{"id":"https://openalex.org/W2169999992","doi":"https://doi.org/10.2478/v10037-008-0046-7","title":"Stability of the 4-2 Binary Addition Circuit Cells. Part I","display_name":"Stability of the 4-2 Binary Addition Circuit Cells. Part I","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2169999992","doi":"https://doi.org/10.2478/v10037-008-0046-7","mag":"2169999992"},"language":"en","primary_location":{"id":"doi:10.2478/v10037-008-0046-7","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-008-0046-7","pdf_url":"https://sciendo.com/pdf/10.2478/v10037-008-0046-7","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://sciendo.com/pdf/10.2478/v10037-008-0046-7","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058596471","display_name":"Katsumi Wasaki","orcid":"https://orcid.org/0000-0002-4719-459X"},"institutions":[{"id":"https://openalex.org/I137975476","display_name":"Shinshu University","ror":"https://ror.org/0244rem06","country_code":"JP","type":"education","lineage":["https://openalex.org/I137975476"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Katsumi Wasaki","raw_affiliation_strings":["Shinshu University Nagano, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shinshu University Nagano, Japan","institution_ids":["https://openalex.org/I137975476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5058596471"],"corresponding_institution_ids":["https://openalex.org/I137975476"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.17866524,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"16","issue":"4","first_page":null,"last_page":null},"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":1.0,"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":1.0,"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/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/T11032","display_name":"VLSI and Analog Circuit Testing","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/mathematics","display_name":"Mathematics","score":0.7038475275039673},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.6014337539672852},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4764140844345093},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4243353605270386},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3776278495788574},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21202734112739563},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.08624309301376343}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7038475275039673},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.6014337539672852},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4764140844345093},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4243353605270386},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3776278495788574},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21202734112739563},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.08624309301376343}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2478/v10037-008-0046-7","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-008-0046-7","pdf_url":"https://sciendo.com/pdf/10.2478/v10037-008-0046-7","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:49ad2cff040b40d6bcbad349978d5561","is_oa":true,"landing_page_url":"https://doaj.org/article/49ad2cff040b40d6bcbad349978d5561","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Formalized Mathematics, Vol 16, Iss 4, Pp 377-387 (2008)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.2478/v10037-008-0046-7","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-008-0046-7","pdf_url":"https://sciendo.com/pdf/10.2478/v10037-008-0046-7","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2169999992.pdf","grobid_xml":"https://content.openalex.org/works/W2169999992.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W86760957","https://openalex.org/W180239714","https://openalex.org/W260340778","https://openalex.org/W1483101703","https://openalex.org/W1576245638","https://openalex.org/W1794809807","https://openalex.org/W1966133222","https://openalex.org/W2121318177","https://openalex.org/W2147436847","https://openalex.org/W2150348213","https://openalex.org/W2155453192","https://openalex.org/W2168539955","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2142036596"],"abstract_inverted_index":{"Stability":[0],"of":[1,29,41,59,69,99],"the":[2,27,30,39,56,66,70,100],"4-2":[3,31],"Binary":[4,32],"Addition":[5,33],"Circuit":[6],"Cells.":[7],"Part":[8],"ITo":[9],"evaluate":[10],"our":[11],"formal":[12],"verification":[13],"method":[14],"on":[15,116],"a":[16,45,113],"real-size":[17],"calculation":[18,42,101,123],"circuit,":[19],"in":[20],"this":[21,108],"article,":[22],"we":[23],"continue":[24],"to":[25,37,63,79,87,111],"formalize":[26],"concept":[28],"Cell":[34],"primitives":[35],"(FTAs)":[36],"define":[38,55],"structures":[40],"units":[43],"for":[44,50,81,107,122],"very":[46],"fast":[47],"multiplication":[48],"algorithm":[49],"VLSI":[51],"implementation":[52],"[11].":[53],"We":[54,92],"circuit":[57,97],"structure":[58],"four-types":[60],"FTAs,":[61],"TYPE-0":[62],"TYPE-3,":[64],"using":[65],"series":[67],"constructions":[68],"Generalized":[71],"Full":[72],"Adder":[73],"Circuits":[74],"(GFAs)":[75],"that":[76],"generalized":[77],"adder":[78],"have":[80],"each":[82],"positive":[83],"and":[84,89,119],"negative":[85],"weights":[86],"inputs":[88],"outputs":[90,102],"[15].":[91],"then":[93],"successfully":[94],"prove":[95],"its":[96,120],"stability":[98],"after":[103],"four-steps.":[104],"The":[105],"motivation":[106],"research":[109],"is":[110],"establish":[112],"technique":[114],"based":[115],"formalized":[117],"mathematics":[118],"applications":[121],"circuits":[124],"with":[125],"high":[126],"reliability.MML":[127],"identifier:":[128],"FTACELL1,":[129],"version:":[130],"7.9.03":[131],"4.108.1028":[132]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}