{"id":"https://openalex.org/W2105011602","doi":"https://doi.org/10.1109/tec.1958.5222579","title":"A New Class of Digital Division Methods","display_name":"A New Class of Digital Division Methods","publication_year":1958,"publication_date":"1958-09-01","ids":{"openalex":"https://openalex.org/W2105011602","doi":"https://doi.org/10.1109/tec.1958.5222579","mag":"2105011602"},"language":"en","primary_location":{"id":"doi:10.1109/tec.1958.5222579","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tec.1958.5222579","pdf_url":null,"source":{"id":"https://openalex.org/S172998616","display_name":"IRE Transactions on Electronic Computers","issn_l":"0367-9950","issn":["0367-9950"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"IRE Transactions on Electronic Computers","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/A5112666383","display_name":"James E. Robertson","orcid":null},"institutions":[{"id":"https://openalex.org/I2801919071","display_name":"University of Illinois System","ror":"https://ror.org/05e94g991","country_code":"US","type":"education","lineage":["https://openalex.org/I2801919071"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"James E. Robertson","raw_affiliation_strings":["University of Illinois, Urbana, IL, USA","Univ. of Illinois Urbana Ill"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Illinois, Urbana, IL, USA","institution_ids":["https://openalex.org/I2801919071"]},{"raw_affiliation_string":"Univ. of Illinois Urbana Ill","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5112666383"],"corresponding_institution_ids":["https://openalex.org/I2801919071"],"apc_list":null,"apc_paid":null,"fwci":7.0876,"has_fulltext":false,"cited_by_count":314,"citation_normalized_percentile":{"value":0.96793249,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"EC-7","issue":"3","first_page":"218","last_page":"222"},"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":0.9958999752998352,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9575999975204468,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/division","display_name":"Division (mathematics)","score":0.9088847637176514},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.8687312602996826},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.7353163957595825},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.609749972820282},{"id":"https://openalex.org/keywords/radix","display_name":"Radix (gastropod)","score":0.5978564620018005},{"id":"https://openalex.org/keywords/numerical-digit","display_name":"Numerical digit","score":0.5672582983970642},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5316192507743835},{"id":"https://openalex.org/keywords/division-algorithm","display_name":"Division algorithm","score":0.513596773147583},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2800220847129822},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.16311007738113403}],"concepts":[{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.9088847637176514},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.8687312602996826},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.7353163957595825},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.609749972820282},{"id":"https://openalex.org/C2779091547","wikidata":"https://www.wikidata.org/wiki/Q287565","display_name":"Radix (gastropod)","level":2,"score":0.5978564620018005},{"id":"https://openalex.org/C94957134","wikidata":"https://www.wikidata.org/wiki/Q82990","display_name":"Numerical digit","level":2,"score":0.5672582983970642},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5316192507743835},{"id":"https://openalex.org/C190715199","wikidata":"https://www.wikidata.org/wiki/Q3526714","display_name":"Division algorithm","level":3,"score":0.513596773147583},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2800220847129822},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.16311007738113403},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/tec.1958.5222579","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tec.1958.5222579","pdf_url":null,"source":{"id":"https://openalex.org/S172998616","display_name":"IRE Transactions on Electronic Computers","issn_l":"0367-9950","issn":["0367-9950"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"IRE Transactions on Electronic Computers","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":3,"referenced_works":["https://openalex.org/W213188661","https://openalex.org/W1578007657","https://openalex.org/W2099528622"],"related_works":["https://openalex.org/W4292003640","https://openalex.org/W2153186231","https://openalex.org/W2112245640","https://openalex.org/W2160043480","https://openalex.org/W1999963363","https://openalex.org/W2000843681","https://openalex.org/W2048249848","https://openalex.org/W2105011602","https://openalex.org/W3143148364","https://openalex.org/W1911588463"],"abstract_inverted_index":{"This":[0],"paper":[1],"describes":[2],"a":[3],"class":[4],"of":[5,35,53,77,100,129,140],"division":[6,22,29,43,91,142],"methods":[7,23,92],"best":[8],"suited":[9],"for":[10,17,63,126,144],"use":[11],"in":[12],"digital":[13],"computers":[14],"with":[15,27],"facilities":[16],"floating":[18],"point":[19],"arithmetic.":[20],"The":[21],"may":[24],"be":[25],"contrasted":[26],"conventional":[28,134],"procedures":[30,143],"by":[31],"considering":[32],"the":[33,42,54,78,90,101,130],"nature":[34],"each":[36,48,72,95],"quotient":[37,49,73,96,131],"digit":[38,50,74,97],"as":[39],"generated":[40],"during":[41],"process.":[44],"In":[45,69],"restoring":[46],"division,":[47,71],"has":[51,75,98],"one":[52,76,99],"values":[55,79,102],"0,1,":[56],".":[57,58,59,81,85,86,105,106,111,112,113],",":[60],"r":[61],"-1,":[62,83,108],"an":[64,119],"arbitrary":[65],"integer":[66,120],"radix":[67,145,148],"r.":[68],"nonrestoring":[70],"-(r-1),.":[80],".,":[82,87,107],"+1,":[84],"+(r-1).":[88],"For":[89],"described":[93],"here,":[94],"-n,":[103],"-(n-1),":[104],"0,":[109],"1,":[110],"n-1,":[114],"n,":[115],"where":[116],"n":[117],"is":[118,137],"such":[121],"that":[122],"\u00bd(r-1)\u2264n\u2264r-1.":[123],"A":[124],"method":[125],"serial":[127],"conversion":[128],"digits":[132],"to":[133],"(restoring)":[135],"form":[136],"given.":[138,151],"Examples":[139],"new":[141],"4":[146],"and":[147],"10":[149],"are":[150]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":6},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":4}],"updated_date":"2026-06-19T17:40:00.097472","created_date":"2025-10-10T00:00:00"}
