Uhlelo lwe-binary: Luyini, lusetshenziselwani, futhi luvelaphi?

Ezibalweni kukhona iqoqo elikhulu eliyinkimbinkimbi lezinto izinhlelo zezinombolo ezinezisekelo ezahlukene futhi ezinezici ezihlukile phakathi kwazo. Enye yalezi uhlelo lwe-binary, olusebenza ngezinombolo ezimbili, u-“0” no-“1”. 

Lolu hlelo lubaluleke kakhulu kwisayensi yamakhompyutha, njengoba kulapho leli gama livela khona Kancane. Ngokusebenzisa ama-impulse nama-bits kagesiIsofthiwe yenza izenzo kukhompyutha.

Ezigabeni ezilandelayo uzothola ulwazi oluphelele kakhulu mayelana nalesi simiso sesisekelo sesi-2. Sizokukhombisa izinyathelo ezidingekayo zokuguqula izinombolo ze-binary zibe yi-hexadecimal, i-octal, kanye ne-decimal..

Iyini isistimu ye-binary futhi isetshenziselwani kwisayensi yamakhompyutha kanye nekhompyutha?

Izinombolo ze-binary ziyisimiso sezibalo esinesisekelo sesi-2, okusho ukuthi amanani avunyelwe yi-"0" kanye ne-"1". Ngakho-ke, kunomehluko omkhulu ngesistimu yedesimali esivame ukuyisebenzisa ezicini ezahlukene zokuphila kwethu. Ekubaleni, izinombolo zero kanye neyodwa zibizwa ngokuthi izinombolo ezimbili futhi zihunyushwa ngokuthi "Idijithi enambambili" noma eyaziwa ngokuthi "ingxenye".

Ngakho-ke, yini engathiwa... "Ingxenye 0" futhi i "Ingxenye 1" ukumela ama-pulse kagesi, ngokuvamile kusetshenziswa u-0 njengokunqamula kanye no-1 njengoxhumano noma isignali enhle. Ngale ndlela, Izinhlelo ezifakwe kukhompyutha zingamela imiyalelo yekhompyutha, zifunde imibhalo, noma zimele idatha..

Lokhu kufezwa ngomsebenzi wama-microprocessor ekuboneni ukuba khona noma ukungabikho kwezimpawu zokushaya kwenhliziyo kagesi. Ama-processor anezinga lokudlulisa elihlukile kuye ngenqubo yawo yokukhiqiza kanye Zingaqoqa amabhithi afinyelela kwangu-8 abe isignali eyodwaLe sethi yilokho okubizwa ngokuthi "ibhayithi" futhi iyiyunithi yokulinganisa esetshenziswa ekubaleni.

Umlando kanye nemvelaphi: Yatholakala nini isimiso se-binary futhi kwaba yini umthelela waso?

Ukuvela kokuqala kwe uhlelo kanambambili umkhuba ngokusebenzisa isazi sezibalo uPingala, emakhulwini amathathu eminyaka ngaphambi kokuzalwa kukaKristuNokho, abanye bathi kukhona umsebenzi encwadini yesiprofetho sesiShayina. I Chin, owadalwa kusukela ngo-1200 BC futhi lapho kwakhiwa khona amaphethini athile ngezinombolo ezimbili. Ngale ncwadi efanayo yomthandazo, kwenziwa ilungiselelo lokuba kube khona ukulandelana kwedesimali okuhlanganisa izinombolo kusukela ku-0 kuya ku-63.

Lo msebenzi wenziwa yisazi sefilosofi UShao Yong futhi wakwenza ngekhulu le-11 AD. Kodwa kwaze kwaba ngo-1605 lapho uShansela waseNgilandi, isazi sefilosofi nesazi sezibalo uFrancis Bacon wathiWasebenzisa uhlelo lapho asungula khona ukuthi izinhlamvu zingamelwa ngezinombolo ezimbili.

Lokhu kwaholela ekushicilelweni kwakhe, eminyakeni engama-70 kamuva Indela yaseSpain uJuan Caramuel yanikeza incazelo engokoqobo yalolu hlelo lwesisekelo-2Kakade ngekhulu le-19, yini eyayizoba yi- ukushintsha kwesimo sesistimu yezinombolo ezimbiliKwasungulwa indlela eningiliziwe yokuthi lezi zinombolo kufanele ziphathwe kanjani. Lokhu kwenziwa nguGeorge Boole waseBrithani, kamuva eyaziwa ngokuthi i-algebra ye-Boolean.

Ngasekupheleni kweminyaka yama-1890, i-United States kwakudingeka yenze ukubalwa kwabantu bayo, ngakho yaqasha UHerman Hollerith ukuze enze lo msebenziAmaJalimane asebenzisa uhlelo lwe-binary ngokusebenzisa amakhadi ashaywayo ngokusekelwe ku- UJoseph Marie Jacquard, eqalise ukulawula okubili kwezinsimbi zayo zokuthunga. Kungalesi sikhathi lapho izinombolo ezimbili zingena khona ezweni lokubala.

Kusukela ngaleso sikhathi kuqhubeke, ulwazi lwaqala ukucutshungulwa ngokuzenzakalelayo ngaphandle kokungenela komuntu. Eminyakeni eminingi kamuva, umsebenzi wonjiniyela kagesi wavela. UClaude Shannon kanye nososayensi uGeorge Stibitz. Laba babengabokuqala ukusungula amazinga okusetshenziswa kohlelo lwe-binary ekubaleni.

I-Binary vs decimal vs octal vs hexadecimal: Uyini umehluko phakathi kwazo?

Isistimu kanambambili Inesisekelo esingu-2, okusho ukuthi izinombolo ezisetshenzisiwe yizo 0 no-1. Ngakolunye uhlangothi i uhlelo lwedesimali isisekelo salo singu-10 Futhi uhlelo esilusebenzisa nsuku zonke. Kanti uhlelo i-octagonal Isisekelo singu-8 futhi izinombolo zisetshenzisiwe 0, 1, 2, 3, 4, 5, 6, 7. Ekugcineni, uhlelo I-Hexadecimal inesisekelo esingu-16 futhi imelelwa izinombolo zesi-Arabhu nezinhlamvu zamagama, okuyi 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.

Uhlelo lwe-binary lwamukela izinombolo ezi-negative noma ezi-inverse.U-0 uyiphuzu lokubhekisela ekufakweni kwesibonakaliso, kodwa lezi zinombolo zimelelwe ngendlela ethile. Ngenkathi ohlelweni lwedesimali Izinombolo eziphelele kanye nezingxenyana ziyamukelwa futhi zingaba nezimpawu ezinhle nezimbi ezimelelwe ngo-a – phambi kwenombolo ngayinye ngaphambi kuka-zero.

Ngokuphathelene nesistimu ye-octal Yamukela izingxenyana kanye nezinombolo ezinhle nezimbi. I-Hexadecimal ibheka noma yiliphi inombolo engaphansi kuka-7 njengenegative.Ngakho-ke, konke F Uma kuvela njengenombolo yokuqala, kusho ukuthi i-negative futhi akufanele ibalwe.

Ukuguqulwa Kwesistimu: Idatha ithuthwa kanjani isuka kwesinye isistimu iye kwesinye?

Ukuze uguqule izinombolo kusuka ohlelweni olulodwa uye kolunye, kuzodingeka wenze izinyathelo ezimbalwa, esizokukhombisa zona ngezansi:

I-Binary kanye ne-Decimal

Ukuguqula inombolo ye-binary Kumelwe uqale ukubala izinombolo kusukela kwesokudla, eyokuqala ingu-"0".Ngale ndlela, uma unenombolo 11011 uzobala kusukela kokugcina "1" njengenombolo 0. Ngakho-ke, i-akhawunti yakho izobukeka kanje:

• 1(4) 1(3) 0(2) 1(1) 1(0)> 4, 3, 2, 1, 0

Okulandelayo, kuzodingeka wenze isamba samandla esisekelo 2, lapho ama-exponents kuyizinombolo 4, 3, 2, 1, 0. Ku-addend ngayinye kumele yande ngezinombolo ezimbili. Okungukuthi, ngo-1, 1, 0, 1, 1.

Ngakho-ke, ukuguqulwa kuzoveza:

• 2⁴ 1.2 +³ 0.2 +² 1.2 +¹ 1.1 +⁰ =
• 16 + 8 + 0 + 2 + 0 =
• 26

Leyo, 11011 Kuhlelo lwe-binary, lulingana nenombolo 26 ohlelweni lwedesimali.

Uma ufuna ukuguqula kusuka ku-decimal kuya ku-binary kuzodingeka uthathe inombolo yedesimali bese uyihlukanisa kabiliNgemuva kwalokho kuzodingeka uphinde usebenzise lowo mphumela. hlukanisa kube yi-2 njalo njalo kuze kube yilapho kuphela.

Uma Okunye okutholile bekuyi-1Kuzodingeka ukuthi ucabangele lokhu, ngoba uzobe uthatha zonke izilinganiso bese uziveza ngokulandelana okuphambene ukuze yakha inombolo ye-binary.

Isibonelo, uma unenombolo 100, kuzodingeka wenze okulandelayo:

• 100/2 = 50 okusele kungu 0
• 50/2 = 25 okusele kungu 0
• 25/2 = 12 okusele kungu 1
• 12/2 = 6 okusele kungu 0
• 6/2 = 3 okusele kungu 0
• 3/2 = 1 okunye kungukuthi 1

Ngakho-ke, inombolo kanambambili lokho kwakhiwa 1100100Lokhu kusho ukuthi inombolo engu-100 ku- Uhlelo lwedesimali lulingana nenombolo ye-binary etholakele..

I-Binary kanye ne-Hexadecimal

Ukuguqula i- Ukuze uguqule inombolo ye-binary ibe inombolo ye-hexadecimal, kufanele uqoqe izinombolo ngamaqembu angu-4.Uma unezinombolo ezimbalwa, kuzodingeka uqedele nge ama-zero aholayo.

Ngemuva kwalokho kuzodingeka ufake izinombolo kudijithi ngayinye. 8, 4, 2, 1Okulandelayo, kuzodingeka uphindaphinde lezo zinombolo ngenombolo ngayinye bese uzihlanganisa ndawonye. Isibonelo, uma unenombolo enambambili 1010 uzodinga ukwenza okulandelayo: 8 x 1 + 4 x 0 + 2 x 1 + 1 x 0 = 10 Futhi njengoba u-10 mkhulu kuno-9, inombolo ehambisanayo ingu- A.

Ngakho-ke, inombolo ye-binary I-1010 imele inombolo u-A ohlelweni lwe-hexadecimalUma unezinombolo ezinkulu, kufanele ulandele izinyathelo ezifanayo, kodwa eqenjini ngalinye lezinombolo ezine.

Ngamanye amazwi, uma unenombolo engu-1100101101, kufanele wenze okulandelayo:

• Hlukanisa ngezinombolo ezine 11 0010 1101.
• Qedela iqembu lokuqala ngama-0 uze ube neqembu labantu abangu-4. Okusho ukuthi, uzoba nalo 0011 0010 1101.

Yenza izinyathelo zangaphambilini ngokuphindaphinda nokwengeza iqembu ngalinye:

• 8 x 0 + 4 x 0 + 2 x 1 + 1 x 1 = 3
• 8 x 0 + 4 x 0 + 2 x 1 + 1 x 0 = 2
• 8 x 1 + 4 x 1 + 2 x 0 + 1 x 1 = 13 > mkhulu kuno-9, ngakho-ke inombolo u-D ihambisana

Lokhu kusho ukuthi inombolo ye-binary engu-1100101101 ilingana no-32D ohlelweni lwe-hexadecimal.

Uma ufuna Guqula inombolo ye-hexadecimal ibe yi-binary Kuzodingeka ukuthi ufake inombolo ehambisanayo ngqo esikhundleni sayo inombolo ye-binary.

Ukuze wenze lokho, kuzodingeka ucabangele ubudlelwano obulandelayo:

• 0 = 0000
• 1 = 0001
• 2 = 0010
• 3 = 0011
• 4 = 0100
• 5 = 0101
• 6 = 0110
• 7 = 0111
• 8 = 1000
• 9 = 1001
• A = 1010
• B = 1011
• C = 1100
• D = 1101
• E = 1110
• F = 1111

Uma sikwenza ngecala elidlule 32D, Kuzodingeka sishintshe inombolo ngayinye.

Ukuze:

• 3 = 0011
• 2 = 0010
• D = 1101

Lena indlela eyakhiwa ngayo inombolo enamabinary 001100101101, noma ngamanye amazwi 1100101101Okusho ukuthi, inombolo eyakhiwayo yileyo efanayo esasiyisebenzisa ukuyiguqula esinyathelweni kanambambili kuya ku-hexadecimal.

Okubili kanye nokwesine

Njengoba nge ukuguqulwa kube uhlelo lwe-hexadecimal Kuzodingeka uqoqe izinombolo, kodwa kulokhu ngamaqembu anezinombolo ezintathuKuzodingeka futhi ugcwalise ngo-0 ngakwesobunxele uma bengafinyeleli eqenjini lezinombolo ezintathu.

Ngaphezu kwalokho, kufanele ukhumbule ithebula elilandelayo lokufaka esikhundleni, lapho izinombolo zokuqala ziyi-binary kanti eyesibili izinombolo zazo ze-octal ezihambisanayo:

• 0 = 0
• 001 = 1
• 010 = 2
• 011 = 3
• 100 = 4
• 101 = 5
• 110 = 6
• 111 = 7

Okufanele ukwenze manje qoqa bese ushintsha izinombolo ngokusebenzisa ibhodiIsibonelo, uma unenombolo 1011101.

Kuzodingeka ulandele le nqubo:

• Yenza i- amaqembu anezinombolo ezi-3Okusho ukuthi, uzoba ne-1 011 101.
• Manje, Qedela iqembu lokuqala ngo-0., uzothola umphumela ongu-001 011 101.

Shintsha ngokuvumelana uhlu esikubonise lona ngaphambili.

Uzogcina unalokhu:

• 001 = 1
• 011 = 3
• 101 = 5

Ngakho-ke, inombolo ye-binary 1011101₂ ihambisana nesimiso esinonxantathu nenombolo 135₈. Uma ufuna ukuguqula inani le uhlelo olunezinhlangothi ezine kuya ku-binary Kuzodingeka ulandele indlela hlehlaOkusho ukuthi, kuzodingeka ukuthi ufake inombolo ngayinye onayo esikhundleni sayo. i-octal yesistimu ngamaqembu anezinombolo ezintathu ze-binary. Uzodinga Khumbula uhlu esikhulume ngalo ekuqaleni..

Ngakho-ke, uma unenombolo 2457₈ futhi ufuna ukuyiguqula ibe yi- kanambambiliKuzodingeka uyihlukanise ibe 2, 4, 5, 7.

Okulandelayo, kuzodingeka ulandele ukushintshwa kwenombolo ngayinye:

• = 2 010
• = 4 100
• = 5 101
• = 7 111

Ngakho-ke kuphethwa ngokuthi inombolo 2457₈ = 10100101111₂