Chizvidavirire hurongwa. Table kukarukureta hurongwa. Base: Informatics

Vanhu havafaniri kudzidza kuverenga. Chinyakare nzanga yaitungamirirwa vashoma nyaya - mumwe kana vaviri. Zvose zvakanga zvakawanda maererano default zita "yakawanda." Zvinonzi vaiona kutanga ano chizvidavirire hurongwa.

Brief Historical Background

Mukuita yebudiriro, vanhu vakatanga kuonekwa kudiwa kugoverana chiduku muunganidzwa zvinhu, vakabatanidzwa zvakafanana zvinhu. Rotanga chokuita pfungwa: "vatatu", "mana" uye zvichingodaro kusvika "nomwe". Zvisinei, raiva rakavharwa, kuduku series, ekupedzisira pfungwa iyo ichiri kubereka zvinorehwa kwokutanga "yakawanda." Muenzaniso unoshamisa iyi ngano, vaburukira kwatiri yaro yepakutanga chimiro (somuenzaniso, achiti "Unoyera kaviri - cheka kamwe").

The chidzoke muchina nzira azvidavirire

With upenyu uye vose dzinotsanagura basa evanhu kuwedzera kunzwisisa pamusoro nguva. Izvi zvakatungamirira, uyewo, kuti chidzoke ane zvikuru kunzwisisa hurongwa kukarukureta. Panguva iyoyowo vanhu vakashandisa nokuda Kujeka mashoko nyore invoicing chokushandisa. Havana kudziwana kumativi: vakasundidzira chimuti riri bako pamadziro pamwe kugadzirwa rinoreva, kuita notch, akaisa ruoko chinofadza nhamba yavo netsvimbo uye matombo - izvi zvinongova chiduku mazita raivapo panguva iyoyo kusiyana. Mune ramangwana, kwakadai nyanzvi ano akapiwa rakasiyana zita "unary hurongwa kukarukureta." Chaizvoizvo Its kunoratidzwa kurekodha vachishandisa kuroorwa vatambi mhando. Nhasi ndiro zvikuru yokuita maitiro unokubvumira nemaziso enzanisa uwandu zvinhu uye vatambi. The kushandiswa dzakawanda akagamuchira muzvikoro zvepuraimari (tichiverenga zvimiti). Legacy "Kameshkovo nhoroondo" unogona zvakanaka kufunga kuti michina yemazuva avo okunatsiridza siyana. Interesting uye ano pakuonekwa mashoko "yera", vane midzi dzinobva rechiLatin calculus, zvisingagone kushandurwa chete se "dombo".

Chibozwa pamusoro nemimwe

Patinosangana shomanana zvikuru mashoko ose chinyakare murume nemasaini kazhinji aishanda rinokosha mukwanisi ruzivo zvitange. Kunakisa minwe vaiva munyika yose dzavo uye vari kugara kuwana chinhu kuti vangada kutaura mashoko. Zvisinei, pane zvinokosha zvainovhiringidzawo: zvinokosha zvausingakwanisi uye pfupi ya nokupfuuridzirwa. Naizvozvo, rose mari vanhu vakanga akashandisa "munwe nzira" dzisina zvinove multiples mukuwanda minwe 5 - anoenderana nenhamba nezvigunwe paruoko rumwe; 10 - maoko maviri; 20 - The uwandu maoko nemakumbo. Nokuda pfupi kunonoka kukura kusanganiswa kuchengeterwa ino yakatora nguva refu zvakakwana nguva.

kuvandudzika okutanga

With kukura ezvinhu kukarukureta uye kuwedzera mikana uye zvinodiwa vanhu vaishandisa kunonyanyisa nhamba iri tsika pamarudzi mazhinji akanga 40. Below zvakanga ainzwisisawo nokusingaperi (kwete kupa nhoroondo) nhamba. MuRussia, kwakapararira okuti "mana nguva mana". Zvaaireva aihuitira nokuwanda zvinhu zvisingagoni dzaona. Inotevera Danho okukura - ndiwo pakuonekwa nhamba 100. akabva atanga weboka kupinda vakawanda. Naizvozvo akatanga kuonekwa pamusoro 1000, 10000 uye zvichingodaro, chimwe nechimwe vakatakura rinoreva zvakafanana vanomwe uye mana. Munyika yemazuva pakupedzisira miganhu vasiri kunorondedzerwa. Today akasuma zvakasikwa yokuti "kusaverengeka".

Integers uye zvikamu zviduku

Modern chizvidavirire marongedzero mudukusa uwandu nyaya kutora chimwe. Kazhinji hazvisi indivisible ukoshi. Zvisinei, kupfuura yakarurama kuyerwa, uyewo wapera. Hwakabatana nayo akazviratidza imwe padanho yepfungwa ose fractional nhamba. Somuenzaniso, Bhabheri gadziriro mari (pachiyero) raiva 60 Maminitsi, chakanga 1 Talanov. Uyewo, 1 wangu akanga akaenzana mashekeri 60. Zviri maererano eBhabhironi masvomhu zvikuru kuiswa sexagesimal unorema. Zvinowanzoshandiswa Russia bara vakauya kwatiri kubva vaGiriki vekare uye maIndia. Panyaya iyi, zvinyorwa pachavo vari akafanana kune Indian. The zvishomanana musiyano iri kusavapo ekupedzisira sitiroko. VaGiriki ushandiswe kubva kumusoro numerator uye dhinomineta pazasi. Indian chiperengo zvikamu zviduku akagamuchira zvakawanda kukura muAsia uye Europe nekuvongwa masayendisiti maviri: Mohammed Khorezm uye Leonardo Fibonacci. Roman kukarukureta hurongwa equaled zviumbu 12 akadana Ounces, rose (1 dhongi), ukuwo, mune Masvomhu vose yakavakirwa duodecimal hacho. Pamwechete mureza aiwanzoshandisa uye chinokosha kupesana. Somuenzaniso, nyanzvi kusvikira XVII remakore, vakashandisa anonzi sexagesimal zvikamu zviduku, vakazochinja vakanga kwaidarika ne grade (sezvaari Simon Stevin - musayendisiti uye injiniya). kwaidiwa kuti mamwe zvinokosha kuwedzera nhamba dzinotevedzana Somugumisiro kufambira mberi kwevanhu. Saka pakanga kunaka, musoro uye kunzwisisa nhamba. Avanoziva zvose razero achiri ichangopfuura. Akatanga kushandiswa munhanganyaya hwemazuva ezvinhu pakuverenga kunaka nhamba.

Kushandisa nepozitsionnyh arufabheti

Chii chinonzi arufabheti? Nokuti ichi kukarukureta maitiro tsika hazvichinji kukosha nhamba kubva placement yavo. Nepozitsionnyh arufabheti vanowanzotevedzera kuvapo risingaperi nhamba zvinhu. In Pakuurayiwa hurongwa zvakavakwa nemhaka iyi mhando nearufabheti, kwakavakirwa nheyo additivity. Nemamwe mashoko, zvachose kukosha nhamba pakuverengwa ose nhamba zvinosanganisira yakarekodwa. Chiitiko nepozitsionnyh hurongwa chakaitika kwokutanga chinzvimbo. Zvichienderana nzira yekuverenga zvachose kukosha nhamba rinorondedzerwa so musiyano kana Verengai vose digits kuitika nhamba.

Kune zvazvakashatira vakadaro gadziriro. inofanira dzinounzwa pakati zvihombe:

• Sumo nhamba itsva paumbwe vazhinji;
• nekusagona kuratidza kunaka uye fractional nhamba;
• kuoma kuita svomhu kwacho.

siyana kukarukureta hurongwa zvinoshandiswa munhoroondo yevanhu. Zvakanakisisa kuvazivisa ndiwo: Greek, Roman, arufabheti, unary, veIjipiti yekare, yeBhabhironi.

Imwe rakajairika nzira vazvidavirire

sezviverengo Roman, akachengetedzwa nhasi anenge kuchinja, mumwe kupfuura vakakurumbira. Achibatsirwa vake vakasarudzwa yemichindwe siyana, okupemberera uyewo. rinoshandiswawo chaizvo mabhuku, sayenzi uye zvimwe zvinhu zvoupenyu. The Hurongwa weRoma kukarukureta yaishandiswa nomwe chete tsamba earufabheti Latin, chimwe nechimwe unoenderana imwe nhamba: I = 1; V = 5; X = 10; L = 50; = 100 C; D = 500; M = 1000.

chidzoke

Mabviro sezviverengo yeRoma haisi pachena, nyaya haachengeti mashoko yakarurama chitarisiko chavo. Kana chokwadi ichi hazvirambiki: chinokosha kukanganisa yeRoma vakaverengwa hurongwa kukarukureta aiva kashanu nhamba. Zvisinei, muna Latin hamutaurwi payo. On hwaro ichi, mumwe pfungwa pamusoro nokukwereta ekare Romans Gadziriro yavo nevamwe vanhu (anofungidzirwa, kubva Etruscans).

Features

Record integers zvose (5000) rinoitwa nokudzokorora-pamusoro apa nhamba. Chinokosha ndiko nzvimbo kwezviratidzo:

• Kuwedzera kunoitika chete proviso kuti zvakawanda anomira pamberi yakaderera (XI = 11);
• kubvisa chinoitika kana munhu duku riri kusangana mukuru (IX = 9);
• chete chiratidzo angasava kanopfuura katatu mumutsetse (semuenzaniso, MS 90 yakanyorwa pachinzvimbo LXXXX).

Zvakaipira ndiro kuzvuzvungudza kuita svomhu kwacho. Muchiitiko chino, akazosvika zvikuru nguva vakarega kushandiswa muEurope sezvo kumboenda kukarukureta gadziriro tichishandisa yapfuura - muna 16 remakore fung.

Ezvinhu kukarukureta Roman hakunganzi zvachose nonpositional. Izvi imhaka yokuti mune zvimwe zviitiko, kubvisa ndepana mukuru kwazvo (semuenzaniso, IX = 9).

Nzira nhoroondo muIjipiti yekare

Chiuru chemakore chechitatu BC ichaongororwa kuva nguva panowanikwa Gadziriro kukarukureta muIjipiti yekare. Chaizvoizvo Its une iri rinokosha kurekodha mavanga nhamba 1, 10, 102, 104, 105, 106, 107. All dzimwe nhamba akanyorwa sezvo ibatanidzo pakutanga mashoko zviratidzo. Panguva iyoyowo, paiva zvatisingakwanisi - mumwe mufananidzo rinofanira kudzokororwa hakuna kupfuura kapfumbamwe. Hwaro nzira iyi kuverengwa, izvo nyanzvi ano vanodana "nepozitsionnyh grade mamiriro kukarukureta", uri nyore musimboti. Zvarinoreva iri yokuti nhamba zvakanyorwa vakaenzana uwandu digits zvose icho rinoumbwa.

Unary nzira kuverengwa

Base umo imwe hunhu inoshandiswa kurekodha nhamba - I - inonzi unary. tevera nhamba Mumwe inotengwa nokuwedzera kuti yapfuura itsva I. Kuwanda I akaenzana ukoshi chakanyorwa achivashandisa.

Octal Number System

nzira iyi kuverengwa chinzvimbo, riri mujinga nhamba 8. Kuti digital kuratidzira nhamba siyana 0 kusvika 7. akasiyana kushandiswa ino yave kugadzirwa uye kushandiswa digitaalinen mano. chikuru mukana Its ndiyo shanduro nyore nenhamba. Vanokwanisa kutendeuka kuva binary maitiro ndiEzekieri. manipulations aya kuitwa kutsiva nhamba. Kubva octal mamiriro dzikwanise binary vatatu (semuenzaniso, 28 = 0102, 68 = 1102). Nzira iyi Nhoroondo zvaizoparadzirwa mumunda mapurogiramu ekombiyuta uye kugadzirwa.

Hexadecimal kukarukureta

Recently mumunda kombiyuta, nzira iyi nhoroondo kushandiswa nokushingaira. Munyika ino mudzi nechigadziko - 16. Base, kunobva payo, ndiko kushandisa nhamba kubva 0 kusvika 9 uye uwandu earufabheti (A kuna F), izvo rinoshandiswa kureva penguva kubva 1010 kusvika 1510. nzira iri kuverenga se kare ambotaurwa, rinoshandiswa kweShanduro Software uye mapepa chokuita makombiyuta uye yenhengo dzavo. Inobva ehupfumi imwe kombiyuta yemazuva ano, zvinokosha chairema kuri 8-ikakuruma ndangariro. Zviri nyore kuti exchange uye kunyora vaviri hexadecimal digits. Muvambi izvi raiva IBM / 360 hurongwa. Documentation nokuti pakutanga rinoshandurwa nenzira iyi. Unicode mureza anopa panopindwa chero chimiro mu hexadecimal muchimiro kushandisa zvinenge 4 digits.

kutsikisa Nzira

The kwemasvomhu Pfungwa yacho nzira inobva nhoroondo iwe zvakanyatsonanga panzvimbo dzakaderera indekisi iri grade ino. Somuenzaniso, nhamba 1444 zvakanyorwa sezvo 144410. zvirongwa mitauro kunyora hexadecimal hurongwa vane syntaxes dzakasiyana:

• muna C uye Java mitauro vanoshandisa chivakashure "0x";
• mureza inotevera rinoshandisirwa muna Ada uye VHDL - "1516 # 5A3 #";
• assemblers dzinosanganisira kushandiswa tsamba "H", iro anoiswa mushure nhamba ( "6A2h") kana chivakashure "$", iro kwese kuti AT & T, Motorola, Pascal ( "$ 6B2");
• rakawanawo kupinda mhando "# 6A2", mubatanidzwa "& H", iro anoiswa pamberi nhamba ( "& h5A3") uye vamwe.

mhedziso

Sezvatinodzidza kwegadziriro kukarukureta? Computing - chikuru chirango mukati iyo umbowo kuwanda, muitiro kwokunyoreswa kwavo chimiro dzinokodzera mutengi. Nokushandiswa dzinokosha zvishandiso kuitika magadzirirwo shanduro mashoko ose anowanika mumutauro zvirongwa. Gare gare kushandiswa paaisika Software uye kombiyuta mapepa. Nokudzidza dzakasiyana hurongwa kukarukureta, kombiyuta sainzi kunosanganisira kushandiswa, sezvo pamusoro apa, nhumbi dzakasiyana. Vazhinji vavo kubatsira Implementation ari nokukurumidza kutapurirana nhamba. Mumwe "maturusi" izvi ndizvo tafura kukarukureta enyika. Chishandisei zvikuru zvakanaka. Kushandisa matafura izvi zvinogona Somuenzaniso, kuti nokukurumidza uchatamisa kubva hexadecimal nhamba kuti binary, pasina tinazvo zivo chaiwo yesayenzi. Nhasi, mukana kuita digitaalinen kutendeuka anenge munhu wose anofarira munhu uyu, nokuti zvakafanira zvokushandisa zvinowanikwa vanoshandisa pachena zvinhu. Uyezve, pane paIndaneti zvirongwa rokushandura. Izvi nyore zvikuru basa rokutendeutsa nhamba uye kunoderedza kushanda.