Mlandu dongosolo. Table mawerengedwe kachitidwe. Base: Informatics

Anthu osati aphunzira kuwerenga. anthu wosazindikira ankatsogoleredwa ndi ochepa nkhani - imodzi kapena ziwiri. Onse amene anali ndi kusakhulupirika dzina "kwambiri." Amaona chiyambi cha dongosolo ano mlandu.

Mwachidule Chiyambi Chawo

Mu ndondomeko ya chitukuko, anthu kwayamba kuoneka kuti ndi bwino kuuza gulu ka zinthu, ogwirizana ndi mbali wamba. Anayamba uka mfundo zokhudzana: "atatu" "anayi" ndi zina zotero kuti "zisanu ndi ziwiri". Komabe, chatsekedwa, zochepa zino, yotsirizira mfundo zomwe akupitiriza kunyamula tanthauzo la kale "kwambiri." A chitsanzo chapadera cha ichi ndi nthano yatsikira kwa ife mu maonekedwe ake apachiyambi (mwachitsanzo, kunena kuti "Mumati kawiri - kudula kamodzi").

Zikamera wa njira yotha chifukwa

Ndi moyo ndi njira zonse za zochita za anthu kukhala zovuta zambiri pa nthawi. Zimenezi zinachititsa, zinachititsa kuti zikamera a dongosolo zovuta zambiri za mawerengedwe. Pa nthawi yomweyo anthu ntchito chifukwa ndi losavuta kumva za mfundo invoicing chida. Iwo anapeza iwo mozungulira: adakokera ndodo pa makoma phanga ndi njira improvised, kuchita mphako, anaika chidwi chiwerengero chawo timitengo ndi miyala - izi ziri basi yaing'ono mndandanda wa zosiyanasiyana ndiye alipo. M'tsogolo, mtundu wa akatswiri a masiku ano apatsidwa dzina lakuti "unary dongosolo la mawerengedwe." Kwenikweni ake tichipeza mu kujambula ntchito mtundu umodzi wa anthu otchulidwa. Lero ndi dongosolo yabwino kwambiri kuti amalola kuti zowoneka yerekezerani chiwerengero cha zinthu ndi zilembo. Ambiri ntchito analandira ku sukulu zapulaimale (Pachiwerengero timitengo). Legacy "Kameshkovo nkhani" mukhoza bwinobwino amaganiza kuti makina amakono mu zosintha zawo zosiyanasiyana. Chidwi ndi amakono maonekedwe a mawu "Chiyerekezo" amene mizu kubwera ku kakyulasi Latin, amene silingamasuliridwe yekha monga "mwala".

Mphambu pa zala

Mu nkhope ya mawu zochepa kwambiri za manja wosazindikira munthu zambiri anali womuyenerera zofunika pa zomwe opatsirana. The ntchito zala anali padziko lonse awo ndi zonse ndi kupeza chinthu amene angafune popereka mauthenga. Komabe, pali zovuta kwambiri: zofooka kwambiri ndi lalifupi nthawi ya ndimakokedwe. Choncho, mtengo wonse wa anthu amene anagwiritsa ntchito "njira chala" manambala zochepa zimene multiples chiwerengero cha zala 5 - limafanana ndi chiwerengero cha zala pa dzanja limodzi; 10 - pa manja onse; 20 - The chiwerengero cha manja ndi miyendo. Chifukwa chitukuko ndi wozengereza malo n'zosangalatsa kumva dongosolo inatenga nthawi yaitali moti nthawi.

The patsogolo choyamba

Ndi chitukuko cha dongosolo la mawerengedwe ndi kukula kwa mipata ndi zofuna za anthu ntchito nambala pazipita mu zikhalidwe za mitundu yambiri anali 40. Pansipa izo anazindikira kalekale (osati kupereka ndondomeko) chiwerengero. Mu Russia, ambiri akuti "nthawi makumi anai". tanthauzo lake zinali zochepa chiwerengero cha zinthu zimene simungathe kuchita masamu. Siteji yotsatira chitukuko - Maonekedwe a nambala 100. Kenako anayamba kugawikana mu ambirimbiri. Kenako anayamba kuoneka wa 1000, 10000 ndi zina zotero, omwe ankanyamula ofanana ndi asanu ndi anai. Masiku ano pamapeto pake malire si kumatanthauza. Today anayambitsa mfundo chilengedwe "osawerengeka".

Integers ndi tuzigawo twa

Modern mlandu dongosolo la zochepa za nkhani kutenga unit. Nthawi zambiri ndi kufunika indivisible. Komabe, muyeso zolondola kwambiri, komanso ndi wophwanyidwa. Kumakhudzana ndi mmene zimaonekera pa siteji zina za chitukuko ndi maganizo manambala fractional. Mwachitsanzo, Babele dongosolo la ndalama (moyenera) anali 60 Mph, omwe anali 1 Talanov. Nayenso, 1 wanga wofanana masekeli 60. Ndi pamaziko a masamu Babulo ankagwiritsa ntchito sexagesimal onongani. Ankagwiritsa ntchito mu Russia kuwombera anabwera kwa ife kuchokera Agiriki akale ndi Amwenye. Pankhaniyi, mbiri okha zofanana kwa Indian. Kusiyana pang'ono ndi pakalibe sitiroko masika. Agiriki Kwalamulidwa pamwamba pa numerator ndi chimene chachititsa pansipa. Indian kalembedwe tuzigawo twa analandira chitukuko zambiri Asia ndi Ulaya zikomo asayansi awiri: Mohammed Khorezm ndi Leonardo Fibonacci. Roman mawerengedwe dongosolo inde ndipo sipadzakhalanso mayunitsi 12 otchedwa aunsi, kuti lonse (1 bulu), motero, mu kuwerengetsera onse zochokera duodecimal nusu. Pamodzi ndi muyezo kawirikawiri amagwiritsidwa ntchito ndi kugawikana wapadera. Mwachitsanzo, zakuthambo mpaka m'zaka XVII, ntchito otchedwa sexagesimal tuzigawo twa, amene kenako utaposedwa decimal (anayambitsa Simon Stevin - wasayansi ndi injiniya). panali kufunika zina kuwonjezeka yofunika kwambiri mndandanda chiwerengero Chifukwa cha patsogolo pa anthu. Choncho panali zoipa, zopanda chilungamo ndi zovuta manambala. Bwino onse ziro zimakhalanso posachedwapa. Iye anayamba kugwiritsidwa ntchito yoika yamakono ya kuwerengetsa manambala negative.

Ntchito zilembo nepozitsionnyh

Kodi zilembo? Pakuti dongosolo mawerengedwe khalidwe limene sizisintha kufunika kwa manambala kuyambira Kusinthaku awo. Nepozitsionnyh zilembo amakonda kupezeka losaŵerengeka la zinthu. Kumbali ya kachitidwe inamangidwa pa maziko a mtundu wa zilembo lagona pa mfundo za additivity. M'mawu ena, phindu okwana nambala ndi Uwerenge manambala onse womwenso kujambula. Zadzidzidzi nepozitsionnyh machitidwe zinachitika malo kale. Malinga njira kuwerengera phindu okwana chiwerengero amatanthauziridwa kuti kusiyana kapena Uwerenge manambala onse kupanga chiwerengero.

Pali kuipa madongosolo otero. ayenera allocated pakati pa anthu chachikulu:

• oyamba a manambala latsopano mu mapangidwe ambiri;
• kulephera kuonetsa manambala zoipa ndi fractional;
• n'kovuta kuchita ntchito masamu.

machitidwe osiyana mawerengedwe ntchito mbiri ya anthu. The wodziwika ndi: Greek, Roman, zilembo, unary, ku Egypt, Babulo.

Njira imodzi ambiri chifukwa

mawerengero achiroma, anasunga lero pafupifupi zikutsatiridwa, ndi mmodzi wa anthu otchuka kwambiri. Mothandizidwa ndi masiku ake anatchulidwa osiyana, chidzatha liti komanso. nawonso ankagwiritsa ntchito mabuku, sayansi ndi mbali zina za moyo. Kachitidwe ka Chiroma ka mawerengedwe ntchito ndi zilembo zisanu ndi ziwiri zokha za alifabeti Latin, aliyense wa Chofanana nambala inayake: I = 1; V = 5; X = 10; L = 50; = 100 C; D = 500; M = 1000.

zikamera

Magwero a mawerengero achiroma si bwino, nkhani sasunga deta yolondola maonekedwe awo. Pamene mfundo imeneyi wakuti: kukhudzanso dongosolo manambala Roma cha mawerengedwe anali ndi manambala fivefold. Komabe, mu Latin silikukambapo za izo. Pa mfundo imeneyi, kungoganizira za pobwereka Aroma wakale wa kachitidwe kawo anthu ena (mwina, kuchokera Etruscans).

Features

Lembani integers onse (5000) imagwiridwa ndi kubwereza pamwamba ananena kuti manambala. Mbali yaikulu ndi malo Zizindikiro:

• Kuwonjezera amapezeka ndi proviso zambiri waima patsogolo pa apansi (XI = 11);
• wochotsera zimachitika ngati zing'onozing'ono chithunzi chinayang'ana wamkulu (IX = 9);
• chizindikiro chomwecho sangakhale nthawi zoposa zitatu pa mzere (mwachitsanzo, wa MS 90 Zalembedwa m'malo LXXXX).

The sangathe wa ndi anachitazi wochita ntchito masamu. Pankhaniyi, zinatha ndithu nthawi yaitali anasiya ntchito ku Ulaya dongosolo zofunika mawerengedwe ndi posachedwapa - mu 16 m'ma TH.

Kachitidwe ka Chiroma ka mawerengedwe si nonpositional mwamtheradi. Ichi ndi chifukwa chakuti nthawi zina, wochotsera limapezeka pa ochuluka a (mwachitsanzo, IX = 9).

Njira nkhani ku Iguputo

Lachitatu Zakachikwi BC imatengedwa kuti nthawi yatsoka a dongosolo la mawerengedwe ku Egypt. Kwenikweni ake tichipeza mu wapadera zizindikiro kujambula ya manambala 1, 10, 102, 104, 105, 106, 107. Zonse manambala ena olembedwa monga Kuphatikiza zizindikiro choyambirira deta. Pa nthawi yomweyo, panali zofooka - lililonse chithunzi ayenera kubwereza zosaposa kanayi. Chifukwa cha njira imeneyi ochuluka, omwe akatswiri a masiku ano amachitcha "nepozitsionnyh dongosolo decimal wa mawerengedwe", mfundo yosavuta. Tanthauzo kwagona kuti manambala olembedwa liri Uwerenge manambala onse umene analemba.

Unary njira yowerengera

Base imene munthu wina ntchito manambala kujambula - I - otchedwa unary. Nambala iliyonse wotsatira analandira powonjezera kwa I. yapita latsopano chiwerengero cha Ine wofanana ndi mtengo olembedwa kudzera mwa iwo.

Octal Number System

Zimene malo ochuluka, lomwe lili m'munsi mwa chiwerengero 8. kuwonetsera digito a manambala osiyanasiyana monga 0 kuti 7. Kugwiritsa ntchito lonse a dongosolo lino lakhala kupanga ndi kugwiritsa ntchito zipangizo yadigito. mwayi waukulu amamasulira kosavuta kwa manambala. Iwo akhoza n'kukhala ndi dongosolo bayinare ndi mosemphanitsa. mwai akutsatiridwa ndi kuchotsa manambala. Ku dongosolo octal mtima mu atatu bayinare (mwachitsanzo, 28 = 0102, 68 = 1102). Nkhani ili njira anawagawira m'munda wa mapologalamu apakompyuta ndi kupanga.

Hexadecimal mawerengedwe

Posachedwapa m'munda computer, njira iyi nkhani ntchito mwakhama. Mu dongosolo ili muzu m'munsi - 16. Base, zochokera m'mwemo, ndi kugwiritsa ntchito manambala kuyambira 0 9 ndi chiwerengero cha makalata a zilembo (A ku F), amene ntchito potanthauza imeneyi kuchokera 1010 mpaka 1510. Izi powerenga monga tanenera kale, kuti ntchito yopanga mapulogalamu ndi zolembedwa zokhudza makompyuta ndi zigawo zawo. Zachokera katundu wa kompyuta ano, unit zikuluzikulu zomwe ndi 8-bit kukumbukira. Ndi yabwino kutembenuka ndi kulemba ndi manambala awiri hexadecimal. Woyambitsa wa ntchito imeneyi anali IBM / 360 dongosolo. Kumasulira chifukwa loyamba kumasuliridwa mu njira iyi. Unicode muyezo amapereka kulowa khalidwe lililonse mwa mawonekedwe hexadecimal ntchito manambala osachepera 4.

Njira kujambula

Chiphunzitso masamu njira zachokera nkhani musankhe izo mu index m'munsi mwa dongosolo decimal. Mwachitsanzo, chiwerengero 1444 kwalembedwa monga zinenero 144410. mapulogalamu kulemba machitidwe hexadecimal ndi syntaxes osiyana:

• mu C ndi Java zinenero ntchito manambala oyambirira "0x";
• mfundo yotsatirayi umagwiritsidwa ntchito Ada ndi VHDL - "1516 # 5A3 #";
• assemblers idzagwiritsa ntchito kalata "H" omwe aikidwa pambuyo chiwerengero ( "6A2h") kapena manambala oyambirira "$" imene ili lililonse kwa AT & T, LG, Pascal ( "$ 6B2");
• Anapezanso kulowa mtundu "# 6A2", osakaniza "& H", umene amapereka kwa chiwerengero ( "& h5A3") ndi ena.

Pomaliza

Tikamaphunzira dongosolo la mawerengedwe? Kompyuta - chilango zofunika mwa zomwe kudzikundikira deta ndondomeko kulembetsa awo mu mawonekedwe yabwino ogula. Ntchito zipangizo zapadera zikuchitika kapangidwe ndi kumasulira kwa nkhani zonse zimapezeka chinenero mapulogalamu. Iye anagwiritsa ntchito polenga pulogalamu ndi zolembedwa kompyuta. Mwa kuphunzira dongosolo losiyana la mawerengedwe, sayansi kompyuta kumatanthauza ntchito, monga zanenedwa pamwambapa, zida zosiyanasiyana. Ambiri a iwo amathandiza kuti kukhazikitsa kulanda mofulumira manambala. Mmodzi mwa "zida" ndi tebulo kachitidwe mawerengedwe. Ntchito ndithu bwinobwino. Ntchito matebulo awa akhoza Mwachitsanzo, mwamsanga kusamutsa ku hexadecimal nambala kuti bayinare, popanda okhala yeniyeni sayansi. Lero, mwayi kuchita kutembenuka digito ndi pafupifupi aliyense chidwi munthu uyu, chifukwa zida zofunikira zilipo kuti owerenga pamanambala anthu. Komanso, pali Intaneti mapulogalamu yomasulira. Zimenezi zimatithandiza kwambiri ntchito manambala akatembenuka ndipo kumachepetsa ntchito ya.