{"id":"https://openalex.org/W2072656343","doi":"https://doi.org/10.1109/tcsii.2014.2387620","title":"Radix-2<sup>r</sup> Arithmetic for Multiplication by a Constant: Further Results and Improvements","display_name":"Radix-2<sup>r</sup> Arithmetic for Multiplication by a Constant: Further Results and Improvements","publication_year":2015,"publication_date":"2015-01-05","ids":{"openalex":"https://openalex.org/W2072656343","doi":"https://doi.org/10.1109/tcsii.2014.2387620","mag":"2072656343"},"language":"en","primary_location":{"id":"doi:10.1109/tcsii.2014.2387620","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsii.2014.2387620","pdf_url":null,"source":{"id":"https://openalex.org/S93916849","display_name":"IEEE Transactions on Circuits & Systems II Express Briefs","issn_l":"1549-7747","issn":["1549-7747","1558-3791"],"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 II: Express Briefs","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/A5023220437","display_name":"Abdelkrim K. Oudjida","orcid":"https://orcid.org/0000-0003-2923-7258"},"institutions":[{"id":"https://openalex.org/I4210102186","display_name":"Centre de D\u00e9veloppement des Technologies Avanc\u00e9es","ror":"https://ror.org/01ay87255","country_code":"DZ","type":"facility","lineage":["https://openalex.org/I4210102186"]}],"countries":["DZ"],"is_corresponding":true,"raw_author_name":"Abdelkrim K. Oudjida","raw_affiliation_strings":["Centre de D\u00e9veloppement des Technologies Avanc\u00e9es (CDTA), Algiers, Algeria","Centre de Dev. des Technol. Av. (CDTA), Algiers, Algeria"],"affiliations":[{"raw_affiliation_string":"Centre de D\u00e9veloppement des Technologies Avanc\u00e9es (CDTA), Algiers, Algeria","institution_ids":["https://openalex.org/I4210102186"]},{"raw_affiliation_string":"Centre de Dev. des Technol. Av. (CDTA), Algiers, Algeria","institution_ids":["https://openalex.org/I4210102186"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5104753316","display_name":"Nicolas Chaillet","orcid":null},"institutions":[{"id":"https://openalex.org/I2802759292","display_name":"Franche-Comt\u00e9 \u00c9lectronique M\u00e9canique Thermique et Optique - Sciences et Technologies","ror":"https://ror.org/004fmxv66","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2802759292","https://openalex.org/I37553959","https://openalex.org/I4210095849","https://openalex.org/I4407990293","https://openalex.org/I53262699"]},{"id":"https://openalex.org/I37553959","display_name":"Universit\u00e9 de technologie de belfort-montb\u00e9liard","ror":"https://ror.org/05bn3m307","country_code":"FR","type":"education","lineage":["https://openalex.org/I37553959"]},{"id":"https://openalex.org/I53262699","display_name":"\u00c9cole Nationale Sup\u00e9rieure de M\u00e9canique et des Microtechniques","ror":"https://ror.org/05813w841","country_code":"FR","type":"education","lineage":["https://openalex.org/I53262699"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nicolas Chaillet","raw_affiliation_strings":["FEMTO-ST Institute, UFC/CNRS/ENSMM/UTBM, Besan\u00e7on, France","FEMTO-ST Inst., UTBM, Besan\u00e7on, France"],"affiliations":[{"raw_affiliation_string":"FEMTO-ST Institute, UFC/CNRS/ENSMM/UTBM, Besan\u00e7on, France","institution_ids":["https://openalex.org/I37553959","https://openalex.org/I2802759292","https://openalex.org/I53262699","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"FEMTO-ST Inst., UTBM, Besan\u00e7on, France","institution_ids":["https://openalex.org/I37553959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046752508","display_name":"Mohamed L. Berrandjia","orcid":null},"institutions":[{"id":"https://openalex.org/I4210102186","display_name":"Centre de D\u00e9veloppement des Technologies Avanc\u00e9es","ror":"https://ror.org/01ay87255","country_code":"DZ","type":"facility","lineage":["https://openalex.org/I4210102186"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Mohamed L. Berrandjia","raw_affiliation_strings":["Centre de D\u00e9veloppement des Technologies Avanc\u00e9es (CDTA), Algiers, Algeria","Centre de Dev. des Technol. Av. (CDTA), Algiers, Algeria"],"affiliations":[{"raw_affiliation_string":"Centre de D\u00e9veloppement des Technologies Avanc\u00e9es (CDTA), Algiers, Algeria","institution_ids":["https://openalex.org/I4210102186"]},{"raw_affiliation_string":"Centre de Dev. des Technol. Av. (CDTA), Algiers, Algeria","institution_ids":["https://openalex.org/I4210102186"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5023220437"],"corresponding_institution_ids":["https://openalex.org/I4210102186"],"apc_list":null,"apc_paid":null,"fwci":2.4536,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.89488599,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"62","issue":"4","first_page":"372","last_page":"376"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10363","display_name":"Low-power high-performance VLSI design","score":0.996399998664856,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.794319212436676},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.748740017414093},{"id":"https://openalex.org/keywords/adder","display_name":"Adder","score":0.7208223342895508},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.720299482345581},{"id":"https://openalex.org/keywords/sublinear-function","display_name":"Sublinear function","score":0.6126874685287476},{"id":"https://openalex.org/keywords/radix","display_name":"Radix (gastropod)","score":0.5931060314178467},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.5430717468261719},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4995999336242676},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4539891481399536},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4017001986503601},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3343103229999542},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32080113887786865},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.21097755432128906},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.07521745562553406},{"id":"https://openalex.org/keywords/latency","display_name":"Latency (audio)","score":0.05797553062438965},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.05762374401092529}],"concepts":[{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.794319212436676},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.748740017414093},{"id":"https://openalex.org/C164620267","wikidata":"https://www.wikidata.org/wiki/Q376953","display_name":"Adder","level":3,"score":0.7208223342895508},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.720299482345581},{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.6126874685287476},{"id":"https://openalex.org/C2779091547","wikidata":"https://www.wikidata.org/wiki/Q287565","display_name":"Radix (gastropod)","level":2,"score":0.5931060314178467},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5430717468261719},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4995999336242676},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4539891481399536},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4017001986503601},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3343103229999542},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32080113887786865},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.21097755432128906},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.07521745562553406},{"id":"https://openalex.org/C82876162","wikidata":"https://www.wikidata.org/wiki/Q17096504","display_name":"Latency (audio)","level":2,"score":0.05797553062438965},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.05762374401092529},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcsii.2014.2387620","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsii.2014.2387620","pdf_url":null,"source":{"id":"https://openalex.org/S93916849","display_name":"IEEE Transactions on Circuits & Systems II Express Briefs","issn_l":"1549-7747","issn":["1549-7747","1558-3791"],"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 II: Express Briefs","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":14,"referenced_works":["https://openalex.org/W1574449651","https://openalex.org/W1590193206","https://openalex.org/W1955859268","https://openalex.org/W1982417643","https://openalex.org/W1986644367","https://openalex.org/W2001254103","https://openalex.org/W2033151302","https://openalex.org/W2056545685","https://openalex.org/W2099124997","https://openalex.org/W2103244632","https://openalex.org/W2131256658","https://openalex.org/W2154656381","https://openalex.org/W2167110608","https://openalex.org/W2169315416"],"related_works":["https://openalex.org/W90906771","https://openalex.org/W2018828772","https://openalex.org/W3217463396","https://openalex.org/W2529185025","https://openalex.org/W2790557758","https://openalex.org/W2939566708","https://openalex.org/W2516396101","https://openalex.org/W3204929712","https://openalex.org/W4295102875","https://openalex.org/W2015457513"],"abstract_inverted_index":{"In":[0,23],"a":[1,6,15,55,60],"previous":[2],"brief,":[3,25],"we":[4],"proposed":[5,48],"new":[7],"sublinear-runtime":[8],"recoding":[9,57],"heuristic":[10,49],"for":[11],"the":[12,31,35,41,47],"multiplication":[13],"by":[14,18,59],"constant,":[16],"accompanied":[17],"its":[19],"upper":[20],"bound":[21],"complexity.":[22],"this":[24],"further":[26],"results":[27],"are":[28,50],"provided,":[29],"namely,":[30],"analytic":[32],"expressions":[33],"of":[34,38],"average":[36],"number":[37],"additions":[39],"and":[40],"maximum":[42],"adder":[43],"depth.":[44],"Improvements":[45],"to":[46],"considered":[51],"as":[52],"well,":[53],"using":[54],"redundant":[56],"followed":[58],"common-digit-elimination":[61],"step.":[62]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}