{"id":"https://openalex.org/W2946695067","doi":"https://doi.org/10.1109/tc.2019.2916817","title":"Low-Power Unsigned Divider and Square Root Circuit Designs Using Adaptive Approximation","display_name":"Low-Power Unsigned Divider and Square Root Circuit Designs Using Adaptive Approximation","publication_year":2019,"publication_date":"2019-05-14","ids":{"openalex":"https://openalex.org/W2946695067","doi":"https://doi.org/10.1109/tc.2019.2916817","mag":"2946695067"},"language":"en","primary_location":{"id":"doi:10.1109/tc.2019.2916817","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.2019.2916817","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","0016-9340","1557-9956","2326-3814"],"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 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/A5019717600","display_name":"Honglan Jiang","orcid":"https://orcid.org/0000-0003-3705-4240"},"institutions":[{"id":"https://openalex.org/I4210119392","display_name":"Institute of Microelectronics","ror":"https://ror.org/02s6gs133","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210119392"]},{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Honglan Jiang","raw_affiliation_strings":["Institute of Microelectronics, Tsinghua University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-3705-4240","affiliations":[{"raw_affiliation_string":"Institute of Microelectronics, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I4210119392","https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100358856","display_name":"Leibo Liu","orcid":"https://orcid.org/0000-0001-7548-4116"},"institutions":[{"id":"https://openalex.org/I4210119392","display_name":"Institute of Microelectronics","ror":"https://ror.org/02s6gs133","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210119392"]},{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Leibo Liu","raw_affiliation_strings":["Institute of Microelectronics, Tsinghua University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0001-7548-4116","affiliations":[{"raw_affiliation_string":"Institute of Microelectronics, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I4210119392","https://openalex.org/I99065089"]}]},{"author_position":"middle","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"],"raw_orcid":"https://orcid.org/0000-0003-3152-3245","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Northeastern University, Boston, MA, USA","institution_ids":["https://openalex.org/I12912129"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005550142","display_name":"Jie Han","orcid":"https://orcid.org/0000-0002-8849-4994"},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Jie Han","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada"],"raw_orcid":"https://orcid.org/0000-0002-8849-4994","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada","institution_ids":["https://openalex.org/I154425047"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5534,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.82323658,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"68","issue":"11","first_page":"1635","last_page":"1646"},"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9994000196456909,"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/square-root","display_name":"Square root","score":0.6312189698219299},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.5142845511436462},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4824965000152588},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.45115625858306885},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.4160740375518799},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4153556823730469},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.403281569480896},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.37263140082359314},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.2680107355117798},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16201910376548767},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.11361026763916016},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10548526048660278}],"concepts":[{"id":"https://openalex.org/C11577676","wikidata":"https://www.wikidata.org/wiki/Q134237","display_name":"Square root","level":2,"score":0.6312189698219299},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.5142845511436462},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4824965000152588},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.45115625858306885},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.4160740375518799},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4153556823730469},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.403281569480896},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.37263140082359314},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.2680107355117798},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16201910376548767},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.11361026763916016},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10548526048660278},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tc.2019.2916817","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.2019.2916817","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","0016-9340","1557-9956","2326-3814"],"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 Computers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3500963698","display_name":null,"funder_award_id":"RES0025211","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W8703017","https://openalex.org/W1560133025","https://openalex.org/W1584008964","https://openalex.org/W1972663233","https://openalex.org/W1981577150","https://openalex.org/W2016015925","https://openalex.org/W2016400276","https://openalex.org/W2018259397","https://openalex.org/W2020217519","https://openalex.org/W2081359092","https://openalex.org/W2085787197","https://openalex.org/W2107971525","https://openalex.org/W2118495140","https://openalex.org/W2128953988","https://openalex.org/W2136001068","https://openalex.org/W2142441514","https://openalex.org/W2166343165","https://openalex.org/W2371314631","https://openalex.org/W2404585587","https://openalex.org/W2460228185","https://openalex.org/W2567480418","https://openalex.org/W2614355230","https://openalex.org/W2623212251","https://openalex.org/W2742536119","https://openalex.org/W2789518040","https://openalex.org/W2798894566","https://openalex.org/W2917592041","https://openalex.org/W2963451778","https://openalex.org/W2999283151","https://openalex.org/W3198838445","https://openalex.org/W4210830821","https://openalex.org/W4298036988","https://openalex.org/W6633070339","https://openalex.org/W6645816922","https://openalex.org/W6739113106"],"related_works":["https://openalex.org/W2389267936","https://openalex.org/W2010941966","https://openalex.org/W3102623159","https://openalex.org/W140150844","https://openalex.org/W2099873975","https://openalex.org/W2217961521","https://openalex.org/W2366911843","https://openalex.org/W4235558922","https://openalex.org/W4238090084","https://openalex.org/W2049680169"],"abstract_inverted_index":{"In":[0,21],"this":[1,22],"paper,":[2],"an":[3,150,236],"adaptive":[4,207],"approximation":[5],"approach":[6],"is":[7,26,101,138,154,241,276],"proposed":[8,155,231,314],"for":[9,45],"the":[10,24,71,76,82,94,104,115,118,142,158,162,204,217,255,258,263,269,289,306,328,333],"design":[11,271],"of":[12,96,106,117,216,254,257,288,305,308],"a":[13,16,30,35,46,123,168,183,197,226,273,296],"divider":[14,137,219,234,240],"and":[15,34,56,78,196,220,284,336],"square":[17],"root":[18],"(SQR)":[19],"circuit.":[20],"design,":[23],"division/SQR":[25],"computed":[27],"by":[28,37,161,225],"using":[29,164,235,295],"reduced-width":[31],"divider/SQR":[32],"circuit":[33,153,195,294,301],"shifter":[36,163,198],"adaptively":[38],"pruning":[39,100,177],"some":[40],"insignificant":[41],"input":[42],"bits.":[43],"Specifically,":[44],"$2n/n$":[47],"2":[48,54,125,144,170,185,191,243],"n":[49,51,63,171],"/":[50,131,146],"division,":[52],"$2k$":[53,184,190],"k":[55,58,61,127,133,145,147,186,192],"$k$":[57],"($k<":[59],"n$":[60],"<":[62],")":[64,130,136],"consecutive":[65],"bits":[66,88,98,107],"are":[67,90,112,179,199],"selected":[68],"starting":[69],"from":[70],"most":[72],"significant":[73,87],"\u20181\u2019":[74],"in":[75,320],"dividend":[77],"divisor,":[79],"respectively.":[80],"At":[81],"same":[83],"time,":[84],"redundant":[85],"least":[86],"(LSBs)":[89],"truncated":[91],"or":[92],"if":[93],"number":[95,105],"remaining":[97],"after":[99],"smaller":[102],"than":[103],"to":[108,114,140,156,181,202,210,262],"be":[109],"kept,":[110],"\u20180's":[111],"appended":[113],"LSBs":[116],"inputs.":[119],"To":[120],"avoid":[121],"overflow,":[122],"$2(k+1)/(k+1)$":[124],"(":[126,132],"+":[128,134],"1":[129,135],"used":[139,180],"compute":[141,203],"$2k/k$":[143],"division.":[148],"Finally,":[149],"error":[151,159,214,228],"correction":[152],"recover":[157],"caused":[160],"OR":[165],"gates.":[166],"For":[167],"$2n$":[169],"-bit":[172,187,193],"approximate":[173,218,233,270,292,318],"SQR":[174,194,221,267,293,300,334],"circuit,":[175,268],"similar":[176],"schemes":[178],"obtain":[182],"radicand.":[188],"A":[189],"then":[200],"utilized":[201],"SQR.":[205],"This":[206],"operation":[208],"leads":[209],"very":[211],"small":[212],"maximum":[213],"distances":[215],"circuits,":[222],"as":[223,247,282],"shown":[224],"theoretical":[227],"analysis.":[229],"The":[230,291,313],"16/8":[232],"8/4":[237],"exact":[238],"array":[239,266],"$2.5\\times$":[242],".":[244,279],"5":[245],"\u00d7":[246,281],"fast":[248,283],"but":[249],"only":[250],"consumes":[251,285,302],"34.42":[252],"percent":[253,287,304],"power":[256,307],"accurate":[259,264,311],"design.":[260,312],"Compared":[261],"16-bit":[265],"with":[272],"6-bit":[274,297],"radicand":[275],"$3.9\\times$":[277],"3":[278],"9":[280],"20.66":[286],"power.":[290],"lookup":[298],"table-based":[299],"7.15":[303],"its":[309],"corresponding":[310],"designs":[315,319],"outperform":[316],"other":[317],"image":[321,337],"processing":[322],"applications":[323],"including":[324],"change":[325],"detection":[326,331],"(for":[327,332,339],"divider),":[329],"envelope":[330],"circuit)":[335],"reconstruction":[338],"both":[340],"designs).":[341]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":7}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
