Isistimu yenombolo yesimiso: isisekelo, izibonelo kanye nokuhunyushwa kwezinye izinhlelo zamanani

Kusukela ngomzuzu lapho umuntu eqala ukuzibona njengento yokuzimela emhlabeni, wabheka nxazonke, ephazamisa umjikelezo ononya wokuphila okungenangqondo, waqala ukutadisha. Ngangibuka, ngiqhathanisa, ngibalwa, ngenza iziphetho. Kulezi zenzo ezibonakala ziyisisekelo, manje ezisebusweni kanye nengane, yaqala ukwakha isayensi yanamuhla.

Sizosebenza ngani?

Okokuqala, kuyadingeka ukunquma ukuthi yiyiphi inqubo yenombolo evamile. Lena isimiso esinemibandela yezinombolo zokubhala, ukubonakaliswa kwazo okubukwayo, okwenza kube lula ukucubungula. Kuzo, izinombolo azikho (ake uPythagoras asithethelele, obona ukuthi inombolo iyisisekelo somhlaba wonke). Lokhu kuyinto nje engabonakali, enokulungiswa ngokomzimba kuphela ekubalweni, uhlobo lwesilinganiso. Izinombolo yizinto okuvela kuzo inombolo.

Qala

I-akhawunti yokuqala eyaziwayo yayingokwemvelo kakhulu. Manje ibizwa ngokuthi uhlelo lwezinombolo okungewona isikhundla. Ngokwenzayo, kuyinombolo lapho isikhundla sezinto zayo ezibalulekile kungabalulekile. Thatha, isibonelo, ama-dashes avamile, ngalinye elihambisana nento ethize: abantu abathathu bayalingana |||. Noma ngabe yini ongayisho, ama-dashes amathathu ayizinhlanzi ezintathu ezifanayo. Uma sithatha izibonelo eziningi ezifanayo, ama-Novgorodians asendulo asebenzisa amagama alandelayo eSlavic uma ebala. Uma kunesidingo ukukhetha inombolo ngenhla yocingo, maneka nje ~. Futhi, uhlelo lwezinombolo ze- alfabeti lwaluthandwa kumaRoma asendulo, lapho izinombolo ziphinde zibe khona izincwadi, kodwa ziyizinhlamvu zamaLatini.

Ngenxa yokuhlukaniswa kwamandla asendulo, ngamunye wabo wazakhela isayensi eyedwa, obani obuningi. Okuphawulekayo ukuthi enye inqubo yesimiso sedayimali yenziwa amaGibhithe. Kodwa-ke, "isihlobo" somqondo esiwajwayele asikwazi ukucatshangwa, ngoba isimiso sokubala sasiluhluke: izakhamuzi zaseGibhithe zasebenzisa inombolo eyishumi njengesisekelo, esebenza nge degrees.

Ngentuthuko kanye nezinkinga zenqubo yokuqashelwa kwezwe, kwakukhona isidingo sokunikeza ukukhishwa. Cabanga ukuthi udinga ngandlela-thile uqophe amandla ebutho lombuso, elilinganiselwa ezinkulungwaneni (okungcono kakhulu). Yini manje, bhala ngokungapheli umjikelezi? Ngenxa yalokho ososayensi baseSumeriya balawo minyaka bahlukanisa uhlelo lwenombolo, lapho indawo yesimboli yayingenxa yezinga layo. Futhi, isibonelo: izinombolo ezingu-789 no-987 zinokuthi "ukuhlanganiswa" okufanayo, kodwa, ngenxa yokushintsha kokuhlelwa kwamadijithi, okwesibili kunkulu kakhulu.

Iyini uhlelo lokubala lwenombolo yedesimali? Ukulungiswa

Yiqiniso, ukuziphatha nokuhlala njalo kwakungavumelani kuzo zonke izindlela zokubala. Isibonelo, eBabiloni inani lalingu-60, eGrisi - uhlelo lwezinhlamvu zamagama (inombolo yayiyizinhlamvu). Kuyaphawuleka ukuthi indlela yokubala izakhamuzi zaseBabiloni iphila kuze kube yilolu suku - ithole indawo yayo in astronomy.

Kodwa-ke, leyo isisekelo sesistimu yenombolo eyishumi ihlezi phansi futhi isakazeka, njengoba kuhambisana ngokuqondile neminwe yezandla zomuntu. Zahlulela ngokwakho - ngokunye ukuguqa iminwe yakho, ungabala esetheni esingapheli.

Ukuqala kwalesi simiso kwafakwa eNdiya, futhi kubonakala ngokushesha ngesisekelo se "10". Ukwakhiwa kwamagama ezinomboro kwakunezinhlangothi ezimbili - isibonelo, 18 kungabhalwa ngegama futhi ngokuthi "ayishumi nesishiyagalolunye", futhi "ngaphandle kokubili kwamashumi amabili." Kwakungokuthi ososayensi baseNdiya abanikeza umqondo onjengokuthi "zero", ukubonakala kwayo ngokusemthethweni kwakuhlelwe ngekhulu le-IX. Lesi yisinyathelo esasisisekelo ekubunjweni kwezinhlelo zezinombolo ze-classic positional, ngoba zero, naphezu okufanekisela ukungabi nalutho, akukho lutho, ukwazi ukugcina amandla amanani wenombolo, ukuze ingaphumeleli incazelo yayo. Isibonelo: I-100000 no-1. Inombolo yokuqala ihlanganisa amadijithi ayisithupha, owokuqala kuyiyunithi, kanti amahlanu okugcina abonisa ukungabi nabulungisa, ukungabikho, kanye nenombolo yesibili imane nje iyunithi. Ngokusobala, kufanele balingane, kodwa ngokwenza lokhu akude neze. Ama-Zero ku-100000 akhomba ukutholakala kwalawo makhakha, okwenziwe inombolo yesibili. Lapha kuwe futhi "akukho".

Isimanje

Isistimu yenombolo yedasimali inezinombolo kusuka ku-zero kuya ku-9. Izinombolo ezihlanganiswe ngohlaka lwazo zakhiwe kule mithetho elandelayo:

Idijithali eliqondile likhomba amayunithi, shiya isinyathelo esisodwa kwesobunxele - thola inqwaba, isinyathelo esisodwa ngaphezulu kwesobunxele - amakhulu namakhulu njalo njalo. Ingabe kunzima? Ayikho into enjalo! Eqinisweni, izibonelo zesimiso sesimiso sedayimali zingahlinzeka ngokubukwa kakhulu, kuthathe okungenani inombolo 666. Iqukethe amadijithi ayisithupha, ngayinye ekhombisa isikhundla sayo. Futhi le fomu yokurekhoda iyanqamuka. Uma ufuna ukugcizelela ukuthi yiluphi uhlobo lwenombolo, ungayisebenzisa, unikeze ifomu ebhaliwe ukuthi yiliphi izwi lakho langaphakathi "elikhuluma" njalo uma ubona inombolo - "amakhulu ayisithupha namashumi ayisithupha nesithupha." Umbhalo ngokwayo uhlanganisa wonke amayunithi afanayo, amashumi namakhulu, okungukuthi, idijithi ngayinye yesikhundla yanda ngamandla athile ka- 10. Ifomu elivezwe yilona nkulumo elandelayo:

666 ₁₀ = 6х10 ² + 6 * 10 ¹ + 6 * 10 ⁰ = 600 + 60 + 6.

Izindlela ezingezansi zezingqikithi

Esesibili ethandwa kakhulu ngemuva kwenqubo yesimiso sedasimali inguqulo enhle kakhulu - kanambambili (kanambambili). Wabonakala ngenxa ye-Leibniz yonke indawo, owayekholelwa ukuthi ezimweni ezinzima kakhulu, ekutadisheni inkolelo yezinombolo, ubunikazi bekungaba lula kakhulu kunamadayimenti. Ukusabalalisa okusabalalisiwe, kwamukelwe ngokuthuthukiswa kobuchwepheshe bedijithali, ngoba kunombalo wesibili esisekelweni, futhi izakhi kuwo zakhiwa ngamadijithi 1 no-2. Ukwaziswa ngekhodi kwenzeka kulesi simiso, kusukela 1 - ukuba khona kwesignali, 0 - ukungabi khona kwayo. Ngesisekelo salesi simiso, izibonelo eziningana ezibonisa ukuthi ukuguqulwa kwesistimu yenombolo yedesimali kungaboniswa.

Ngokuhamba kwesikhathi, izinqubo ezihlotshaniswa nezinhlelo zaba yinkimbinkimbi, ngakho-ke zafaka izindlela zokubhala izinombolo ezine-8 no-16 ezansi. Kungani kunjalo? Okokuqala, inani labalingiswa likhulu, okusho ukuthi inombolo ngokwayo iyoba mfushane, futhi okwesibili, isisekelo salokhu amandla amabili. Uhlelo lwe-octal luqukethe amadijithi 0-7, kanti i-hexadecimal yizinombolo ezifanayo njengedayimali, kanye nezinhlamvu A kuya ku-F.

Izimiso nezindlela zokuhumusha kwenombolo

Ukuhumusha kusistimu yenombolo yedesimali umane nje, kwanele ukunamathela kumgomo olandelayo: inombolo yokuqala ibhaliwe njenge-polynomial, equkethe inani lemikhiqizo yenombolo ngayinye ngesisekelo se- "2", ephakanyiswe kwidijithi yedijithi ehambelanayo.

Ifomula eyisisekelo yekhompyutha:

_X2 = y _k 2 ^k-1 + y _k-1 2 ^k-2 + y _k-2 2 ^k-3 + ... + y ₂ 2 ¹ + y ₁ 2 ⁰ .

Izibonelo zokuhumusha

Ukuze ulungise, cabangela izinkulumo eziningana:

(1x2) + (1x2 ³ ) + (1x2 ² ) + (1x2 ¹ ) + (1x2 ⁰ ) = 32 + 8 + 4 + 2 + 1 = 47 ₁₀ .

Siyinkimbinkimbi inkinga, ngoba uhlelo luhlanganisa ukuhunyushwa kwezinombolo eziyingqayizivele, ngoba lokhu sicabangela ngokwehlukana ingxenye ephelele kanye nengxenye ehlukaniswe ngokwehlukana - 111110,11 _2. Ngakho:

(1x2) + (1x2) + (1x2 ¹ ) + (0x2 ⁰ ) = 32 + 16 + 8 + 4 + 2 = 62 ₁₀ ;

11 ₂ = 2 ^-1 x1 + 2 ^-2 x1 = 1/2 + 1/4 = 0.75 _10.

Ngenxa yalokho, sithola lokho 111110,11 ₂ = 62.75 ₁₀ .

Isiphetho

Naphezu kwazo zonke "zesikhathi esidlule", uhlelo lokubala lwenombolo yedesimali, izibonelo esasizicabangele ngenhla, zisase "zihamba ngehhashi", futhi akufanelekile ukuyivala. Nguye oba isisekelo sematheksthi esikoleni, ngesibonelo sakhe imithetho yemigomo yematheksthi ifundwa, ikhono lokwakha ubudlelwane obuhlanganisiwe lithathwe. Kodwa yikuphi ngempela lapho - cishe wonke umhlaba usebenzisa lolu hlelo oluthile, ungabi namahloni ngenxa yokungaphumeleli kwalo. Isizathu salokhu sinye: kuyinto elula. Ngokuyisisekelo, ungathatha isisekelo se-akhawunti, kuyoba i-apula, uma kunesidingo, kodwa kungani kuyinkimbinkimbi? Inombolo eqinisekisiwe yenombolo yamadijithali ingabalelwa uma kunesidingo nangeminwe.