Iinkqubo zeenombolo. Umzekelo weenombolo zeenombolo ezingenasimo

Iinkqubo zeenombolo - yintoni na? Ngaphandle kokungazi impendulo yalo mbuzo, ngamnye wethu ungasenanto ebomini bethu usebenzisa iinkqubo zeenombolo kwaye akayikrokreli ngazo. Kunene, kubuninzi! Akunjalo, kodwa ezininzi. Ngaphambi kokuba sinikeze imizekelo yeenkqubo ezingenanto zendlela, makhe sijonge kule ngxaki, makhe sixoxe ngeenkqubo zesimo.

Kufuneka iakhawunti

Ukususela kumaxesha amandulo, abantu banesidingo se-akhawunti, oko kukuthi, baqonda ngokuqinisekileyo ukuba kubalulekile ukuvakalisa ngandlela-thile umbono wokubaluleka wezinto kunye neziganeko. Ingqondo iphakamisa ukuba kufuneka usebenzise izinto ze-akhawunti. Ezona zinto zilungele ukuhlala zikhona iminwe ezandleni zabo, kwaye oku kuyaqondakala, kuba zihlala zikhona (ngezinye izinto ezingaqhelekanga).

Kwaye kwakudingeka ukuba abameli basendulo bentloko yabantu bagobe iminwe ngendlela engokoqobo-ukubonisa inani lamammoth abulawe, umzekelo. Amagama aloo maqhosha e-akhawunti ayengakabi khona, kodwa kuphela umfanekiso obonakalayo, umzekeliso.

Iinkqubo zeenombolo zanamhlanje

Inkqubo yenkqubo yindlela (indlela) yokuveliswa kwexabiso lexabiso kunye nenani ngeendlela ezithile (imiqondiso okanye iileta).

Kubalulekile ukuqonda into enemeko kwaye engekho imeko kwi-akhawunti, ngaphambi kokuba unike imizekelo yeenombolo zeenombolo ezingezizo. Inkqubo yenani lexeshana lininzi. Ngoku basebenzise oku kulandelayo kwimimandla eyahlukeneyo yolwazi: ibinari (iquka izinto ezimbini ezibalulekileyo: 0 kunye no-1), idijithi ezintandathu (inani labalinganiswa - 6), i-octal (imiqondiso - 8), i-duodecimal (abalinganiswa abalishumi elinesibini), i-hexadecimal (iquka abalinganiswa abalishumi elinesithandathu). Yaye yonke iluhlu lweempawu kwiinkqubo luqala ukususela kwi-zero. Ubugcisa bekhompyutheni banamhlanje busekelwe ekusebenziseni iikhowudi zobuncinci - inkqubo yenani lebhinqa.

Inkqubo yenombolo yesistim

Ubuninzi bobukho bukho kwiimilinganiselo eziphambili zezikhundla apho imiqondiso yenani ifumaneka khona. Oku kungabonakaliswa ngokugqithisileyo ngomzekelo wenkqubo yenombolo yokugqibela. Emva koko, sasiyisebenzisa ukususela ebuntwaneni. Impawu kule nkqubo zilishumi: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Thatha inombolo 327. Kukho imiqondiso emithathu: 3, 2, 7. Ngamnye wabo uhlala kwindawo yayo Indawo). Ezi sixhenxe zihlala kwindawo egcinwe kwixabiso leyunithi (iiyunithi), iimbini ezimbini, kunye namakhulu amathathu. Ekubeni inani lixabiso elithathu, ngoko ke, kukho izikhundla ezintathu kuphela.

Ngokusekelwe kulo mbandela, inamba elinezididi ezintathu zamanqaku ingachazwa ngale ndlela: ngamakhulu amathathu, amabini amabini kunye neeyunithi eziyisixhenxe. Kwaye ukubaluleka (ukubaluleka) kwezikhundla kubalwa ukusuka kwesobunxele kuya kwesokudla, ukusuka kwindawo ebuthathaka (iyunithi) ukuya kunamandla (amakhulu).

Siziva sikhululekile kwi-system position decimal. Sineminwe eyishumi ezandleni zethu, ngokunjalo. Iintlanu kunye neyintlanu - ngoko, ngenxa yeminwe, sisuka ebuntwaneni sicinga ngokuphindaphindiweyo. Yingakho kulula ukuba abantwana bafunde itafile yokuphindaphinda ngeyesihlanu kunye neyeshumi. Kwaye kulula ukuba ufunde ukubala amanqaku eemali, ezidla ngokuphindaphindiweyo (oko kukuthi, bahlula ngaphandle kweyasala) ngamahlanu kunye neshumi.

Ezinye iinkqubo zokubeka indawo

Ukumangaliswa kwamaninzi, kufuneka kuthiwe kungekuphela kwenkqubo yokugqibela ye-akhawunti yethu ingqondo ijwayele ukwenza izibalo ezithile. Kuze kube ngoku, uluntu lusetyenzise iinkqubo zeenombolo ezili-6 kunye neeshumi elinambini. Okokuthi, kwinkqubo enjalo kunamalungu ayisithandathu kuphela (kwi-hexadecimal): 0, 1, 2, 3, 4, 5. Kwinqanaba leshumi elinesibini kukho ezilishumi elinesibini: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 , A, B, apho A-ichaza inombolo 10, B - inombolo 11 (ekubeni uphawu kufuneka libe linye).

Zigwebe. Sicinga ukuba ixesha lesithandathu, akunjalo? Iyure enye imithandathu imaminithi (ishumi elinesithandathu), olunye usuku luyiiyure ezingama-24 (iihlandlo ezilishumi elinesibini), unyaka iinyanga ezilishumi elinesibini kwaye njalo njalo. Kodwa sisetyenzisiwe ukuba asinakucinga ngokubala ixesha.

Iinkqubo zeenombolo ezingezizo. Engabhalwanga

Kubalulekile ukucacisa ukuba yintoni - inkqubo yeenombolo ezingekho phantsi. Yisistim somqondiso, apho kungekho zikhundla zeempawu zeenombolo, okanye umgaqo "wokufunda" inombolo ukusuka kwisikhundla ayixhomekekanga. Inemithetho yayo yokubhala okanye yokubala.

Sinika imizekelo yeenombolo zeenombolo ezingenalo isikhundla. Masibuyele kumandulo. Abantu babedinga i-akhawunti kwaye beza kunye nokuveliswa okulula - iigununu. Inkqubo engeyiyo yokumiswa yinkqubo ye-nodal. Into enye (isikhwama selayisi, inkunzi, inkunzi ye- hay , njl.) Yabalwa, umzekelo, xa uthengisa okanye uthengisa kwaye ubophe iqhosha kumtya.

Ngenxa yoko, kwintambo kwaphuma amaninzi amaninzi, zingaphi iisayiti zerayisi ezithengiweyo (umzekelo). Kananjalo kungenokuba iincwadana kwintonga yomthi, kwi-slab yamatye, njl. Inkqubo enjalo yokubala iye yaziwa ngokuba yinkqubo ye-nodal. Unalo igama lesibini - unary, okanye elinye ("uno" lithetha "enye" ngesiLatini).

Kuyacaca ukuba le nkqubo yeenombolo ayikho imeko. Emva koko, zeziphi iimeko apho kunokuthi (isikhundla) sinye kuphela! Okumangalisayo kukuba, kwezinye iindawo zomhlaba kusekho inkqubo yeenombolo ezingabonakaliyo kwinombolo kwenkqubo.

Kwaye nakwiinkqubo ezingezizo zokubeka indawo:

• AmaRoma (ngokubhalwa kwamanani asebenzise iileta - iimpawu zesiLatini);
• UmYiputa waseMandulo (ofana nomRoma, naye wasebenzisa iimpawu);
• I-Alphabetic (ii-letters ze-alfabhethi zisetyenzisiweyo);
• IBhabhiloni (i-cuneiform - isetyenziswe "iqhosha" elichanekileyo nelingenanto);
• IsiGrike (esabizwa ngokuba yi-alfabhethi).

Inkqubo yamaRoma

Ubukumkani baseRoma bamandulo, kunye nesayensi yayo, yayihamba phambili. AmaRoma anika ihlabathi ezininzi izinto ezinobuncedo zenzululwazi nobugcisa, kuquka inkqubo yabo ye-akhawunti. Kwiminyaka emakhulu mabini edlulileyo, iinombolo zamaRoma zazisetyenziselwa ukubhekisela kwiimali zamaphepha-shishini (oko kukuphepha ukucima).

Ukubala kwenani lomRoma ngumzekelo wenkqubo ye-non-position number, kwaziwa kuthi ngoku. Kwakhona inkqubo yaseRoma iyasetyenziswa ngokuthe tye, kodwa kungekhona ekubalweni kwemathematika, kodwa ngenxa yezenzo ezicetywayo. Ngokomzekelo, ngoncedo lweenombolo zamaRoma kuyisiko lokukhetha imbali yamandulo, iminyaka, imiqulu, amacandelo kunye nesahluko kwimiqulu yeencwadi. Ngokuqhelekileyo basebenzisa imiqondiso yaseRoma ukuze bahobise idial of watch. Kwaye kunye nenani lamaRoma ngumzekelo wenkqubo ye-non-positioning system.

AmaRoma ayichaza amanani kwiileta zesiLatini. Kwaye manani abhala phantsi ngemithetho ethile. Kukho uluhlu lweempawu eziphambili kwinkqubo yesibalo samaRoma, ngoncedo lwabo bonke amanani abhalwe ngaphandle ngaphandle.

Imigaqo yokuhlanganisa amanani

Inombolo efunyenweyo yafunyanwa ngokungeza iimpawu (iilatini zesiLatin) nokubala isamba sabo. Cinga indlela iimpawu kwiinkqubo zaseRoma zibhalwa ngendlela engokomfanekiso nendlela 'yokuzifunda' ngayo. Makhe sibhale imithetho esemiselweyo yokubunjwa kwamanani kwi-system ye-Roman non-position number system.

1. Inani eline-IV, liqukethe impawu ezimbini (I, V - enye kunye nohlanu). Ifunyenwe ngokukhupha umqondiso omncinci ukususela kumkhulu xa kukho ngakwesobunxele. Xa ibonakaliso encinci lifumaneka ngakwesokudla, kuyimfuneko yokongeza, ngoko kuya kufumaneka inani le-VI.
2. Kubalulekile ukongeza ezimbini iimpawu ezifanayo zimi caleni. Umzekelo: CC i-200 (C-100), okanye i-XX-20.
3. Ukuba umlingisi wokuqala wenani ungaphantsi kweyesibini, kwaye okwesithathu kulolu chungechunge lunokuba ngumqondiso onenani lakhe lingaphantsi kweyokuqala. Ukuze sidideke, makhe sinike umzekelo: CDX-410 (ekudeni).
4. Ezinye iinombolo ezinkulu zinokumelwa ngezindlela ezininzi, enye yezinto ezingenakwenzeka kwi-akhawunti yeRoma. Nazi ezinye izibonelo: I-MVM (inkqubo yamaRoma) = 1000 + (1000 - 5) = 1995 (inkqubo yeshumi) okanye i-MDVD = 1000 + 500 + (500 - 5) = 1995. Ayezona zonke iindlela.

Izindlela ze-arithmetic

I-system ye-non-positioning system ngezinye iinkqubo yinkqubo edibeneyo yokusekwa kwamanani, ukucwangciswa kwazo (izenzo kuzo). Imisebenzi ye-Arithmetic kwiisistim zeenombolo ezingenalo isikhundla akulula kubantu banamhlanje. Ungabi nomona ngabafundi beMathematika basendulo bamaRoma!

Umzekelo wokongeza. Masizame ukongeza amanani amabini: XIX + XXVI = XXXV, lo msebenzi wenziwa ngezenzo ezimbini:

1. Okokuqala, sithatha kwaye songeza amancinci amanani amanani: IX + VI = XV (mna emva kweV kwaye mna phambi kwe X "sitshabalalisa" omnye).
2. Okwesibini, songeza iinqhezu ezinkulu zamanani amabini: X + XX = XXX.

Ukukhupha kunzima kakhulu. Inombolo ecetywayo kufuneka iphulwe ibe yizinto ezidibeneyo, kwaye emva koko, iimpawu eziphindiweyo ezincitshisiwe kunye nezithintekayo kufuneka zinciphise. Kususela kwinani le-500 sithatha i-263:

D - CCLXIII = CCCCLXXXXVIIIII - CCLXIII = CCXXXVII.

Ukuphindaphinda kwamanani aseRoma. Ngendlela, kuyimfuneko ukukhankanya ukuba amaRoma ayengenayo imiqondiso yemisebenzi ye-arithmetic, bawachazela ngamagama.

Ukuphindaphinda ukuphindaphinda kwakudingeka kwisimboli ngasinye ngabanye abaphindaphindiweyo, okubangelwa kwimisebenzi embalwa eyayidinga ukudibaniswa. Ngale ndlela, ukuphindaphinda kwamapolynomials kwenziwa.

Ngokuphathelele ukwahlula, le nkqubo kwinkqubo yesibalo samaRoma ibe kwaye ihlala ingqongqo. Apha wasebenzisa i-abacus yamaRoma yamandulo - i-abacus. Ukusebenza kunye naye, abantu baqeqeshelwa ngokukhethekileyo (kwaye akuwona wonke umntu okwazi ukuqonda loo nzu lulwazi).

Kwizinto ezingalunganga zeenkqubo ezingekho phantsi kweendawo

Njengoko kuchazwe ngasentla, kwiinkqubo ezingenabani-nqanaba zikhona izinto ezingenakulungeleka, ukuphazamiseka kokusetyenziswa. Unary isilula ngokwaneleyo ukubala ngokulula, kodwa akufanelekanga kwizibalo ze-arithmetic neziyinkimbinkimbi kuzo zonke.

KwiRoma akukho mithetho ifanayo yokubunjwa kwamanani amakhulu kunye nokudideka, kwaye kunzima ukwenza izibalo kuyo. Ukongezelela, inani elikhulu amaRoma asendulo angayibhalela ngoncedo lwenkqubo yawo yayingu-100,000.