Iimephu zeKarnaugh: Gqibezela iSikhokelo

Itheyibhile ebonisa ixabiso ngalinye lexabiso elinye okanye amaninzi amacandelo amaninzi yiTheyibhile yeNyaniso. Sisisombululo sabafundi ukwenza ubalo oluqiqiweyo lwesiphakamiso okanye ngeBoolean Algebra. Nangona, kukho enye indlela elingana neetafile zenyaniso, kodwa yenza lula umsebenzi, obizwa iimephu zekarnaugh.

I-KARNAUGH Imephu 1

Yintoni iimephu zeKarnaugh?

Luyilo oluhlala lusetyenziselwa ukunciphisa kunye nokunciphisa usetyenziso kunye nexesha lokusebenza kwezibalo zeBoolean, ukwenza ischema somfuziselo esikhokelela ekubeni kwenziwe imisebenzi emikhulu ngendlela enye yeBoolean.

Ifana kakhulu neTheyibhile yeNyaniso, ibala iimali ezinokuboniswa kwiinguqu ezahlukeneyo ezinegalelo kwaye zinike umphumo kwisiphumo. Ikwabizwa ngokuba "imephu-k", kwaye ichazwa njengoluhlu lweebhokisi apho nganye kuzo inikwe inombolo yokubini, ngokubhekiselele kwiimali ezifunyenwe kwigalelo.

Inani leebhokisi okanye iiseli ezifunyenwe kwi Iimephu zeKarnaugh iyafana netotali yokwakheka kweemali ezikwigalelo, kanye njengoko isebenza kwiTheyibhile yeNyaniso, iseti yeekholamu isetyenzisiwe, umzekelo, kwimephu enamaxabiso amathathu, ngoko xa ezi zimbini ziphakanyiswa. kwisithathu isiphumo sisibhozo (23=8).

En los Iimephu zeKarnaugh Amaxabiso kufuneka abekwe ngendlela yokuba iikholamu kunye neebhokisi ezithe tyaba zihlale zingumahluko wesixa esinye, ngale ndlela iyancitshiswa ibe yindlela elula yamaxabiso amathandathu.

Iimpawu zeKarnaugh Maps

Yindlela yokusebenza eneentlobo ngeentlobo zeeprototypes ezinika uluhlu lomxholo kunye neenjongo:

  • Enye yeendlela ezisetyenziswa rhoqo ukunciphisa izibalo ze-Boolean algebraic.
  • Igama elinikezelwe kuyo ngu "Itafile yaseKarnaugh"okanye"Umzobo weVeitch".
  • Yaziwa ngendlela eyenziwe lula egameni layo njenge "I-K-Map okanye i-KV-Map".
  • Ingcali yefiziksi uMaurice Karnaugh nokwayingcali yezibalo owayengoweBell Laboratories, wayengumyili ngonyaka ka-1950.
  • Inceda ukwenza lula iziphumo zezibalo.
  • Sisiphumo sesimbuku okanye umanyano lweziphumo ezithile.
  • Kukuqulunqwa kweqela lamaxande.
  • Isekelwe kwimisebenzi ezenzekelayo.
  • Ibhokisi nganye yenza umqolo wetafile yenyaniso.
  • Kule theyibhile izixa zenyaniso zommiselo ocwangcisiweyo zibekiwe.
  • Ngokuxhomekeke kumaxabiso abanawo kwitheyibhile yenyani, amaxabiso eeyunithi zabo anokubekwa.
  • Yitafile ebonisa indibaniselwano yamaxabiso eminye imisebenzi ye “N" ixabiso.
  • Yenziwe ngamabini aphakanyiselwe ukuba "N" imiqolo yetyu (2N).
  • Apho izikwere ezibini zidityanisiwe kwaye ixabiso elinye liyacinywa, xa izikwere ezine zidityanisiwe amaxabiso amabini ayacinywa, ngale ndlela inkqubo ilandelwa.
  • Kwibhokisi nganye ixabiso libekiwe, elinokuba “0"Okanye"1".
  • Kuxhomekeke kwimali eyabelwe umsebenzi ngamnye woluhlu. Isetyenziswa de ifikelele kumaxabiso amathandathu.
  • Inokuthi yenzelwe imisebenzi enobuncinane beziphumo ezimbini zoluhlu lweziphumo.
  • Lukhetho ukuba amaxabiso ahlukeneyo afunyenwe, nokuba ayafana.
  • Xa kusenziwa umsebenzi umanyano lwamaxabiso lwenziwa, ngendlela efanayo iimali ezidityanisiweyo ziyapheliswa.
  • Iibhokisi ezikhululekile zisetyenziswe ngendlela yokuba, phakathi kweebhokisi, kungakhathaliseki ukuba siphi na isikhundla, zinomlinganiselo osengqiqweni.
  • Kwezi mephu zika-"K", kukho iiminterms ezidityanisiweyo, ezicaciswe njengezibini zazo, ezinomahluko kwizinto eziguquguqukayo.
  • Iqela ngalinye lamaqela limisela ukubonakaliswa kwesiphumo, kwaye igama eliqukumbelayo kufuneka libe “.OR"(yintoni isibalo) kuwo onke amaxabiso esiphumo.
  • Ukuba izikwere kwimaphu ye-K zinxulumene, ixabiso le-minterms liyadityaniswa, okukhokelela kumandla enani “2".
  • Iyacetyiswa kwimisebenzi enobuninzi bamaxabiso amathandathu.

  • Xa iibhokisi zifunyenwe inani elikhulu "1” imanyene, ukupheliswa kuhlala kukho amaxabiso amabini, xa isibhozo sidityanisiwe “1” Amaxabiso amathathu kufuneka apheliswe ukuze afike kwixesha elinexabiso elinye.
  • Le misebenzi ichazwa ngendlela yecanonical.
  • Ngale mephu unokwakha isekethe yedijithali, elungele imisebenzi ukusuka kwi-algebra ukuya kwi-elektroniki.
  • Inoluhlu olubanzi lweemanyano zabasebenzi
    kwiimephu.
  • Imephu iyakuxhomekeka kwinani lamaxabiso afunyenwe ekuqaleni komsebenzi.

Injani indlela yokwenza i-K-Maphu

Kwitshathi yematriki unokuba neenkqubo ezahlukeneyo ezinika impendulo elindelekileyo, kokulandelayo indlela yokusebenza yale mephu iya kuboniswa.

Inyathelo lokuqala

  • Izinto ezintathu eziguquguqukayo kufuneka zibekwe kwitafile enengqiqo, echongwe ngoonobumba “ABC".
  • Emva koko usebenzisa ingqiqo, eya kukunyamekela ukwenza inkqubo yokufumana umphumo "Y” oko kuyimfuneko.
  • Isiphumo ngokulandelelanayo silungile. Ukunikezela ngeendleko eziphezulu zokuphunyezwa kwayo.
  • Ngolu hlobo lweetafile zeKarnaugh, ukwenziwa lula kuyenziwa kwaye indlela yokubeka izinto eziguquguqukayo etafileni iphuculwe, ifumana indawo “1” yomsebenzi “Y” kwindawo ehambelana nayo.

karnaugh-imephu-7

Inyathelo lesibini

  • Apha imigca yoluhlu inikwa inkcazo.
  • Njengesampulu, umgca weflethi apho iziguquko zinikezelwa khona "AB", kwaye kwikholomu ixabiso elithi "C".
  • Amaxabiso kufuneka anyuswe, apha i-null kufuneka iboniswe ngomgca kwindawo ephezulu ye-variable okanye uphawu locaphulo lukwasetyenziswa.

Inyathelo lesithathu

  • Amaxabiso abekwe kwimephu "ABC” ngokulandelelanayo kunye nemali enexabiso eliphezulu leendleko “Y".
  • Ngalinye kumaxabiso kufuneka abekwe, kwiindawo zawo.
  • "1” kwisikhundla A′BC′; “1” kwisikhundla uABC′ kunye “1” kwindawo ethi A′BC.
  • Ezi ziguquguqukayo zibizwa ngokuba yi-minterms.

Inyathelo leSine

  • Siyaqhubeka ukwenza unciphiso nge-k-maphu.
  • Iintetha ezilandelelanayo ezinengqiqo zisondele, zisusa amaxabiso angaphezulu.
  • Kwiimeko ezithile, isimbuku samagama ahlukeneyo abizwa ngokuba yiminterms of “Z” libeka ngaphezulu ixabiso elithi “A”, kuba ibonakaliswe ukongeza.
  • Ilandelwa yintshukumo yeBoolean logic.
  • Kwinkqubo elula, kufuneka uchaze ukuba ixabiso kufuneka litshitshiswe ngexesha lokudibanisa.
  • Ukugqiba isamba se "Z+X” sisiphumo sonxulumano olwenziwe lula lwamaxabiso etheyibhile yamaxabiso.

Yintoni i-advanteji yeeMaphu zeKarnaugh?

Ngonyaka we-1953, owavelisa indlela yokusebenza okanye indlela yokunciphisa imisebenzi yayiyinjineli uMaurice Karnaugh, esebenzisa iitshathi okanye iitheyibhile ezithile, enikela ezinye iindlela, apho kunikelwa umzekelo koku kulandelayo.

I-KARNAUGH Imephu 2

Kwiitheyibhile zaseKarnaugh kuvunyelwe ukukhetha indlela yokuguqula itafile yenyaniso yemisebenzi yeBoolean, ngendlela ye-SOP eyenziwe lula. Ngoko ke, inika iinketho zemithetho elula yokwenza ukunciphisa kunye nokugxininisa ekunikeni ukulula ukuphumeza indlela.

Ukunika ithuba lokuba indlela ilula kwaye ayithathi ixesha elininzi ukuyenza, ibonisa ukuba inokusebenza kakuhle xa ithelekiswa nezinye iindlela zokuqiqa.

Imithetho yemephu yaseKarnaugh

Ukwakhiwa kwale grafu makulawulwe yimigaqo njengoko icacisiwe, ngenxa yesi sizathu kubonisiwe uluhlu lwemiyalelo ekufuneka yenziwe ngenxa yale njongo.

Into yokuqala ekufuneka yenziwe kukuqinisekisa ukuba ekuphela kwendlela yokuzalisekisa amaqela emigaqo kukuthatha ixabiso “1".

La maqela angenziwa kuphela acaba kwaye abe nomgca. Kufuneka kuqatshelwe ukuba onke amaqela kufuneka enziwe ngo-2n amaxabiso, ukuzama ukuba iqela ngalinye lenziwe ngezinto eziguquguqukayo (1,2,4, 8,…,2n) inani lamasuntswana ukusuka kwelinye ukuya kwelinye.

Ukuze itheyibhile okanye imephu iphele ngokuncitshiswa okulungileyo, ukuhlelwa ngokwamaqela kufuneka kuphathwe ngobunzima obukhulu.

Kuya kufuneka uhlale uyazi kwaye ungashiyi ecaleni ukuguquguquka "1”. kwaye ivumela amaqela e "1".

karnaugh-imephu-8

Amaqela angadityaniswa nezikwere ezifumaneka ekupheleni kwemephu. Inani elincinci lamaqela anokuthi ahlalutywe kufuneka kwakhona ahlalutywe, zonke phantsi kwemigaqo ekhankanywe ngasentla.

Ngawaphi aManyathelo okuNcitshiswa kweMaphu yeKarnaugh?

Ukwenza amanyathelo oku kuncitshiswa kwetheyibhile ye-K, indlela yokusebenza kufuneka ilandelwe ngamaxabiso ahlukeneyo ekuqaleni kunye nokusetyenziswa kweemali ezimbini ukuya kwezintlanu kuyacetyiswa. Yiyo loo nto oku kulandelayo kuchaza indlela yonke ekufuneka yenziwe ukwenza ukuncipha okuchanekileyo.

Uzenza njani iimephu zeKarnaugh?

Okulandelayo, khumbula oko kuza kuboniswa:

  • Kufuneka babeneendlela ezininzi zezakhelo ze-2n, ukuba "n” ixabiso lexabiso.
  • Isampulu iya kuba yi-2 yetafile eguquguqukayo, iya kuvela kwizakhelo ezine, kwimeko yamaxabiso ama-3 isakhelo sihambelana nesibhozo kwaye ukuba lixabiso lesi-4 ke izakhelo ziya kuba lishumi elinesithandathu.
  • Ekugqibeleni unokubona ukuba imephu iya kujongeka njani malunga nenani lamaxabiso ekuqaleni.

Unako Ingaba iiValues ​​kwiFakelo lidityanisiwe?

Yintoni efunekayo kukuba ekupheleni kwemephu izigaba zi-0 kunye ne-1 kuxhomekeke ekubunjweni kwamaxabiso abekwe ekuqaleni.

Kumzekelo wemephu enamaxabiso ama-3.

  • Amaxabiso ka-A kunye no-B kufuneka ancanyathiselwe phezulu kwindawo ephezulu, ekwimigca ethe nkqo.
  • Kule migca ethe nkqo yemephu kukho imixube enokwenzeka yala maxabiso mi-2: 00, 01, 11 okanye 10.
  • Kwindawo ethe tye, kufuneka ubeke amaxabiso aseleyo.
  • Amaxabiso ka C, kunye neemeko ezinokwenzeka kumgca ngamnye ukuba ngu-0 okanye u-1.
  • Kufuneka uhlale uqaphela ukuba i-0 kunye ne-1 yexabiso ngalinye zi-odolwe njengoko zikwimephu ekufikelelwe kuzo.

  • Kuyinxalenye yesiqhelo ukuba xa unxulumano lwenziwa kwenye imephu, into ekufuneka itshintshile sisixa soguqulo ngalunye.

Gcwalisa iiNqobo zeZiphumo

Iimephu ze-Kamaugh emva kokudalwa kwazo zigqitywe ngolwazi, iinguqu zesiphelo kwiqela ngalinye lezinto eziguquguqukayo zokuqala.

Kukho iinketho ezimbini kuphela, enye kukuba itheyibhile yenyaniso ikhona kwaye enye kukuba inkcazo enengqiqo yemephu yombane iyafumaneka. Ngokuqhelekileyo, itafile yenyaniso isetyenziswa.

Emva koko umxholo onengqiqo ugqithiswa, ubala kwidatha yetafile eyenziwe. Kule theyibhile kufuneka ubeke "0» kwibhokisi apho ukubunjwa kwamaxabiso okugqibela kwenziwa, ukuguquguquka «0» kule tafile kunye ne "1» kwibhokisi equlathe ukwakheka kwamaxabiso ekupheleni «1»kuloo tafile.

Ukuba unodibaniso olunengqiqo, kufuneka ulumkele iintlobo ezahlukeneyo zamaxabiso eziphumo, ezi zenziwe ngesiphumo ngesiphumo kwi «1«.

Lenziwa njani iQela lesi-1?

La maxabiso kufuneka adityaniswe ngokulinganayo, ezine ukuya kwezine, isibhozo ukuya kwesibhozo, njalo njalo. Xa amaqela e «1Kwimephu, kufuneka wenze amaqela ahlukeneyo «1»ye (2n), kuyimfuneko ukuba la maqela abambe zonke1» Apho kuyimfuneko, akufanele kuthathelwe ingqalelo ukuba ezi xabiso sele zingamanye amaqela.

Into ebalulekileyo kukuba la maqela kufuneka athobele imigaqo, akanako ukujoyina i-diagonally, kuphela ngokuthe nkqo nangokuthe tye.

Indlela yokufumana uBudlelwane obuNcitshisiweyo obutsha?

Ixabiso lifunyenwe kwiqela ngalinye le «1«, Esi sisiphumo sesimbuku sale nto. Iziphumo kufuneka zongezwe.

Ukufumana ixabiso lomsebenzi, iqela le «1«, kwangaxeshanye kufuneka kuqinisekiswe ukuba amaxabiso atshintsha kwisixa.

Ukuba kukho naluphi na utshintsho kwixabiso, nokuba ukusuka (0 ukuya ku-1) okanye ukusuka (1 ukuya ku-0), elo xabiso liba lilize.

Zeziphi izizathu eziguquguqukayo zoTshintsho Icinyiwe?

Okwangoku kufunyenwe ukuguquguquka kwexabiso eliguqulwayo, kumaqela "1", kwenzeka ukuba olu tshintsho luphindaphinda amaxesha amaninzi, elinye kwelinye icala kwaye elinye kwelinye icala. Kwaye into efunekayo kukunciphisa umsebenzi.

Zifumaneka njani iimephu zeKarnaugh?

Ilele kwingqikelelo enamacala amabini omsebenzi oza kuncitshiswa. Xa oku kuboniswa njengetafile yenyani, kulo mzekelo imephu ye K iyakuboniswa ngendlela efana ne "2D".

Kuba itafile yokuqala ine "n” ixabiso kwaye uno-2n ikholam, imephu ye K yenziwe ngeeseli ngokulinganayo ngo-2n. Ulwakhiwo lwemephu ye K lufaka ikhowudi nganye kwiigridi ngenani lokubini, ngale ndlela ibhokisi nganye edibanayo ikwabelwa idijithi enye.

Kumfanekiso wangaphambili ungabona isampuli yekhowudi yokubini xa umsebenzi wamaxabiso ama-4 uboniswa. Iinguqu ezibhadlileyo ezibonisiweyo (A, B, C, D) ngokulandelelanayo yinxalenye yesuntswana enye yekhowudi yokubini.

Xa usetyenziswa, akuyomfuneko ukuba uchaze ibhokisi nganye; kwanele ukutolika isihloko esithe nkqo nesithe tye ngokulandelelanayo, njengoko kubonisiwe.

Xa usebenziso lwe khowudi yokubini sele lusekiwe, ibhokisi nganye yabela i “1” ukuba siyasebenza ngokwesigama secanonical somsebenzi, kwaye ukuba akunjalo “0”. Xa yenziwe njengetheyibhile yenyaniso, kukho ukhetho lokusebenzisa intetho ye-canonical ukwazisa umsebenzi.

Into echanekileyo kukukhetha leyo equlathe amanani angaphantsi kwamanani. Kule nto, kuyimfuneko kuphela ukukhetha indlela ebandakanya inani elincinci lamaxabiso. Kufuneka nje wazi ukuba mangaphi amanani akhoyo kutoliko olunengqiqo (lungqamana neekholamu ezino"1").

Ukuba inani lokutolika ligqithise ifomyula kwaye lingaphantsi kwenani lamanani angancediyo afunyenweyo, ngoko ke indlela ye-canonical ye-DNF ithathwa. Ukuba ifom ye-CNF ayikhethwanga.

Xa imephu ye-K sele yenziwe, ukwenziwa lula kwamanani kuqala, ukuba kunokwenzeka. Ukwenza amaqela eebhokisi ezihambelanayo kunye ne-variable "1".

Okulandelayo, i-DNF canonical ways decrement algorithm iya kuchazwa ngokufutshane.

Ukuncitshiswa koMsebenzi oQinisekileyo ngeDNF Expression

Xa uyenzile i iimephu zekarnaugh ebonisa imisebenzi esengqiqweni kwi-DNF, inkqubo imi ngolu hlobo lulandelayo.

Into yokuqala ekufuneka yenziwe kukudityaniswa kwamaqela emigulukudu aneenguqu “1” kuthathelwa ingqalelo imigaqo:

Amaqela kufuneka enziwe kuphela ngexabiso "1".

Inani leeseli ezinexabiso "1" ezikwiqela kufuneka ibe namandla enani "2" Intoni (1, 2, 4, 8, 16, ..., n).

Ekudalweni kwamaqela, kufuneka kuthathelwe ingqalelo ukuba iitafile zi-toroidal, kuba iindawo ezikude okanye iindawo zidibene: indawo egqithiseleyo kwicala lasekunene ihambelana nommandla ogqithiseleyo kwicala lasekhohlo, ngokufanayo. indlela eyenzeka ngayo kwicala elingasentla nelisezantsi. Njengoko unokubona kumfanekiso ongezantsi.

Iiseli ezinotshintsho "1” imele ibe kwiqela elinye ubuncinane.

Iiguquguquko "1” ezisebhokisini zinokuba ngamaqela ahlukeneyo.

Inani lamachibi kufuneka libe lincinci.

Ngelixa amaqela emakhulu, ukuhla kuya kuba kukhulu, kwinani lamagama, kunye nenani lee-litreals ezinekota.

Amaqela angahluka ngobukhulu.

Ukuba umsebenzi ufumana utoliko ngexabiso "x” ayinakuconjululwa. Iibhokisi ezisecaleni kwayo zabelwe ixabiso elithi "x”. Kwaye ezi akufuneki ukujoyina ichibi, nangona zingasetyenziselwa ukwandisa amachibi esele enziwe.

Amanqaku anokuba nomdla kuwe:

Iimpawu zoMthombo waMandla: Isishwankathelo ngasinye

Fumanisa Iindidi zeMixholo yoMbane

ufunde konke Iimpawu ze-injini yokukhangela


Yiba ngowokuqala ukuphawula

Shiya uluvo lwakho

Idilesi yakho ye email aziyi kupapashwa. ezidingekayo ziphawulwe *

*

*

  1. Uxanduva lwedatha: Okwenziweyo Ibhlog
  2. Injongo yedatha: Ulawulo lwe-SPAM, ulawulo lwezimvo.
  3. Umthetho: Imvume yakho
  4. Unxibelelwano lwedatha: Idatha ayizukuhanjiswa kubantu besithathu ngaphandle koxanduva lomthetho.
  5. Ukugcinwa kweenkcukacha
  6. Amalungelo: Ngalo naliphi na ixesha unganciphisa, uphinde uphinde ucime ulwazi lwakho.