{"id":"https://openalex.org/W3086584843","doi":"https://doi.org/10.1109/tetc.2020.3022290","title":"Design of Unsigned Approximate Hybrid Dividers Based on Restoring Array and Logarithmic Dividers","display_name":"Design of Unsigned Approximate Hybrid Dividers Based on Restoring Array and Logarithmic Dividers","publication_year":2020,"publication_date":"2020-09-08","ids":{"openalex":"https://openalex.org/W3086584843","doi":"https://doi.org/10.1109/tetc.2020.3022290","mag":"3086584843"},"language":"en","primary_location":{"id":"doi:10.1109/tetc.2020.3022290","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tetc.2020.3022290","pdf_url":null,"source":{"id":"https://openalex.org/S2496326734","display_name":"IEEE Transactions on Emerging Topics in Computing","issn_l":"2168-6750","issn":["2168-6750","2376-4562"],"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 Emerging Topics in Computing","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/A5023734605","display_name":"Weiqiang Liu","orcid":"https://orcid.org/0000-0001-8398-8648"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Weiqiang Liu","raw_affiliation_strings":["College of Electronic Information and Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China"],"affiliations":[{"raw_affiliation_string":"College of Electronic Information and Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021867626","display_name":"Tao Xu","orcid":"https://orcid.org/0000-0002-8394-7421"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tao Xu","raw_affiliation_strings":["College of Electronic Information and Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China"],"affiliations":[{"raw_affiliation_string":"College of Electronic Information and Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100336782","display_name":"Jing Li","orcid":"https://orcid.org/0000-0001-7027-7513"},"institutions":[{"id":"https://openalex.org/I30809798","display_name":"ShanghaiTech University","ror":"https://ror.org/030bhh786","country_code":"CN","type":"education","lineage":["https://openalex.org/I30809798"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jing Li","raw_affiliation_strings":["School of Information Science and Technology, ShanghaiTech University, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"School of Information Science and Technology, ShanghaiTech University, Shanghai, China","institution_ids":["https://openalex.org/I30809798"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055800000","display_name":"Chenghua Wang","orcid":"https://orcid.org/0000-0001-8415-0548"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chenghua Wang","raw_affiliation_strings":["College of Electronic Information and Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China"],"affiliations":[{"raw_affiliation_string":"College of Electronic Information and Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083219829","display_name":"Paolo Montuschi","orcid":"https://orcid.org/0000-0003-2563-2250"},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Polytechnic University of Turin","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Paolo Montuschi","raw_affiliation_strings":["Control and Computer Engineering Department, Politecnico di Torino, Torino, Italy"],"affiliations":[{"raw_affiliation_string":"Control and Computer Engineering Department, Politecnico di Torino, Torino, Italy","institution_ids":["https://openalex.org/I177477856"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001979328","display_name":"Fabrizio Lombardi","orcid":"https://orcid.org/0000-0003-3152-3245"},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fabrizio Lombardi","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Northeastern University, Boston, MA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Northeastern University, Boston, MA, USA","institution_ids":["https://openalex.org/I12912129"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5023734605"],"corresponding_institution_ids":["https://openalex.org/I9842412"],"apc_list":null,"apc_paid":null,"fwci":0.822,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.72816796,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"10","issue":"1","first_page":"339","last_page":"350"},"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/T10323","display_name":"Analog and Mixed-Signal Circuit Design","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T10558","display_name":"Advancements in Semiconductor Devices and Circuit Design","score":0.9993000030517578,"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/adder","display_name":"Adder","score":0.6856944561004639},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6346978545188904},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.5561255812644958},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.5461704134941101},{"id":"https://openalex.org/keywords/division","display_name":"Division (mathematics)","score":0.5353569984436035},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5224494338035583},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47185373306274414},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44965577125549316},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.43564194440841675},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35208800435066223},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.08408844470977783},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08311963081359863},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07684659957885742}],"concepts":[{"id":"https://openalex.org/C164620267","wikidata":"https://www.wikidata.org/wiki/Q376953","display_name":"Adder","level":3,"score":0.6856944561004639},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6346978545188904},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.5561255812644958},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.5461704134941101},{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.5353569984436035},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5224494338035583},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47185373306274414},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44965577125549316},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.43564194440841675},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35208800435066223},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.08408844470977783},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08311963081359863},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07684659957885742},{"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/C82876162","wikidata":"https://www.wikidata.org/wiki/Q17096504","display_name":"Latency (audio)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tetc.2020.3022290","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tetc.2020.3022290","pdf_url":null,"source":{"id":"https://openalex.org/S2496326734","display_name":"IEEE Transactions on Emerging Topics in Computing","issn_l":"2168-6750","issn":["2168-6750","2376-4562"],"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 Emerging Topics in Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.8700000047683716,"display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G1634376968","display_name":null,"funder_award_id":"2018-XYDXX-009","funder_id":"https://openalex.org/F4320326182","funder_display_name":"Six Talent Peaks Project in Jiangsu Province"},{"id":"https://openalex.org/G3794796724","display_name":null,"funder_award_id":"NE2019102","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G4070429046","display_name":null,"funder_award_id":"62022041","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G619348379","display_name":null,"funder_award_id":"61871216","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320326182","display_name":"Six Talent Peaks Project in Jiangsu Province","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1998305460","https://openalex.org/W1998824039","https://openalex.org/W2005865544","https://openalex.org/W2016400276","https://openalex.org/W2020217519","https://openalex.org/W2020429547","https://openalex.org/W2056489774","https://openalex.org/W2100344492","https://openalex.org/W2105011602","https://openalex.org/W2111013824","https://openalex.org/W2124651102","https://openalex.org/W2126044301","https://openalex.org/W2135089667","https://openalex.org/W2143384051","https://openalex.org/W2159009871","https://openalex.org/W2244005500","https://openalex.org/W2404585587","https://openalex.org/W2460228185","https://openalex.org/W2554131156","https://openalex.org/W2589986623","https://openalex.org/W2608093348","https://openalex.org/W2613107232","https://openalex.org/W2621166576","https://openalex.org/W2889553421","https://openalex.org/W4206519171","https://openalex.org/W4210830821","https://openalex.org/W4245558464","https://openalex.org/W4249697915","https://openalex.org/W4253998042","https://openalex.org/W6708559005"],"related_works":["https://openalex.org/W4390550886","https://openalex.org/W3217463396","https://openalex.org/W2790557758","https://openalex.org/W2516396101","https://openalex.org/W3204929712","https://openalex.org/W4295102875","https://openalex.org/W2015457513","https://openalex.org/W2300671402","https://openalex.org/W4312888585","https://openalex.org/W3212668432"],"abstract_inverted_index":{"Approximate":[0],"computer":[1],"arithmetic":[2],"has":[3,45,56],"been":[4,31,39],"extensively":[5],"studied":[6],"due":[7],"to":[8,11,79,94,124,164,181],"its":[9],"advantages":[10],"further":[12,137],"reduce":[13],"power":[14,131],"consumption":[15],"and":[16,28,48,77,86,134,194,198,202,214,233,251],"increase":[17],"performance":[18,85],"at":[19],"reduced":[20,159],"accuracy.":[21,87],"Although":[22],"a":[23,34,57,81,106,118,141,158,172],"number":[24],"of":[25,74,101,127,240],"approximate":[26,36,65,122,144,216,227],"adders":[27],"multipliers":[29],"have":[30,38],"studied,":[32],"only":[33],"few":[35],"dividers":[37,228,238],"proposed.":[40,70,153],"A":[41],"logarithmic":[42],"divider":[43,54,67,90,146,161],"(LD)":[44],"low":[46],"complexity":[47],"accuracy,":[49],"while":[50,109],"an":[51,64,121],"exact":[52],"array":[53,177,186],"(EXD)":[55],"high":[58,107],"complexity.":[59],"Therefore,":[60],"in":[61,168],"this":[62,155],"article,":[63],"hybrid":[66,145,237],"(AXHD)":[68],"is":[69,151,162,179],"It":[71],"takes":[72],"advantage":[73],"both":[75,231],"LD":[76,119,213],"EXD":[78,167],"achieve":[80],"tradeoff":[82],"between":[83],"hardware":[84,139,203],"Exact":[88],"restoring":[89],"cells":[91],"are":[92,114,196,208,239],"used":[93,163,180],"generate":[95],"the":[96,102,110,166,183,222],"most":[97],"significant":[98],"bits":[99],"(MSBs)":[100],"quotient":[103,112],"for":[104,171,243],"attaining":[105],"accuracy":[108],"other":[111],"digits":[113],"generated":[115],"by":[116,229],"using":[117,200],"as":[120,130,248],"scheme":[123],"improve":[125],"figures":[126],"merit":[128],"such":[129,247],"consumption,":[132],"area":[133],"delay.":[135],"To":[136],"save":[138],"resources,":[140],"so-called":[142],"eliminated":[143],"(E-AXHD)":[147],"based":[148],"on":[149],"AXHD":[150,193],"also":[152,209],"In":[154],"improved":[156],"design,":[157,174],"width":[160],"replace":[165,182],"AXHD.":[169],"Specifically,":[170],"16-by-8":[173],"<inline-formula><tex-math":[175,184,188],"notation=\"LaTeX\">$n/(n+1)$</tex-math></inline-formula>":[176],"division":[178,187],"notation=\"LaTeX\">$n/8$</tex-math></inline-formula>":[185],"notation=\"LaTeX\">$(n&lt;8)$</tex-math></inline-formula>":[189],".":[190],"The":[191,205,218,235],"proposed":[192,206,223,236],"E-AXHD":[195],"evaluated":[197],"analyzed":[199],"error":[201,244],"metrics.":[204],"designs":[207,224],"compared":[210],"with":[211],"EXD,":[212],"previous":[215,226],"dividers.":[217],"results":[219],"show":[220],"that":[221],"outperform":[225],"considering":[230],"energy":[232],"error.":[234],"particular":[241],"interest":[242],"tolerant":[245],"applications":[246],"image":[249],"processing":[250],"machine":[252],"learning.":[253]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}