Iinkqubo zeCalus. Uluhlu lweendlela zokubala. Iinkqubo zokubala: i-informatics

Abantu abazange bafunde ngokukhawuleza ukubala. Uluntu olungummiselo lukhokelwa yintwana encinci yezinto - enye okanye ezimbini. Konke okwakungaphezulu, ngokuzenzakalelayo kwabizwa ngokuba "yinto eninzi". Oku kubonwa njengesiqalo senkqubo yesimanje yokubala.

Inkcazo yeNgxelo emfutshane

Kwinkqubo yokuphuhliswa kwempucuko, abantu baqala ukubonakalisa isidingo sokuhlukanisa iqoqo elincinci lezinto, babumbene nempawu eziqhelekileyo. Waqala ukuphakamisa imiqondo ehambelanayo: "ezintathu", "ezine" kwaye njalo "ukuya kwi sixhenxe." Nangona kunjalo, yayingumxholo ovalwe, ogqityiweyo, ingcamango yokugqibela eyaqhubeka nokuphatha umthwalo we-semantic "omkhulu." Umzekelo ocacileyo walolu hlobo lwengqungquthela, olusifinyelela kwifomu yalo yangaphambili (umzekelo, umzekeliso "Isiqingatha sexesha elisixhenxe.").

Ukuvela kweendlela zeakhawunti ezinzima

Ngexesha elide, ubomi kunye nazo zonke iinkqubo zemisebenzi yabantu ziye zaba nzima nakakhulu. Oku, kukhokelela ekuveleni kweenkqubo ezinzima kakhulu zokubala. Ngelo xesha, abantu basebenzisa izixhobo zokubala ezilula ukucacisa ukuthetha. Bawafumana bezungezile: bafaka iintonga kwiindonga zomqolomba ngeendlela ezilungelelweyo, abazange bachithe, bathumele inani lamatye kunye namatye ababenomdla kuzo, nje kuphela uluhlu oluthile lweentlobo ezahlukahlukeneyo ezikhoyo. Kamva, izazinzulu zanamhlanje zanikezela eli gama kwigama eliyingqayizivele "i-calculation". Ingundoqo yayo kubhala inombolo usebenzisa uphawu olulodwa. Namhlanje, le yinkqubo efanelekileyo kakhulu, ikuvumela ukuba ukhangelelanise inani lezinto kunye nemiqondiso. Ukusabalalisa kuninzi kwakuseklasini zezikolo eziprayimari (ukubala iintonga). Ilifa le "akhawunti ye-pebble" lingabonwa ngokukhuselekileyo ngeekhompyutha zamanqaku atshintsho ahlukeneyo. Inomdla kunye nokuvela kwegama lamanje elithi "ukubalwa", iingcambu zawo zivela kwi-Latin calculus, eguqulela kuphela "i-pebble".

Ukubala kwiminwe

Ngeemeko zesigama esilukhuni kakhulu sabantu abathandekayo, impawu ezithatyathwa ngokuqhelekileyo zibanjiswa njengongeziweyo olubalulekileyo kwiinkcukacha ezithunyelwayo. Inzuzo yeminwe yayisezingeni eliphezulu kwaye ihlala ihlala kunye nento eyayifuna ukuhambisa ulwazi. Nangona kunjalo, apha kukho izinto ezingenakwenzekayo: ukukhawuleka okukhulu kunye nokuthunyelwa kwexesha elifutshane. Ngako ke, i-akhawunti yonke yabantu abasebenzisa "indlela yokunweba", inqunyanyelwe kumanani aphindaphindiweyo yenani leminwe: 5 - iyafana nenani leminwe ngakwesinye icala; 10 - ezandleni zombini; 20 - inani elipheleleyo kwiingalo nasemilenzeni. Ngenxa yokuphuculwa kancinci kwendawo yokugcinwa kwamanani, le nkqubo yayikho ixesha elide.

Ukuphuculwa kokuqala

Ngokuphuhliswa kwenkqubo yokubala kunye nokwandiswa kwamandla kunye neemfuno zoluntu, inani eliphezulu elisetyenzisiweyo kwiinkcubeko zezizwe ezininzi lilingama-40. Kwakhona kwaqondwa ukuba ithetha ukungapheliyo (okungabonakaliyo) ubuninzi. ERashiya, igama elithi "imilingo engamashumi amane" lasasazeka. Injongo yalo yancitshiswa ibe inani lezinto ezingenakubalwa. Isigaba esilandelayo sokuphuhliswa kukubonakala kwenani le-100 Emva koko, iinombolo ezili-1000, ezili-10 000 njalonjalo, ngasinye sazo sithatha umthwalo we-semantic, esifana nesixhenxe nesine. Kwilizwe lamanje, imida yeakhawunti yokugqibela ayichazwa. Kuza kube yimini, ingcamango yendalo yonke "ye-infinity" iye yaziswa.

Amanani apheleleyo kunye nenxalenye

Iinkqubo zanamhlanje zokubala ngenani elincinci lezinto zithatha inyunithi. Kwiimeko ezininzi, ubuninzi obungabonakaliyo. Nangona kunjalo, ngokulinganisa okuchanileyo, kwakhona kuhlaselwa. Ngaloo nto imbono yenani le-fraction livele kwinqanaba elithile lophuhliso. Ngokomzekelo, inkqubo yeBabiloni yemali (ubunzima) yayiyimitha engama-60, eyayiyi-talan eyi-1. Ngako oko, i-mine yam 1 yayilinganiswa namaashekeli angama-60. Kungenxa yesi sizathu ukuba imathematika yaseBabiloni yayisetyenziswa ngokubanzi ngokuxhatshazwa ngokwesondo. Ukusetyenziswa ngokubanzi emaqenjini aseRashiya kwavela kumaGrike nakumaNdiya yakudala. Iirekhodi ngokwabo zifana nabaseIndiya. Ukwahlukana okuncinane kukungabikho komgca wecandelo lokugqibela. AmaGrike anqunywe yi-numerator evela ngasentla, kwaye i-denominator evela ngaphantsi. Uhlobo lwe-Indiya lwamacandelo eencwadi abhaliweyo lwaphuhliswa kakhulu e-Asia naseYurophu ngenxa yabososayensi ababini: U-Mohammed Khorezmsky noLeonardo Fibonacci. Inkqubo yaseRoma yama-calculus equle iiyunithi ezili-12, ezibizwa ngokuthi i-ounces, kuzo zonke (1 acc), ngokulandelanayo, kwisiseko sazo zonke izibalo zazinxalenye ezilishumi elinesibini. Kanye kunye nolwamkelekileyo, ngokuqhelekileyo, ukwahlula okukhethekileyo. Ngoko, ngokomzekelo, ngeenkulungwane ze-17 zeenkwenkwezi zeenkwenkwezi zasebenzisa iindawo ezinjalo ezibizwa ngokuba ngamaqhezu angamashumi amathandathu-ama-decimal, emva koko aphakanyiswa ziimpawu eziqingqiweyo (uSimon Stevin, isayensi yenzululwazi, wazisa). Ngenxa yenkqubela phambili yoluntu, kwakukho isidingo sokwandiswa okubaluleke ngakumbi kwimixholo yamanani. Ngoko kwakukho amanani angenabulungisa, angenangqiqo kwaye anzima. Uhlobo oluqhelekileyo luye lwabonakala ngathi lwakutsha nje. Kwaqala ukusetyenziswa xa kungeniswa kwiinkqubo zanamhlanje zokubala kweenombolo ezimbi.

Ukusetyenziswa kwe-alfabhethi engeyiyo

Yiyiphi i-alphabet? Kwi-calculus system, unikezela ukuba ixabiso leenombolo alitshintshi kwilungiselelo lawo. I-alfabhethi engeyona indawo ibonakaliswa ngobuninzi benani lezinto. Kwinqanaba leenkqubo ezakhiweyo ngokwelolu hlobo lwesibarfabhe yimiqathango yokongeza. Ngamanye amazwi, inani elipheleleyo leenombolo liqukethe isamba sawo onke amadijithi apho irekhodi liquka. Ukuvela kweenkqubo ezingekho phantsi kweemeko zenzeke ngaphaya kweenkqubo zesimo. Ngokuxhomekeke kwindlela yokubala, inani elipheleleyo leenombolo lichongiwe njengomlinganiselo okanye isamba sazo zonke idijithi ezenza inombolo.

Kukho ukungalungi kwezi nkqubo. Phakathi kwezona zinto ziza kubelwa:

• Ukuqaliswa kwamanani amasha ekwakheni inombolo enkulu;
• Ukungenakwenzeka ukubonakalisa iinombolo ezingenanto kunye neenxalenye zeqhekeza;
• Ukunyaniseka kokwenza imisebenzi ye-arithmetic.

Kwimbali yoluntu, iinkqubo ezahlukeneyo zokubala zazisetyenziswa. Izona zidumileyo zi: isiGrike, isiRoma, i-alfabhethi, isiqabane, isiYiputa saseYiputa, iBhabhiloni.

Enye yeendlela eziqhelekileyo zokubhaliweyo

Ukubalwa kwenani lamaRoma, okwenzekayo nanamhla kungatshintshi, yinto enye edumileyo. Ngoncedo lwayo, imihla ngemihla imakishwe, kubandakanywa neentlokoma. Kwakhona kufumana isicelo esikhulu kwiincwadi, inzululwazi nezinye iindawo zobomi. Kwimimandla yaseRoma yokubala kuphela iileta ezisixhenxe zeelatrafti ezisetyenzisiweyo, ngasinye sihambelana nenombolo ethile: I = 1; = =; X = 10; L = 50; C = 100; D = 500; M = 1000.

Isiganeko

Imvelaphi yamaxabiso aseRoma ayinakuqondakala, imbali ayizange igcine idatha echanekileyo yokubonakala kwayo. Ngelo xesha, inyaniso ayinakuphikiswa: impembelelo ephawulekayo kwinani lamaRoma linikezelwa yinkqubo emihlanu yokubala amanani. Nangona kunjalo, ngesiLatini akukho nto ikhankanywe ngayo. Ngaloo ndlela, kwavela ingcamango malunga nokuboleka ngamaRoma asendulo kwinkqubo yabo kwabanye abantu (mhlawumbi kwi-Etruscans).

Izixhobo

Ingxelo yazo zonke i-integers (ukuya ku-5000) yenziwa ngokuphinda amanani achazwe ngasentla. Into ebalulekileyo yilungiselelo leempawu:

• Ukongezwa kwenzeka phantsi kwemeko yokuba omkhulu umi phambi komncinane (XI = 11);
• Ukukhutshwa kwenzeka ukuba inani elincinci limi phambi kwekhulu (IX = 9);
• Uphawu olufanayo alukwazi ukuma ngaphezu kweethathu ngokulandelana (umzekelo, 90 ibhaliwe i-XC esikhundleni seLXXXX).

Ukungonakali kwayo kukuphazamiseka kokwenza imisebenzi ye-arithmetic. Ngelo xesha, bekukho ixesha elide kwaye layeka ukusetyenziswa eYurophu njengeyona ndlela ehamba phambili ekuhlaleni - ngekhulu le-16.

Inkqubo yamaRoma yokubala ayithathwa njengento engenamposiso. Oku kubangelwa kukuba kwinani lamacala kukho ukususwa kwenani elincinci ukusuka kwelinye elikhulu (umzekelo, IX = 9).

Indlela yeAkhawunti kwiYiputa yaseYiputa

Inkulungwane yesithathu yeminyaka ye-BC ithathwa njengomzuzu wokuvela kwenkqubo yokubala kwiYiputa YaseYiputa. Isiseko salo senziwa ekurekhodweni kweenombolo ezikhethekileyo 1, 10, 102, 104, 105, 106, 107. Zonke ezinye iinombolo zabhalwa njengombutho wolwazi lweempawu zangaphambili. Ngelo xesha, kwakukho umda - umlinganiselo ngamnye kufuneka uphinde uphinde uphindwe kabini. Kwintliziyo yale ndlela yokubala, izazinzulu zanamhlanje zibiza "inqanaba lokugqibela lokubala," liyimigaqo elula. Inentsingiselo yalo kukuba inombolo ebhaliweyo yayilingana nesixa-mali sazo zonke idijithi zazo ezazibandakanya.

Indlela ye-akhawunti engekho

Inkqubo yokubala, apho, xa ubhala izinombolo, isayina enye isetyenzisiweyo - I-ibizwa ngokuba yi-unary. Inombolo nganye elandelelanayo ifunyenwe ngenxa yokufaka entsha kwinto yangaphambili. Kule meko, inani lalo lilinganayo nelingana nenani labhaliweyo ngoncedo lwabo.

Inkqubo ye-Octal yokubala

Le ndlela yendlela yokubala, kwisiseko apho isibalo esingu-8 sibalwa. Inani ukusuka ku-0 ukuya ku-7 lisetyenziselwa ukubonisa iinombolo. Inkqubo iye yasetyenziswa ngokubanzi kwimveliso nokusetyenziswa kwezixhobo zedijithali. Inzuzo eyona nto kukuguqulelwa kwamanani amaninzi. Ziyakwazi ukuguqulwa kwi- binary system kunye nangaphandle koko. Ezi zixhobo ziqhutyelwa ngokufaka amanani. Ukususela kwinkqubo ye-octal bayaguqulelwa kuba kathathu bhinqa (umzekelo, 28 = 0102, 68 = 1102). Le ndlela ye-akhawunti yasasazwa kwintsimi yemveliso yekhompyutheni kunye neprogram.

I-hexadecimal system yokubala

Ngoku kutshanje, kwikhompyutheni yekhompyutheni, le ndlela ye-akhawunti isetyenzisiweyo. Ngengcambu yale nkqubo i-base-16. I-calculus esekelwe kuyo isebenzisa ukusetyenziswa kwamanani ukusuka ku-0 ukuya ku-9 kunye nochungechunge lweencwadi ze-Latin alphabet (ukusuka ku-A ukuya ku-F), ezisetyenziselwa ukubonisa ixesha eliphakathi kwe-1010 ukuya ku-1510. Le ndlela yokubala Kuye kwaphawulwa, isetyenziswe kwimveliso yesofthiwe kunye namaxwebhu anxulumene neekhomputha kunye nezinto zawo. Oku kusekelwe kwiipropati zekhompyutheni yanamhlanje, iyunithi eyisiseko apho imemori ye-8-bit. Kukulungele ukuguqula nokubhala usebenzisa ii-hexadecimal digits. Umsunguli wale nkqubo yindlela ye-IBM / 360. Amaxwebhu alo aqale aguqulelwe ngale ndlela. Umgangatho we-Unicode ubonelela ukubhala nawuphi na umgca kwifom ye-hexadecimal usebenzisa ubuncinane ubunani beenombolo ezine.

Iindlela zokubhala

Uyilo lweMathematika lwenkqubo ye-akhawunti lusekelwe ekuboniseni kwikhowudi engezantsi kwindlela yokugqibela. Umzekelo, inombolo 1444 ibhaliwe kwifomu 144410. Iilwimi zokubhala ngokubhala inkqubo ze-hexadecimal zinama-syntaxes ahlukeneyo:

• Iilwimi ze-C neeJava zisebenzisa isiqalo "0x";
• Ku-Ada kunye neVHDL umgangatho olandelayo usetyenziswa - "1516 # 5A3 #";
• Iintlanganiso zibonisa ukusetyenziswa kweleta "h", ebeka emva kwenani ("6A2h") okanye iqela elithi "$", eliqhelekileyo kwi-AT & T, i-Motorola, Pascal ("$ 6B2");
• Kwakhona kukho iirekhodi ezinjenge "# 6A2", inhlanganisela "& h", ebeka phambi kwenani ("& h5A3") kunye nabanye.

Isiphelo

Iinkqubo zokufunda zifundwa njani? I-Informatics yinkqubo esemgangathweni kwisikhokelo sokufunyanwa kwedatha, inkqubo yobhaliso lwabo kwifomu efanelekileyo yokusetyenziswa. Ngokusetyenziswa kwezixhobo ezizodwa, zonke iinkcukacha ezikhoyo zibhalwa kwaye ziguqulelwe ngolwimi lwenkqubo. Kusetyenziswa kwakhona ekudalweni kwesoftware kunye nekhompyutheni. Ukufunda iindlela ezahlukeneyo zokubala, i-informatics ibandakanya ukusetyenziswa, njengoko sele kukhankanywe ngasentla, kwezixhobo ezahlukeneyo. Abaninzi babo banegalelo ekuphunyezweni kwenguqu eguquguqukayo yamanani. Esinye "isixhobo" esinjalo itafile yeenkqubo zokubala. Kukulungele ukuwusebenzisa. Ngokuncedwa kwezi tafile kunokwenzeka, umzekelo, ukuguqulela ngokukhawuleza inamba ukusuka kwinkqubo ye-hexadecimal ukuya kumbhinqa ongenayo ulwazi olukhethekileyo lwesayensi. Namhlanje, inokwenzeka ukuba kwenziwe ukuguqulwa kwedijithali phantse wonke umntu onomdla kulo mntu, kuba izixhobo ezifunekayo zinikezelwa kubasebenzisi kwizixhobo ezivulekileyo. Ukongeza, kukho iiprogram zokuguqulela kwi-intanethi. Oku kunciphisa kakhulu umsebenzi wokuguqula amanani kunye nokunciphisa ixesha lokusebenza.