{"id":"https://openalex.org/W2121363688","doi":"https://doi.org/10.1109/arith.1983.6158097","title":"Conditions for the distributivity of multiplication with respect to set addition and their effect on the design of array multipliers","display_name":"Conditions for the distributivity of multiplication with respect to set addition and their effect on the design of array multipliers","publication_year":1983,"publication_date":"1983-06-01","ids":{"openalex":"https://openalex.org/W2121363688","doi":"https://doi.org/10.1109/arith.1983.6158097","mag":"2121363688"},"language":"en","primary_location":{"id":"doi:10.1109/arith.1983.6158097","is_oa":false,"landing_page_url":"https://doi.org/10.1109/arith.1983.6158097","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"1983 IEEE 6th Symposium on Computer Arithmetic (ARITH)","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/A5112666383","display_name":"James E. Robertson","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"James E. Robertson","raw_affiliation_strings":["Department of Computer Science, University of Illinois, Urbana-Champaign, Urbana, IL, USA","Department of Computer Science, University of Illinois at Urbana-Champaign, 61801-2987, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Illinois, Urbana-Champaign, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Department of Computer Science, University of Illinois at Urbana-Champaign, 61801-2987, USA","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5112666383"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.27845089,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"67","last_page":"71"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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/T10363","display_name":"Low-power high-performance VLSI design","score":0.9986000061035156,"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":0.9965999722480774,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/distributivity","display_name":"Distributivity","score":0.9651650190353394},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.7359052896499634},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.6690694689750671},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.6334428191184998},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5917534232139587},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5646979808807373},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5362085700035095},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35360604524612427},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3421882390975952},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.207199364900589},{"id":"https://openalex.org/keywords/distributive-property","display_name":"Distributive property","score":0.17307806015014648},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.169520765542984}],"concepts":[{"id":"https://openalex.org/C138390121","wikidata":"https://www.wikidata.org/wiki/Q5283219","display_name":"Distributivity","level":3,"score":0.9651650190353394},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.7359052896499634},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.6690694689750671},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.6334428191184998},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5917534232139587},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5646979808807373},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5362085700035095},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35360604524612427},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3421882390975952},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.207199364900589},{"id":"https://openalex.org/C11821877","wikidata":"https://www.wikidata.org/wiki/Q187959","display_name":"Distributive property","level":2,"score":0.17307806015014648},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.169520765542984},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/arith.1983.6158097","is_oa":false,"landing_page_url":"https://doi.org/10.1109/arith.1983.6158097","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"1983 IEEE 6th Symposium on Computer Arithmetic (ARITH)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W2048773562","https://openalex.org/W2082446321","https://openalex.org/W2084562780"],"related_works":["https://openalex.org/W3017062904","https://openalex.org/W2535873559","https://openalex.org/W2018390992","https://openalex.org/W578326175","https://openalex.org/W2372042768","https://openalex.org/W2057797376","https://openalex.org/W2090319426","https://openalex.org/W2506252583","https://openalex.org/W2048249848","https://openalex.org/W2067758538"],"abstract_inverted_index":{"Some":[0],"conditions":[1],"for":[2,26,57,62,68,72],"distributivity":[3,15,40,69],"of":[4,34,46,75],"multiplication":[5],"with":[6],"respect":[7],"to":[8,38],"set":[9],"addition":[10],"are":[11,20,52],"determined.":[12],"In":[13],"particular,":[14],"holds":[16],"if":[17],"positive":[18],"numbers":[19,28],"used,":[21],"but":[22],"does":[23,55],"not":[24,42],"hold":[25,56],"negative":[27],"in":[29],"radix":[30],"complement":[31],"form.":[32],"Use":[33],"simple":[35],"recoding":[36],"methods":[37],"achieve":[39],"is":[41],"helpful,":[43],"since":[44],"costs":[45],"elementary":[47,76],"multipliers":[48],"and":[49,65],"summing":[50],"networks":[51],"increased.":[53],"Distributivity":[54],"the":[58,66,73],"digit":[59],"sets":[60],"used":[61],"signed-digit":[63],"arithmetic,":[64],"requirement":[67],"provides":[70],"guidance":[71],"design":[74],"multipliers.":[77]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
