Ukuhumusha kusuka kanambambili idesimali - konke nje

Lamagama ukuthi konke entsha - akulutho like kahle ukhohlwe ubudala, ngokugcwele kusebenza uhlelo kanambambili. It kuvela ukuthi e China lasendulo baye basebenzisa into efana 'ubunye-tac-uzwane "yethu, iqiniso alikho ukuba izibalo, futhi ngokubhala umbhalo encwadini Izinguquko. Esiseduzane ukuqonda inombolo izinhlelo ezahlukene babe Inca: babesebenzisa futhi Nokho, idesimali futhi kanambambili izinhlelo, siphile isikhathi eside kuphela imiyalezo efihlekile. Kunengqondo ukuphetha ngokuthi ngisho ke, izinkulungwane 4. Eminyakeni eminingi edlule, ama-Inca wayekwazi ukwenza ukuhumusha kusuka kanambambili uhlelo ledesimali.

A nothayi banamuhla uhlelo kanambambili kwahlongozwa ngu Leibniz, eminyakeni engaba ngu-kuphela 300 edlule, futhi ngemva kweminyaka engamashumi amahlanu- Dzhordzh Bul kwesokunxele igama lakhe inkumbulo umsebenzi oseza algebra logic. izibalo Binary, kanye algebra logic isisekelo ubuchwepheshe digital samanje. Konke lokhu kwaqala ngo-1937, lapho indlela ukuhlaziywa ufanekisela edluliselwe futhi usuke izifunda kwahlongozwa. Lo msebenzi uClaude Shannon baba 'ngomama' ukuze ikhompyutha edluliselwe wenza kwalokho kanambambili kakade 1937. Futhi-ke, omunye Izinjongo zalolu "ukhokho" lwamakhompyutha yesimanje kuhunyushwe kusuka kanambambili idesimali uhlelo.

Kuthatha kuphela sekuphele iminyaka emithathu, futhi enye model of the edluliselwe "ikhompyutha" ithumela umyalo umshini wokubala izinombolo eziyinkimbinkimbi, usebenzisa umugqa yefoni ye-TTY - kahle, nje-inthanethi ubudala esenzweni.

Yiziphi kanambambili, idesimali,-hexadecimal, futhi, ngokuvamile, noma yiluphi uhlelo N-lekile? Ayikho into elukhuni. Thatha inombolo enamadijithi amathathu-e othandekayo idesimali ohlelweni lwethu, ke umelwe ngamadijithi 10 - 0 kuya 9 ngokuhambisana indawo yabo. Nquma ukuthi inombolo kwamadijithi kukhona at izikhundla 0, 1, 2 (inqubo isuka ngowokuqala idijithi yokugcina). Ngezinye isikhundla ngamunye ungaba iyiphi inombolo amasistimu, kodwa ubukhulu le nombolo akuxhomekile nje kuphela esimweni uphawu lwakhe, kodwa futhi isikhundla indawo. Ngokwesibonelo, i-inombolo 365 (ngokulandelana, nekubeka 0 - sibalo 5, inkomba inani 1 - sibalo 6 futhi isikhundla 2 - sibalo 3) ukubaluleka zero isikhundla - 5 endaweni yokuqala - 6 * 10, kanti eyesibili - 3 * 10 * 10. Kuyinto ukwazi ukuthi, kusukela endaweni yokuqala, kantsi sicuketse loku nabaningi idijithi (0 kuya ku-9) kanye ohlelweni base ngokwezinga elilingana inamba yendawo, okungukuthi kungenziwa ebhaliwe ukuthi 345 = 3 * 10 * 10 + 6 * 10 +3 = 3 * 102 + 6 * 101 + 5 * 100.

Esinye isibonelo:

260974 = 2 * 105 + 6 * 104 + 0 * 103 + 9 * 102 + 7 * 101 + 4 * 100.

Njengoba singabona, indawo ngayinye positional yakhiwa inombolo okunenjongo amaqoqo ohlelweni, kanye Isici isizinda uhlelo e ngezinga elilingana inani elithile izikhundla (Nanku umumo kancane inani izikhundla, kodwa elilodwa ngaphezulu).

Kusukela umbono we ukumelwa wesimo sawo kanambambili onemibuzo ngamagama alula - kuphela 2 kohlelo - 0 ne 1. Kodwa ubuhle wezibalo liwukuthi, ngisho nasezindabeni ifomu ufushanisiwe Nakuba kungase kubonakale kuyisimanga, izinombolo kanambambili amalungelo ngokugcwele futhi alinganayo efanayo, kanye zabo ngaphezulu "nabangane ubude." Kodwa indlela eziqhathanisa, isibonelo, nge inombolo yedesimali? Njengoba inketho, ungenawo ukushesha ukuhunyushwa kanambambili inombolo uhlelo libe idesimali. Inkinga akakwazi ngokuthi kunzima, kodwa lo msebenzi onzima odinga ukunakekelwa. Ngakho ake ngiqale.

Ngokusekelwe kulokhu okungenhla, ku-oda Kutsi tinombolo yiluphi uhlelo, futhi sikhumbula elula kubo - kanambambili, ukuthatha noma yisiphi ukulandelana "yabathembekileyo-tac-uzwane." Lokhu sikubiza inombolo vơ (ngesiRashiya IN), bese uzama ukuthola ukuthi yini ukuthi - elihunyushwe kusuka kanambambili idesimali uhlelo. Makube vơ = 11.001.010.010. Uma uthi nhlá, isibalo isibalo. Ake sibone!

Umugqa wokuqala uqukethe inombolo uqobo ngendlela enwetshiwe, kanti eyesibili ukubhala kanjani inani ngalinye nto efomini zezici - idijithi abalulekile (lapha ukukhetha incane - 0 noma 1) kanye nenani 2 emandleni inombolo positional ohlelweni idesimali, nathi senza ukuhumusha kusuka kanambambili idesimali. Manje, emgqeni wesibili udinga nje ukwenza izibalo. Ngokucaca, silayishe futhi umugqa wesithathu nge izibalo Lesisemkhatsini.

Vơ = 1 1 0 0 1 0 1 0 0 1 0;

Vơ = 1 * 210 + 1 * 29 + 0 * 28 + 0 * 27 + 1 * 26 + 0 * 25 + 1 * 24 + 0 * 23 + 0 * 22 + 1 * 21 + 0 * 20;

Vơ = 1 * 1024 + 1 * 512 + 0 * 256 + 0 * 128 + 1 * 64 + 0 * 32 + 1 * 16 + 0 * 8 + 0 * 4 + 1 * 2 + 0 * 1.

Thina ukubala "izibalo" line yesithathu, futhi sinalo yini sasifuna: vơ = 1618. Ngabe yini okunye mkhulu? Futhi iqiniso lokuthi le nombolo - edume kunazo zonke aziwa abantu: exhunywe inani imibhoshongo baseGibhithe, futhi elalidume Mona Lisa, amanothi omculo kanye nomzimba womuntu, kodwa ... Kodwa nge intuthuko kancane - nazi ukuthi zona lezo ezinhle kufanele kube eningi yakhe soMkhulu kunjalo lokhu kwasinika inombolo yezikhathi 1000 inani lamanje - 1,618. Mhlawumbe, ukuthi zonke izinto zahamba. Futhi ngenhlanhla elihunyushwe kusuka kanambambili idesimali basizwe kusuka kolwandle esingapheliyo izinombolo "catch" the ephawulekayo kunazo - ke ubizwa ngokuthi "golden angle".