Absolute Position Encoders Using Double-Track Gray Codes
A slight increase in the physical dimensions of the single-track gray code (STGC) encoders in exchange for using fewer reading heads (fewer bits) is the subject that is addressed in this article. A construction algorithm is proposed to combine two STGCs in order to obtain a double-track gray code (D...
Saved in:
| Published in: | IEEE transactions on instrumentation and measurement Vol. 74; pp. 1 - 7 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
New York
IEEE
01.01.2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects: | |
| ISSN: | 0018-9456, 1557-9662 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | A slight increase in the physical dimensions of the single-track gray code (STGC) encoders in exchange for using fewer reading heads (fewer bits) is the subject that is addressed in this article. A construction algorithm is proposed to combine two STGCs in order to obtain a double-track gray code (DTGC). The proposed algorithm can be repeatedly used to obtain triple-track gray codes (TTGCs) and so on. The proposed algorithm can be used to quickly obtain very high period codes with a sufficiently small number of tracks. Furthermore, it can be used to obtain desirable codes by trading off the number of tracks and the length of the code. For a given desired period, this tradeoff may provide the opportunity of using fewer bits compared to STGCs. In particular, length n period <inline-formula> <tex-math notation="LaTeX">2^{n} </tex-math></inline-formula> encoders can be constructed with almost half the number of tracks of the corresponding conventional gray code encoders. |
|---|---|
| AbstractList | A slight increase in the physical dimensions of the single-track gray code (STGC) encoders in exchange for using fewer reading heads (fewer bits) is the subject that is addressed in this article. A construction algorithm is proposed to combine two STGCs in order to obtain a double-track gray code (DTGC). The proposed algorithm can be repeatedly used to obtain triple-track gray codes (TTGCs) and so on. The proposed algorithm can be used to quickly obtain very high period codes with a sufficiently small number of tracks. Furthermore, it can be used to obtain desirable codes by trading off the number of tracks and the length of the code. For a given desired period, this tradeoff may provide the opportunity of using fewer bits compared to STGCs. In particular, length n period [Formula Omitted] encoders can be constructed with almost half the number of tracks of the corresponding conventional gray code encoders. A slight increase in the physical dimensions of the single-track gray code (STGC) encoders in exchange for using fewer reading heads (fewer bits) is the subject that is addressed in this article. A construction algorithm is proposed to combine two STGCs in order to obtain a double-track gray code (DTGC). The proposed algorithm can be repeatedly used to obtain triple-track gray codes (TTGCs) and so on. The proposed algorithm can be used to quickly obtain very high period codes with a sufficiently small number of tracks. Furthermore, it can be used to obtain desirable codes by trading off the number of tracks and the length of the code. For a given desired period, this tradeoff may provide the opportunity of using fewer bits compared to STGCs. In particular, length n period <inline-formula> <tex-math notation="LaTeX">2^{n} </tex-math></inline-formula> encoders can be constructed with almost half the number of tracks of the corresponding conventional gray code encoders. |
| Author | Fakhri, Ashkan Mallah Livani, Abdolber |
| Author_xml | – sequence: 1 givenname: Ashkan orcidid: 0009-0007-9606-6854 surname: Fakhri fullname: Fakhri, Ashkan email: fakhriashkan@gmail.com, a.fakhri@mazust.ac.ir organization: Department of Mathematics, University of Science and Technology of Mazandaran, Behshahr, Iran – sequence: 2 givenname: Abdolber orcidid: 0000-0003-3976-8482 surname: Mallah Livani fullname: Mallah Livani, Abdolber email: a.mallah@mazust.ac.ir organization: Department of Electrical Engineering, University of Science and Technology of Mazandaran, Behshahr, Iran |
| BookMark | eNpNkL1PAjEYxhuDiYDuDg6XON_59rsdCSKSYHSAubmP1hziFdu7gf-eEhicnuH5eN_8JmjU-c4i9IihwBj0y2b1URAgrKBMU6XkDRpjzmWuhSAjNAbAKteMizs0iXEHAFIwOUZqVkW_H3qbffnY9q3vskVX-8aGmG1j231nr36o9jbfhLL-yZahPGbzZMd7dOvKfbQPV52i7dtiM3_P15_L1Xy2zmvCeJ9rh6FSShFQQpbArRbgGmg4llpzcMTp9H5jGyexqKSTtASGiU6irAZMp-j5snsI_m-wsTc7P4QunTQUU6whjYuUgkuqDj7GYJ05hPa3DEeDwZz5mMTHnPmYK59UebpUWmvtv7jkQBmjJ9CyYGs |
| CODEN | IEIMAO |
| Cites_doi | 10.1109/18.532900 10.3390/s21020577 10.1137/S0036144595295272 10.1504/IJICS.2023.128829 10.3390/s17122903 10.1109/18.796379 10.1016/j.sna.2015.12.027 10.1109/tim.2022.3225052 10.1109/tim.2023.3310074 10.3390/en15165782 10.1002/0471671746 10.1109/jsen.2019.2955381 10.1016/j.cja.2015.05.009 10.1109/TIT.2017.2719710 10.1109/jsen.2016.2517122 10.1016/b978-075067729-5/50055-0 10.1109/TIE.2015.2506630 10.3390/s18082728 10.1109/jsen.2014.2345587 10.1109/18.490544 10.1016/j.sna.2015.04.026 10.1080/0305215X.2014.982633 10.1016/j.measurement.2016.11.026 10.1177/002029400003300206 10.1109/tcsii.2021.3053555 10.1088/1464-4258/8/7/S16 |
| ContentType | Journal Article |
| Copyright | Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2025 |
| Copyright_xml | – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2025 |
| DBID | 97E RIA RIE AAYXX CITATION 7SP 7U5 8FD L7M |
| DOI | 10.1109/TIM.2024.3493887 |
| DatabaseName | IEEE All-Society Periodicals Package (ASPP) 2005–Present IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE Electronic Library (IEL) CrossRef Electronics & Communications Abstracts Solid State and Superconductivity Abstracts Technology Research Database Advanced Technologies Database with Aerospace |
| DatabaseTitle | CrossRef Solid State and Superconductivity Abstracts Technology Research Database Advanced Technologies Database with Aerospace Electronics & Communications Abstracts |
| DatabaseTitleList | Solid State and Superconductivity Abstracts |
| Database_xml | – sequence: 1 dbid: RIE name: IEEE Electronic Library (IEL) url: https://ieeexplore.ieee.org/ sourceTypes: Publisher |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Physics |
| EISSN | 1557-9662 |
| EndPage | 7 |
| ExternalDocumentID | 10_1109_TIM_2024_3493887 10750344 |
| Genre | orig-research |
| GrantInformation_xml | – fundername: University of Science and Technology of Mazandaran grantid: D/1403/0850 funderid: 10.13039/501100009076 |
| GroupedDBID | -~X 0R~ 29I 4.4 5GY 5VS 6IK 85S 8WZ 97E A6W AAJGR AARMG AASAJ AAWTH ABAZT ABQJQ ABVLG ACGFO ACIWK ACNCT AENEX AETIX AGQYO AGSQL AHBIQ AI. AIBXA AKJIK AKQYR ALLEH ALMA_UNASSIGNED_HOLDINGS ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 DU5 EBS EJD F5P HZ~ H~9 IAAWW IBMZZ ICLAB IDIHD IFIPE IFJZH IPLJI JAVBF LAI M43 O9- OCL P2P RIA RIE RNS TN5 TWZ VH1 VJK AAYXX CITATION 7SP 7U5 8FD L7M |
| ID | FETCH-LOGICAL-c245t-9f10b88820867a05e960fd0d5179950f2f9110dedf716b7f73a041293a08e9013 |
| IEDL.DBID | RIE |
| ISICitedReferencesCount | 0 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001362237600016&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0018-9456 |
| IngestDate | Mon Jun 30 10:08:06 EDT 2025 Sat Nov 29 04:38:56 EST 2025 Wed Aug 27 03:06:49 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Language | English |
| License | https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html https://doi.org/10.15223/policy-029 https://doi.org/10.15223/policy-037 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c245t-9f10b88820867a05e960fd0d5179950f2f9110dedf716b7f73a041293a08e9013 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0009-0007-9606-6854 0000-0003-3976-8482 |
| PQID | 3131908886 |
| PQPubID | 85462 |
| PageCount | 7 |
| ParticipantIDs | ieee_primary_10750344 proquest_journals_3131908886 crossref_primary_10_1109_TIM_2024_3493887 |
| PublicationCentury | 2000 |
| PublicationDate | 2025-01-01 |
| PublicationDateYYYYMMDD | 2025-01-01 |
| PublicationDate_xml | – month: 01 year: 2025 text: 2025-01-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | IEEE transactions on instrumentation and measurement |
| PublicationTitleAbbrev | TIM |
| PublicationYear | 2025 |
| Publisher | IEEE The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher_xml | – name: IEEE – name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| References | ref13 ref12 ref15 ref14 ref11 ref10 ref2 ref1 ref17 ref16 ref19 ref18 ref24 ref23 ref26 ref25 ref20 ref22 ref21 ref27 ref7 ref9 ref4 ref3 ref6 ref5 Reingold (ref8) 1977 |
| References_xml | – ident: ref19 doi: 10.1109/18.532900 – ident: ref3 doi: 10.3390/s21020577 – ident: ref6 doi: 10.1137/S0036144595295272 – ident: ref7 doi: 10.1504/IJICS.2023.128829 – ident: ref16 doi: 10.3390/s17122903 – ident: ref21 doi: 10.1109/18.796379 – ident: ref12 doi: 10.1016/j.sna.2015.12.027 – ident: ref4 doi: 10.1109/tim.2022.3225052 – ident: ref26 doi: 10.1109/tim.2023.3310074 – ident: ref27 doi: 10.3390/en15165782 – ident: ref9 doi: 10.1002/0471671746 – ident: ref24 doi: 10.1109/jsen.2019.2955381 – ident: ref15 doi: 10.1016/j.cja.2015.05.009 – ident: ref11 doi: 10.1109/TIT.2017.2719710 – ident: ref23 doi: 10.1109/jsen.2016.2517122 – ident: ref5 doi: 10.1016/b978-075067729-5/50055-0 – ident: ref2 doi: 10.1109/TIE.2015.2506630 – ident: ref25 doi: 10.3390/s18082728 – ident: ref22 doi: 10.1109/jsen.2014.2345587 – volume-title: Combinatorial Algorithms: Theory and Practice year: 1977 ident: ref8 – ident: ref20 doi: 10.1109/18.490544 – ident: ref14 doi: 10.1016/j.sna.2015.04.026 – ident: ref17 doi: 10.1080/0305215X.2014.982633 – ident: ref18 doi: 10.1016/j.measurement.2016.11.026 – ident: ref1 doi: 10.1177/002029400003300206 – ident: ref10 doi: 10.1109/tcsii.2021.3053555 – ident: ref13 doi: 10.1088/1464-4258/8/7/S16 |
| SSID | ssj0007647 |
| Score | 2.4260273 |
| Snippet | A slight increase in the physical dimensions of the single-track gray code (STGC) encoders in exchange for using fewer reading heads (fewer bits) is the... |
| SourceID | proquest crossref ieee |
| SourceType | Aggregation Database Index Database Publisher |
| StartPage | 1 |
| SubjectTerms | Absolute position encoder Algorithms Coders Codes Detectors double track Encoding encoding and decoding gray code Head Heuristic algorithms Light emitting diodes Magnetic heads Mathematical models Radar tracking Reflective binary codes single track |
| Title | Absolute Position Encoders Using Double-Track Gray Codes |
| URI | https://ieeexplore.ieee.org/document/10750344 https://www.proquest.com/docview/3131908886 |
| Volume | 74 |
| WOSCitedRecordID | wos001362237600016&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVIEE databaseName: IEEE Electronic Library (IEL) customDbUrl: eissn: 1557-9662 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0007647 issn: 0018-9456 databaseCode: RIE dateStart: 19630101 isFulltext: true titleUrlDefault: https://ieeexplore.ieee.org/ providerName: IEEE |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3NS8MwFH-4oaAHP-bE6ZQcvHjIzNq0SY8yNvXg2GHCbiVtEhClk3YT_O99STsZiAdPLbSF8kvee7-X9wVwwwULtM4klUjuKY-lopnKGEXLwLSbCJlH1g-bENOpXCySWVOs7mthjDE--cwM3K2P5etlvnZHZSjhLurGeQtaQoi6WOtH7YqY1w0yhyjBSAs2MUmW3M2fntETDPgg5Enos-e2bJAfqvJLE3vzMjn6548dw2HDI8l9vfAnsGOKDhxsdRfswJ7P7syrU5D3md9ihsyaHC0yLlwxe1kRnzNAkEdn74ai5crfyEOpvsgIH1ddeJmM56NH2oxMoHnAoxVN7JBl6NQG6KkIxSKDDorVTEe-8RuzgUXlxrTRFv2kTFgRKtdwK8GLNEgNwjNoF8vCnAMJhbQhirtCisLVUCrkVgmyRZFrGetQ9OB2A2L6UXfGSL1HwZIUAU8d4GkDeA-6DrSt92q8etDfwJ42slOl4RDVAio_GV_88dkl7AduDK8_CelDe1WuzRXs5p-r16q89tviG12LsTw |
| linkProvider | IEEE |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3NS8MwFH_oVNSDnxOnU3Pw4iEzbdMmPY6xueE2dpiwW2mbFETZpN0E_3tf0k4G4sFTC22h_JL33u_lfQHcc8FcpRJJJZJ7ygMZ0yROGEXLwJSZCJn6mR02IcZjOZuFk6pY3dbCaK1t8plumVsby1eLdGWOylDCTdSN823Y8Tl3nbJc60fxioCXLTIdlGEkBuuoJAsfp4MR-oIub3k89Gz-3IYVsmNVfulia2B6x__8tRM4qpgkaZdLfwpben4Ghxv9Bc9gz-Z3psU5yHZiN5kmkypLi3Tnppw9L4jNGiDIpJN3TdF2pW_kKY-_SAcfF3V46XWnnT6thibQ1OX-koaZwxJ0a130VUTMfI0uSqaY8m3rN5a5Gao3prTK0FNKRCa82LTcCvEiNZID7wJq88VcXwLxhMw8FPgYSQqPHRkjuwqRL4pUyUB5ogEPaxCjj7I3RmR9ChZGCHhkAI8qwBtQN6BtvFfi1YDmGvaokp4i8hxUDKj-ZHD1x2d3sN-fjobRcDB-voYD1wzlteciTagt85W-gd30c_la5Ld2i3wDyTe0gw |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Absolute+Position+Encoders+Using+Double-Track+Gray+Codes&rft.jtitle=IEEE+transactions+on+instrumentation+and+measurement&rft.au=Fakhri%2C+Ashkan&rft.au=Mallah+Livani%2C+Abdolber&rft.date=2025-01-01&rft.pub=IEEE&rft.issn=0018-9456&rft.volume=74&rft.spage=1&rft.epage=7&rft_id=info:doi/10.1109%2FTIM.2024.3493887&rft.externalDocID=10750344 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0018-9456&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0018-9456&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0018-9456&client=summon |