Uhlelo lwe-Binary noma lwe-diatic: Umlando, ukumelwa nokuningi

El uhlelo kanambambili Kubaluleke kakhulu endaweni yamakhompiyutha, ngoba benza kube nokwenzeka ukuhunyushwa kolwazi namanani ezinombolo ngobuchwepheshe obuhlukahlukene, obuzochazwa ngalolu lwazi.

Luyini uhlelo olunambambili?

Yifomethi yezinombolo esetshenziselwa ukwenza ikhompiyutha ukuze kwenziwe ikhompyutha, basebenzisa kuphela izinombolo ezimbili, u-zero no-XNUMX, okuyizinto ezidingekayo ukuze bakwazi ukumela imininingwane ngokujwayelekile, okungukuthi kubaluleke kakhulu ngoba ukusebenza kwalawa madivayisi kwenziwa kuphela emazingeni amabili wamandla kagesi, amanje nangaphezulu, avela ngokuya ngenombolo yezinombolo ezisetshenzisiwe.

historia

Isethulo sokuqala se- uhlelo kanambambili Yenziwa yisazi sezibalo eminyakeni eminingi eyedlule, eduze nezikhathi zekhulu lesithathu, kusondele kakhulu ekutholeni inombolo zero, okwakubaluleke kakhulu ukuqala le ntuthuko; ezinye izici ezibalulekile endabeni kwakungu-I Ching owenza uchungechunge olwalunama-bits amathathu nezinombolo eziyisithupha zebhanari, ezisetshenziselwe ukwenza inhlanganisela kanambambili.

Kwakunamalungiselelo ohlobo lwe-kanambambili kusukela ngekhulu le-1605, elenziwa nguShao Yong owethule i-oda kusuka kulokhu kuqaphela, isici sokuba nokulandelana kusuka ku-zero kuye kumashumi ayisithupha nantathu, kukhombisa ukuthi iqhinga lokukhiqiza lale nqubo lalinjani, njengoba Iminyaka idlula , kwaqokonyiswa amaphuzu abaluleke kakhulu kuleso sifundo, ngonyaka we-XNUMX uBacon Francis wanikeza incazelo yokuthi izinhlamvu zazingabekwa kanjani ngezinombolo ezihamba phambili.

Kwenziwa ukushicilelwa kwezincwadi ezagcizelelwa ngokunikeza incazelo yohlelo lwe-kanambambili, kwenziwa nemibhalo okwakwenziwa kuyo lapho kusetshenziswa izinhlobo ezahlukahlukene zezimpawu, zombili amaShayina nezezibalo, zisebenzisa ngqo u-0 no-1 njengoba kukhonjisiwe namuhla, kwathi ngonyaka ka-1854 kwashicilelwa kolwazi lwenziwa nguGeorge Boole, lapho achaza khona uhlelo olunengqondo olubizwa ngeBoolean Algebra.

Lolu hlelo lwasungulwa njengephuzu elibaluleke kakhulu ekwakhiweni kwamasekethe ohlobo lwe-elekthronikhi, lanikela kakhulu kulolu hlobo lomsebenzi, ngakho-ke kwakubalulekile ukwazi ngohlelo lwe-kanambambili namaphuzu ahlukene ayehlobene.

Isethulo kanambambili sethulwe njengomuntu obambe iqhaza elikhulu ekuthuthukisweni kwale ndawo, uma unesithakazelo kuyo, sincoma ukuthi ufunde mayelana ukuvela kwekhompyutha.

Aplicaciones

Isici ngasinye esibalulekile salesi sihloko sisetshenziselwe izinhloso ezahlukahlukene ngochwepheshe abazinikele kuso, phakathi kwabo uClaude Shannon ubizwa ngegama, owethula ithisisi yakhe esebenzisa i-Algebra kaBoola kanye nezibalo kanambambili, ebaluleke kakhulu ngoba bekuyi okokuqala lapho kusetshenziswa ukushintshwa nokudluliswa, eminyakeni edlule uStibitz George wakha i-calculator esebenzisa ama-relays.

Ngo-1940 kwenziwa intuthuko yokwenziwa kwama-calculator, kukhombisa lezo ezazisebenzisa izinombolo eziyinkimbinkimbi, ezazikhonjiswa ngokukhombisa ukusebenza kwazo, njengoba kwenziwa umsebenzi omningi kuso, izinhlobo ezahlukene zemiyalo zadluliselwa kusibali, ngokusebenzisa ifoni umugqa.

Njengamanje uhlelo kanambambili lusetshenziselwa izinhloso ezahlukahlukene, ngoba lususelwa ekusebenzeni okuthile kwezobuchwepheshe, namuhla inqubekela phambili iboniswe ngendlela enhle, ngakho-ke, ukubaluleka kwayo kuye kwethulwa njalo, phakathi kokunye okuvelele kakhulu uhlelo yama-microprocessors, asetshenziswa kakhulu kwikhompyutha.

Ezinye izinhlelo kube ukubethela kolwazi, kulabo abadinga ubumfihlo obuphezulu, ngoba kuyimfihlo, ukusetshenziswa kohlelo kanambambili kube ngempumelelo, ukukwazi ukudlulisa imininingwane ehlukene ezinhlobonhlobo zezinhlelo kube yinzuzo yezikhathi. , futhi ihlobene ngqo nokusetshenziswa kwamaphrothokholi ukuze kube nokuxhumana ngendlela yedijithali.

Uhlelo lwe-kanambambili lwethulwa ekuthuthukisweni nasekuthuthukisweni kobuchwepheshe, njengoba manje kubhekwa, sincoma ukufunda ngakho izibonelo zobuchwepheshe bedijithali.

Ukumelwa

Njengoba kuqokonyiswe phambilini ohlelweni lwe-kanambambili, kusetshenziswa u-0 no-1 kuphela, zingamanani amabili amelwe amanye amadijithi, njengamabhithi, ngoba akhombisa umongo othize wencazelo elungile yawo, echaza ngezibonelo ezilandelayo ukuqonda ngamunye ukulandelana:

Ukwabiwa kwezimpawu kuzoba kubaluleke kakhulu, kwikhompyutha ngayinye yezinombolo ezitholakalayo itholakala ngohlobo oluthile lwamandla kagesi, lokhu kungabuye kuhlobene nezinye izinhlobo zamaphoyinti afana ne-polarities, uzibuthe, kepha konke kuzoncika izimpawu ezisetshenziswayo, azibonwa kalula kangako, ngenxa yalesi sizathu ukumelwa kubalulekile futhi amanani wezinombolo zesi-Arabhu asetshenziswa ngokujwayelekile.

Ngokuvamile, kusetshenziswa u-0 no-1, kepha ezinye izinhlobo zezethulo nazo zingenziwa, ngoba kunokuhlukahluka okuthile, ngakho-ke, kuyadingeka ukubheka la maphuzu alandelayo:

• 100101 kanambambili, le yifomethi esetshenziswa kakhulu.
• 100101b, lokhu okunye ukumelwa ukukhombisa uhlobo lwefomethi kanambambili.
• 100101B, yethulwa ngokufana necala langaphambilini.
• I-Bin 100101, isiqalo esisetshenziselwa ifomethi yohlobo kanambambili.

Ukuguqulwa

Elinye lamaphuzu okufanele liqokonyiswe ukuguqulwa okwenziwa phakathi kwamanambambili kanye namadesimali, kukhona amacala ahlukahlukene, ahlukile ezicini ezithile, ngakho-ke, yonke imininingwane kufanele ibhekwe ukuze inqubo efakiwe ifanele futhi ingabi yinkimbinkimbi ukwenza, okulandelayo kuyakhonjiswa.

Idesimali kunambambili

Okokuqala, inani ledesimali liyacatshangelwa, okumele lihlukaniswe kabili, umphumela kufanele futhi uhlukaniswe kabili, futhi le nqubo izosetshenziswa kuze kutholakale inombolo engaphansi kwezimbili, ukwenza kube lula ukuyiqonda, kuzogqanyiswa isibonelo esilula, ukuze ukwazi ukubona isinyathelo ngasinye okufanele sigcwaliseke ukuze le ndlela elula ifezeke.

• Uthola inombolo kanambambili engu-131.
• Ukwehlukanisa u-131 ngambili kunika imiphumela engu-65 ngensalela engu-1.
• Ngemuva kwalokho ukuhlukaniswa ngababili kuyaqhubeka futhi inombolo engu-32 iyatholakala, iphinde isale ngo-1.
• Iyaqhubeka ngama-32 ukuthi lapho kwehlukaniswa ngababili ngu-16, bethula okusele kuka-0.
• Bese kuthi u-16 phakathi kwababili anikeze u-8, nensalela engu-0.
• Eyisishiyagalombili ihlukaniswe kabili isine, kuthi okuseleyo okutholakele kube ngu-0.
• 4 ihlukaniswe ngemiphumela emibili kabili, okusho ukuthi okusele kungu-0.
• Futhi okubili phakathi kwababili kukodwa, ngakho-ke okusele kungu-0, ukuqeda le nqubo, i-quotient yokugcina iyabhekwa ukuthi inye, lokhu kuyadingeka ukuze sikwazi ukusungula i-oda kahle.
• Kusungulwe i-oda lokuhlehla, kusukela kokusele okusele kuya kwelokuqala, okusho ukuthi uhlelo lwe-kanambambili lwe-131 yi-10000011.

Kuyindlela elula yokuyisebenzisa, i-akhawunti ngayinye kufanele yenziwe ngendlela efanele ukuze ukuhlaziywa okwenziwe kungabi kubi, noma kunjalo, kunezinye izindlela ezizovumela ukuthola le miphumela, kepha ngokujwayelekile lokhu kubhekwa njengokulula kakhulu ukufaka isicelo.

Idesimali (enamadesimali) kuya kunambambili

Leli ngelinye lamacala okufanele abhekelwe ukuguqulwa, uma inombolo itholwe ngamadesimali kungenzeka ukufeza ukuguqulwa kwayo kube yinombolo kanambambili, kulokhu, amanye amaphuzu okufanele asetshenziswe kumele acatshangelwe azokuvumela ukuthi kube Kwenziwe ngendlela efanele.

• Okokuqala ukubheka ingxenye ephelele yenombolo yedesimali, ngoba lokhu kuguqulwe ekuqaleni, esimweni sokuthi kungu-0 noma 1, khona-ke ohlelweni kanambambili kuzoba ngendlela efanayo.
• Ngemuva kwalokho kubhekwa ingxenye ye-fractional, ngayinye yazo kufanele yenziwe ngenombolo yesibili, esimweni lapho umphumela ungaphezu kwenombolo eyodwa kufanele kubekwe u-1, ngoba uyinani eliku-kanambambili, esimweni lapho ngaphansi lapho kufanele kubekwe u-0.
• Ekupheleni kokuphindaphindwa ngakunye kwalokho imiphumela etholwe njengamanani kanambambili kufanele i-odwe ngokuya ngokutholwa kwabo.

Akuyona indlela eyinkimbinkimbi, empeleni ibhekwa njengenye elula kakhulu futhi esheshayo, ngakho-ke, ukugwema ukudideka, kuzoqokonyiswa ezinye izibonelo ezivumela ukuthi iqondakale ngokushesha okukhulu, kube yile elandelayo:

• Inenombolo yedesimali elandelayo: 0,3125.
• Njengoba inani eliphelele lingu-0, libekwa ngendlela efanayo yohlelo kanambambili futhi ukuphindaphindeka kuyaqhubeka.
• Ukuphindaphinda kabili kunika inani elingu-0,625.
• Manje qhubeka nokuphindaphinda inani elitholwe ngababili bese uthola u-0,5.
• Nakulokhu inqubo efanayo iyagcwaliseka futhi inani le-1 liyatholakala.
• Lapho-ke ngokwemiphumela ngayinye etholakele, kucatshangelwa ukuthi ingabe kukhulu kune-1 noma cha, ukuguqulwa kukanambambili kungu-0,0101.

Manje, kuzokwethulwa icala elihlukile, ukuze ube nombono wokuthi wenzeni lapho inani eliphelele lingeyona i-0 noma i-1, okulandelayo kufanele kusetshenziswe:

• Inombolo yedesimali ezoguqulwa ingu-5,5.
• Njengoba inombolo ephelele ingu-5, ukuguqulelwa kubhanari kufanele kufake phakathi u-101.
• Qhubeka ngokuphindaphinda inombolo yedesimali engu-0,5 ngamabili, uthole umphumela ongu-1.
• Ngemuva kwalokho inombolo kanambambili kufanele ibekwe ngokulandelana, ibe ngu-101,1.

Kuyadingeka ukuthi ukuguqulwa kusetshenziswe ngendlela eyiyo, okungukuthi, ehambelana necala, ngoba akuzona zonke ezenziwa ngendlela efanayo, ngokuya ngalokho ofuna ukukuthola, imithetho ethile namaphuzu ahlobene namanani kanambambili Kanye namadesimali, avumela ukuguqulwa kwawo ukuthi kube khona kucatshangelwa zonke izici ezivela ohlelweni lwe-kanambambili.

Kanambambili kuya kudesimali

Ezinye izinqubo ezingenziwa ukuguqulwa kwenombolo kanambambili ibe yinombolo yedesimali, lokhu kwehlukile kumacala wangaphambilini, ngakho-ke kufanele uqaphele kakhulu, kodwa ngendlela efanayo ilula impela.

• Inombolo kanambambili kufanele ithathwe ukusuka kwesokudla kuye kwesobunxele, ukuze kusetshenziswe ukuphindaphinda.
• Idijithi ngayinye kufanele iphindwe kabili futhi kufanele iphakanyiswe kumandla alandelayo.
• Lapho kutholwa ngamunye wemiphumela yokuphindaphindwa, lokhu kufanele kungezwe futhi inombolo etholiwe izothathwa njengedesimali.

I-Binary to decimal (enengxenye kanambambili ye-fractional)

Kuleli cala, inombolo kanambambili iyathathwa, ngaphandle kwalokho, uhlangothi lwangakwesobunxele lubhekwa kuqala, futhi kusetshenziswa ukuphindaphindwa kabili, okumele kuphakanyiswe emandleni aqhubeka nokuphambana kwawo, ngemuva kokwenza ngakunye kwalokhu. engezwa, futhi inombolo etholakele kuzoba idesimali.

Ukusebenza

Izinombolo kanambambili zingaba nezinhlelo ezihlukile zokungezelela, ukukhipha, ukubuyabuyelela, i-quotient, lokhu akutholakali ngendlela efanayo nezinombolo zemvelo zamanye amacala, ngakho-ke, kubalulekile ukwazi ngqo ukuthi imisebenzi yenziwa kanjani ohlelweni kanambambili.

Ukwengeza

Ukuze wenze umsebenzi wokungezelela ohlelweni lwe-kanambambili, kubalulekile ukuhambisana nemithetho ethile futhi ulandele umthetho olandelwayo ovumela ukubalwa ukuthi kwenziwe ngendlela efanele, kubhekwa njengendlela elula kakhulu, ngakho-ke kuqokonyiswa ukuthi imithetho zimi kanje:

• 0 + 0 = 0.
• 0 + 1 = 1.
• 1 + 0 = 1.
• 1 + 1 = 10.

Lawa amaphuzu abalulekile okumele ahlangatshezwe ukuze kwenziwe umsebenzi ofanele wokwengeza ngenombolo kanambambili, inqobo nje uma kuthathwa ukunakekelwa okukhulu ukwenza lezi zibalo, konke ukusebenza ngokujwayelekile kuzokwenziwa ngokushesha futhi kalula, ukuze uqonde okuningi ngakho, isibonelo sizokhonjiswa njengenqubo eyenzekayo.

• Njengesibonelo, ukufingqwa kuka-0011101 no-1101011 kuyenziwa.
• Ukungezwa kufanele kwenziwe kusuka kwesokudla kuye kwesobunxele, ngakho-ke, izibalo zibekwa ngaphansi kwesinye ukusebenzisa isamba kukholamu ngayinye.
• Ngemuva kwalokho, ngokuhambisana nemithetho, ukusebenza kuqala, kuqala 1 + 1 = 10, ngakho-ke, kufanele ubeke u-0 bese uphatha u-1.
• Qhubeka ngokungeza u-1 oqhutshwa no-0, lapho u-1 + 0 = 1 bese lo mphumela wengezwa nge-1 ehambisanayo, ngakho-ke ngu-1 + 1 = 10, u-0 ubekiwe futhi u-1 uyathathwa futhi.
• Qhubeka nekholomu yesithathu, engeza u-1 ophathwa no-1 wethemu yokuqala, abe ngu-1 + 1 = 10, manje-ke i-10 + 0 = 10 isetshenzisiwe, njengamacala adlule, i-0 ibekiwe futhi ithwala 1.
• Kwikholamu yesine, okokuqala ngu-1 + 1 = 10 bese kuthi 10 + 1 = 11, kuzobekwa eyodwa bese kuthathwa futhi.
• Kwikholamu elandelayo kuzoba ngu-1 + 1 = 10 bese kuthi 10 + 0 = 0, ubeke u-zero bese uqhubeka nokuphatha u-1.
• Ikholomu lesithupha liqala ngokungeza u-1 + 0 = 1 futhi ukusuka lapho u-1 + 1 = 10, u-0 uthathelwe indawo bese kuthathwa u-1.
• Kwikholamu yokugcina, bese kungezwa u-1 + 0 = 1 bese kuthi 1 + 1 = 10, bese kugcina uma kubekwe u-10.
• Ngokulandela le nqubo ukwenza isamba, kutholakala umphumela we-10001000, njengoba ulula kakhulu ukuwenza, njalo kufanele wazi amanani aphethwe, ngaleyo ndlela ugweme amaphutha.

Bamba

Ngokusebenza kokukhipha, kufanele kubhekwe nemithetho ethile, kube yile elandelayo:

• 0-0 = 0.
• 1-0 = 0.
• 1-1 = 0.
• 0-1 = 1 futhi kuthatha u-1.

Ngenxa yalokhu, isibonelo sisetshenziswa ngamanani alandelayo, 001100011 no-000011110, ngendlela efanayo okumele yenziwe kusuka kwesokudla kuye kwesobunxele, imithetho isetshenziswa kukholamu ngalinye futhi kutholakale umphumela we-001000101, ukuze kufinyelelwe lo mphumela lo msebenzi wenziwa ngokulandelayo:

• Kwikholamu yokuqala ngu-0, uvela ku-1-0 = 0.
• Kokulandelayo, kusetshenziswa u-1-1 = 0.
• Ukukhipha kwesithathu ngu-0-1 = 1, futhi ngaphezu kwalokho kuthatha u-1.
• Kwikholomu yesine, kuqala kubhekwa ukuthi u-1 uyenziwa, bese kuthi u-1-0 = 1 asetshenziswe, bese kuthi u-1 aqhutshelwe olandelayo, bese kusetshenziswa u-1-1 = 0, okuyiwona okumele ubekwe emphumeleni.
• Manje kowesihlanu kusetshenziswa ngendlela efanayo nasekholomu yesine, ukuthola u-0 kumphumela.
• Kokulandelayo, kwenziwa u-1-1 = 0 bese kuthi 0-0 = 0, kumele kubekwe u-0.
• Ikholomu lesikhombisa ngu-1-0 = 1.
• Bese kulandela u-0-0 = 0.
• Ekugcineni, 0-0 = 0.
• Ngakho-ke, ukwenza ngalinye lalawa makholomu ngokulandelana kuphumela ku-001000101.

Ukuphindaphinda

Endabeni yomkhiqizo enezinombolo zebhanari, ayikho imithetho ethize eyethulwayo yalokhu kusebenza njengakwisimo sokungeza nokususa, ukwenza ukubuyabuyelela umsebenzi kumele usetshenziswe ngendlela efanayo njengoba kwenziwa ngezinombolo zamadesimali, ngakho-ke, kulokhu akukho zinguquko, alukho olunye ulwazi olungeziwe oludingekayo.

Isigaba

Ngendlela efanayo kwenzeka nge-quotient yezinombolo kanambambili, imithetho okufanele igcwaliswe, inqubo okumele isetshenziswe iyafana naleyo eyenziwe ngokwehlukana okujwayelekile ngezinombolo zamadesimali, ngendlela efanayo nokuphindaphinda, azikho izinguquko ekusebenzeni okusetshenzisiwe.