154,161,168,175,186,207,211,215,228,234,255,261],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sup>":[47,53,59,124,129,134,155,169,176,187,208,212,216],"-1,":[48,125],"and":[54,84,105,130,157,171,230,257,277],"+1":[60,135,156,177],"by":[62,275],"virtue":[63],"their":[65],"analogous":[66],"number":[67],"theoretic":[68],"properties":[69],"proposed.":[71],"The":[72,250],"former":[73],"employs":[74,87],"radix-":[76,89,100,106,144,158,225,231,252,258],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[80,104,148,229,256],"Booth":[81,94,111,149,163,181,236,263],"encoding":[82,95],"algorithm":[83],"latter":[86],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">3</sup>":[93,110,162,235,262],"algorithm.":[96],"In":[97],"proposed":[99,190,224,251,290],"encoded":[112,150,164,182,237,264],"multipliers,":[114,288],"modulo-reduced":[116],"products":[117],"moduli":[120],"computed":[137],"successively.":[138],"With":[139],"basis":[141],"-1":[170],"multiplier":[178],"architectures,":[179],"new":[180],"maximally":[192],"share":[193],"architectures.":[200],"Our":[201],"experimental":[202],"results":[203],"on":[204],"{2":[205],"-1,2":[209],",2":[213],"+1}":[217],"based":[218],"RNS":[219],"multiplication":[220],"show":[221],"save":[240],"nearly":[241],"60%":[242],"area":[244],"over":[245],"corresponding":[247,272],"single-modulus":[248,273,287],"multipliers.":[249],"increase":[267],"delay":[269],"18%":[276],"13%,":[278],"respectively":[279],"worst":[282],"case.":[283],"Compared":[284],"incur":[293],"a":[294],"minor":[295],"power":[296],"dissipation":[297],"penalty":[298],"5%.":[300]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
