Shanduro kubva kumabhinari kusvika kuwedzerwa iri nyore

Mutsara wekuti zvinhu zvose zvitsva hazvisi chinhu asi yakakwegura zvakakanganwa, zvinoreva zvakakwana kubhenari yenhamba yenhamba. Zvinotarisa kuti kunyange muChina yekare yakashandisa chimwe chinhu chinotiyeuchidza nezve "imwe-pfungwa-kwete-copi," chokwadi hachisi chemashoko, asi kunyora magwaro ebhuku reZvirevo. Vaya vainge vava pedyo neku kunzwisisa maitiro ehuwandu ehuwandu vaiva maInas: vakashandisa zvose zviri zviviri uye mabhanari masangano, kunyange zvazvo yekupedzisira kwaingova kwemashoko uye ezvo zvakanyorwa. Zvinogona kufungidzirwa kuti kunyange zvakadaro, makore zviuru zvina apfuura, Incas yaiziva nzira yekushandura kubva kubhinari kusvika kuwedzerwa.

Nhasi shanduro yemabhanary yakarongedzwa naLeibniz makore anenge 300 akapfuura, uye shure kweimwe zana nemakore nehafu George Buhl akasiyira zita rake mukuyeuka zvizvarwa zvinoshanda pa algebra yemagariro. Binary arithmetic pamwe chete ne algebra ye logic yakave iyo nheyo yezvinogadzirwa zvekombiyuta yezvino. Uye zvinhu zvose zvakatanga muna 1937, apo nzira yekufananidzira kuongorora kwekutora uye kushandura dunhu yakarongwa. Iri basa raClaude Chenon rakava "amai" rekombiyuta yakashandurwa iyo yakaita kubhadhari kuwedzera muna 1937. Uye, zvechokwadi, rimwe remabasa e "sekurukuru" uyu wemakombiyuta ezuva ranhasi raiva shanduro kubva kubhinari kusvika kuwedzerwa.

Zvakatora makore matatu bedzi uye muenzaniso wekutevera we "kombiyuta" yakatumira mitemo ku calculator yenhamba dzakaoma, uchishandisa nhare yefoni uye teletype - zvakanaka, iyo yeInternet yekare inoshanda.

Chii chinonzi binary, decimal, hexadecimal uye, kazhinji kutaura, chero N-ary system? Hungu, hapana chakaoma. Ngatitorei nhamba nhatu nhamba yedu inofarira padhidhiyo, inomiririrwa kushandiswa nevanhu gumi - kubva pa 0 kusvika ku 9 vachifunga nezvekugara kwavo. Ngatitsanangurirei, kuti nhamba dzeiyo nhamba dziri pane zvigaro 0, 1, 2 (mutemo unoenda kubva kudii yekupedzisira kusvika kune yekutanga). Chimwe chezviitiko chinogona kuva nenhamba yehuwandu hwemamiriro acho, asi kukosha kwehamba iyi kunotsanangurirwa kwete nehupenyu hwayo chete, asiwo nechinzvimbo chechigaro. Semuenzaniso, iyo nhamba 365 (zvakakodzera, nzvimbo 0 ndiyo nhamba 5, nzvimbo 1 ndiyo nhamba 6, uye nzvimbo 2 iyo nhamba 3), kukosha kwenhamba iri munzvimbo ye zero ndeye 5, nzvimbo yekutanga ndeye 6 * 10, uye yechipiri - 3 * 10 * 10. Zvinonakidza apa izvo zvinobva pachinzvimbo chekutanga, nhamba ine chinyorwa chinokosha (kubva kune 0 kusvika ku9) uye nheyo yehutano yakaenzana nenhamba yepamusoro, i.e. Tinogona kunyora izvi 345 = 3 * 10 * 10 + 6 * 10 +3 = 3 * 102 + 6 * 101 + 5 * 100.

Mumwe muenzaniso:

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

Sezvaunogona kuona, nzvimbo imwe neimwe nzvimbo ine nhamba inokosha kubva pachigadziro chehurongwa hwakapiwa, uye kuwedzera kubva kune imwe nheyo yehurongwa kwakaenzana nenzvimbo yeiyo inopa nhamba (iyo nhamba yejimi ndiyo nhamba yezviremera, asi +1 kune imwe).

Kubva pane chinangwa chekumiridzirwa kwechiverengero, bhenari yomufananidzo wepuzzles neyo nyore - nhamba mbiri chete mumutambo - 0 uye 1. Asi kunaka kwemasvomhu ndechokuti kunyange mufomu yakakomberedzwa, zvingaratidzika, nhamba dzebhinari dzakakwana uye dzakaenzana neyadzo Zvimwe "vakomana vakuru". Asi unozvifananidza sei, somuenzaniso, neine decimal decimal? Sekusarudza, iwe unofanirwa kuita shanduro kubva kubhinari kusvika kuwedzerwa. Basa racho haringatumidzi kuti rakaoma, asi basa iri rinorwadza rinoda kutarisirwa. Saka, ngatitange.

Kuenderera mberi kubva pane zvakataurwa pamusoro pamusoro pehutano hwekumiridzirwa kwenhamba mune chero hurongwa, uye uchifunga mupfungwa dzakanyanyisa kwavari, bhinari imwe, tinotora humwe hutano hwe "unit-tick-ticks". Dana nhamba iyi VO (muRussia VO), uye edza kutsvaga kuti chii - shanduro kubva kubhinari kusvika kuwedzerwa. Regai ive VO = 11001010010. Pakutanga kuona, nhamba sehamba. Tichaona!

Mutsara wekutanga, tinoronga nhamba yacho pachayo, uye tinonyora nhamba yechipiri sechiyero chechinzvimbo chimwe nechimwe chezvinhu - chidimbu chechipiri (pano chisarudzo chiduku - 0 kana 1) uye nhamba 2 muine simba rakaenzana nenhamba yezviripo mumutambo wed decimal, tinoita shanduro kubva Bhinari kusvika kuwedzerwa. Iye zvino mumutsara wechipiri iwe unongoda kuita zviyero. Kuti ujekeswe, unogonawo kuwedzera chetatu chechitatu nehupamhi hwekuverenga.

VO = 1 1 0 0 1 0 1 0 0 1 0;

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

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

Isu tinoverenga "arithmetic" mumutsara wechitatu uye tine zvatinotarisira: VO = 1618. Zvakanaka, chii chakakosha pamusoro payo? Uye chokwadi chokuti nhamba iyi ndiyo yakakurumbira kupfuura yose iyo inozivikanwa kuvanhu: kuenzana kwemapiramidhi eEgyptia, maGioconda anozivikanwa, manotsi emimhanzi uye muviri wemunhu zvakabatana nayo, asi ... asi nekujekesa zvishoma-kuziva kuti kunofanira kunge kune zvakawanda zvakanaka, hukuru hwake nyaya Tipei nhamba iyi nhamba 1000 zvakapfuura kukosha kwezvino - 1.618. Zvichida, izvo zvose zvakawana. Uye munzira, shanduro kubva pamabhinari kusvika kumiganhu yakabatsirwa kubva pagungwa risingaperi risina maturo "kubata" rinonyanya kunakidza - rinonziwo "goridhe chikamu".