Radix. MUENZANISO nepozitsionnyh nhamba nehurongwa

nhamba hurongwa - chii? Kunyange pasina kuziva mhinduro yomubvunzo uyu, mumwe nomumwe wedu hazvo muupenyu hwako inahwo nhamba gadziriro uye haazivi nezvazvo. Ndizvozvo, muzvizhinji! Kuti haasi munhu, asi akawanda. Asati apa mienzaniso nepozitsionnyh ukanyora, ngatitarisei nyaya ino, tichataura pamusoro positional hurongwa, zvakare.

Kudiwa kuchikwama

Kubvira kare, vanhu vave kudiwa kumhanya, ndiko intuitively kuziva kuti unofanira zvimwe kuratidza quantitative maonero zvinhu uye zviitiko. Uropi anokuudza kuti unofanira kushandisa zvinhu zvokuverenga. The zvikuru yokuita chagara zvigunwe ake, uye izvi zvinonzwisisika, nokuti nguva dzose dziripo (kusara shoma).

Kuti aiva mukuru nhengo rwevanhu kufonyora minwe yake chaiyo - kureva nhamba mammoths akafa, somuenzaniso. Mazita Nhoroondo dzakadaro zvinhu haripo, asi chete kuona mufananidzo, nokuenzanisa.

Modern positional nhamba hurongwa

Nhamba System - nzira (muitiro) azorore quantitative tsika uye kwazvo nevamwe vatambi (tsamba kana vatambi).

Zvinofanira kunzwisiswa kuti positional nepozitsionnyh kwakadaro uye kutungamirira vasati kupa mienzaniso nepozitsionnyh nhamba enyika. Positional nhamba hurongwa ravira. Zvino kushandiswa muminda siyana sezvinotevera: ari binary (inosanganisira mbiri chete zvikuru zvinoriumba: 0 uye 1) Senary (nhamba pazvinhu - 6), octal (digits - 8) duodecimal (gumi vatambi), HEX (zvinosanganisira gumi vatambi). Mumwe musara vacho hurongwa inotanga pa razero. Yazvino kombiyuta inobva kushandisa binary remitemo - the binary positional notation.

Grade nhamba hurongwa

Positional ndiye kuvapo pakawanda pa- nzvimbo, izvo dziri nhamba chiratidzo. Izvi zvakanaka nezvakaitwa grade nhamba hurongwa. Pashure pezvose, isu vakajaira kubva pauduku. Zviratidzo gumi ino: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Tora nhamba 327. Kune zvitatu digits 3, 2, 7. Mumwe nomumwe wavo riri nzvimbo yayo ( nzvimbo). Seven anotora nzvimbo basa rimwe ukoshi (anokwana zviyero), deuce - dzakawanda, uye katatu - mazana. Sezvo-digit matatu nhamba, saka, woiisa matatu chete.

Inobva kumusoro, mumwe-digit matatu grade nhamba anganzi sezvinotevera: matatu nemakumi, maviri namanomwe dzakabatana. Uye kukosha (kukosha) nzvimbo kuverengwa kubva kuruboshwe kuenda kurudyi, kubva kusimba nzvimbo (chikwata) kuti akasimba (mazana).

Takafara vakasununguka chaizvo vanonzwa ari grade positional nhamba hurongwa. Isu mumaoko minwe gumi netsoka dzavo - uyewo. Five kuwedzera shanu - saka, nemhaka minwe, isu fungidzira nyore uduku vemakumi. Ndokusaka pane nyore kuti vana vadzidze chokuwanziridza patafura shanu uye gumi. Uye saka nyore kudzidza kuverenga Banknotes, izvo kazhinji ndivo multiples (kureva akakamurwa pasina chasara) shanu uye gumi.

Other positional nhamba hurongwa

Chakashamisa zhinji, zvinofanira kutaurwa kuti kwete chete uropi hwedu akajaira kuita zvimwe Masvomhu mu grade kuverengwa hurongwa. Kusvikira zvino, vanhu anoshandisa Senary uye Duodecimal. Kureva, munyika ino mune vatambi nhanhatu chete (mu Senary): 0, 1, 2, 3, 4, 5. Panguva dzavo gumi duodecimal: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 , A, B, apo A - ndiyo nhamba 10, - nhamba 11 (kubvira chiratidzo chinofanira kuva chimwe).

Nditongerei woga. Tinotenda nguva zvitanhatu, handizvo here? Mumwe awa - makumi matanhatu kwemaminitsi (makumi matanhatu), rimwe zuva - ndiwo maawa makumi mana (kaviri gumi) gore - gumi mwedzi, uye zvichingodaro ... All nguva cheap car insurance nyore huchikanganiswa six- uye duodecimal nhamba. Asi isu tiri saka kushandiswa nayo, hatidi kunyange kufunga pamusoro kuverenga nguva.

Nonpositional nhamba hurongwa. unary

Unofanira kusarudza iri - nepozitsionnyh nhamba hurongwa. Ichi rokufananidzira gadziriro yakadaro, umo pasina nzvimbo yokuti nhamba vatambi, kana nheyo "kuverenga" mashoko nzvimbo iri yakazvimirira. Rinewo yayo kupinda mitemo uye Masvomhu.

Heino mimwe mienzaniso nepozitsionnyh nhamba enyika. Ngatidzokerei kune vekare. Users vanoda nhoroondo uye kukwira pamwe zvikuru nyore kuvamba - nodules. Nonpositional nhamba kwava nodular. Imwe nyaya (bhegi mupunga, nzombe, heyisiteki , etc.) Vakanzi Somuenzaniso, kana kutenga kana kutengesa uye yakasungirirwa fundo iri tambo.

Somugumisiro, tambo anowana nokusunungura mapfundo dzakawanda, sei mabhegi vakawanda mupunga yakatengwa (semuenzaniso). Asiwo aigona kuva notch pamusoro yemapuranga chimuti pamusoro dombo rakanyorwa, etc. Izvi vaverengwa hurongwa ainzi Lumpy. It ane yechipiri zita - unary, kana kuroorwa ( "uno" mu nzira Latin "mumwe").

Zviri pachena kuti nhamba hurongwa - nepozitsionnyh. Pashure pezvose, chii nzvimbo chatiri kutaura pamusoro apo (nzvimbo) chete chete! Sezvineiwo, mune dzimwe Nyika iri mufashoni nepozitsionnyh unary nhamba hurongwa achiri.

Uyewo kuti nepozitsionnyh nhamba hurongwa dzinosanganisira:

• Roman (nokuti nhamba kunyora akashandisa tsamba - vatambi Latin);
• Ancient muEgipita (kufanana Roman, zvakashandiswawo zvadzinenge);
• arufabheti (akashandisa earufabheti);
• Babylonian (ecuneiform - kushandiswa zvakananga uye prevernuty "achikanganisa");
• Greek (uyewo vachinzi arufabheti).

The Roman nhamba hurongwa

Ancient Roman Empire, uyewo yaro sainzi, aiva mberi chaizvo. The VaRoma akapa nyika dzakawanda anobatsira zvakagadzirwa nesayenzi uye uri, kusanganisira ayo nhoroondo hurongwa. Makore mazana maviri adarika, sezviverengo Roman vakashandiswa kureva uwandu ebhizimisi (saka tichidzivisa yokunyepera).

sezviverengo Roman - muenzaniso nonpositional nhamba gadziriro, inozivikanwa kwatiri zvino. Roman maitiro uyewo vachishingaira kushandiswa, asi kwete nokuda masvomhu, uye nokuda kusanyatsotsanangurwa zvakanangwa zviito. Somuenzaniso, achishandisa sezviverengo Roman unoratidza nhoroondo misi, remakore, vhoriyamu nhamba, zvikamu, uye zvitsauko mubhuku mabhuku. Inowanzoshandiswa nokuda kushongedzwa zviratidzo weRoma dials maawa. Uye muenzaniso sezviverengo Roman nonpositional radix.

The VaRoma akasarudzwa nhamba tsamba muchiLatin arufabheti. Uye kuwanda chakanyorwa zvimwe mitemo. Pane mazita kiyi vatambi vari Roman nhamba hurongwa, achivashandisa akanyorwa ose nhamba, pasina anosara.

Mitemo richiswedera kukwira nhamba

The nhamba inodiwa inotengwa nokuwedzera vatambi (tsamba Latin) uye pakuverenga pakuverengwa kwavo. Funga kuti yokufananidzira zviratidzo zvakanyorwa Roman ino, uye sei vanofanira "verenga". We nyora mitemo inokosha paumbwe nhamba Roman nhamba hurongwa nonpositional.

1. The nhamba mana - IV, rinoumbwa mabhii maviri (I, V - mumwe uye shanu). Zvinonzi yaunganidzwa Tikabvisa chiratidzo diki zvakawanda kana amira kuruboshwe. Kana chiratidzo duku riri kurudyi, zvakakodzera kuwedzera, ipapo wana nhamba nhanhatu - VI.
2. Zvakakodzera kuwedzera zviviri akafanana chiratidzo vakamira pedyo. Somuenzaniso: SS - iri 200 (C - 100) kana kuti XX - 20.
3. Kana tanga hunhu nhamba iri idukusa wechipiri, wechitatu akatevedzana kungava chiratidzo ane mutengo ichiri duku pane wokutanga. Kuti tidzivise kuvhiringidzika, tinopa muenzaniso: CDX - 410 (grade).
4. Vamwe vazhinji inogona kumiririrwa nenzira dzakasiyana, riri rimwe downsides yeRoma kuverengwa hurongwa. Heino mimwe mienzaniso: MVM (Roman maitiro) = 1000 + (1000 - 5) = 1995 (grade hurongwa) kana MDVD = 1000 + 500 + (500 - 5) = 1995. Uye kuti haasi zvose nzira.

svomhu mazano

Nepozitsionnyh nhamba gadziriro - iyi dzimwe nguva kunzwisisa mitemo yokuva nhamba, kubudiswa yavo (akavhiyiwa pamusoro pavo). Svomhu mabasa nepozitsionnyh nhamba gadziriro - hazvisi nyore kuti vanhu ano. Hatidi kuchiva munhu mathematicians Roman!

MUENZANISO Kuwedzera. Ngatiedzei kuwedzera nhamba mbiri: XIX + xxvi = XXXV, basa iri rinoitwa matanho maviri:

1. The rokutanga - ndokukunda zvinoenderana diki nhamba kuwedzera kumusoro: IX + VI = XV (I V uye shure pamberi X "kubaya" mumwe nomumwe).
2. Chechipiri - wedzera vakakwira migove huru nhamba mbiri: X + XX = XXX.

Kubvisa rinoitwa zvishoma kupfuura kuoma. Kunoderedza uwandu kwaida paradzanisa kupinda kwayo constituent okunze, uye zvadaro zvinoderedza uye subtracts kuderedza nouya zviratidzo. Pakati 500 Bvisa 263:

D - CCLXIII = CCCCLXXXXVIIIII - CCLXIII = CCXXXVII.

Chokuwanziridza sezviverengo Roman. Nenzira, zvakakodzera kutaura kuti vaRoma haana zviratidzo arifmetichekih kushandiswa vanongotevera shoko kwavari.

Multiplicand vawande nhamba inodiwa mumwe nomumwe multiplier chiratidzo, anogamuchira zvinoverengeka zvidimbu zvinofanira akapeta. Saizvozvi zvinosvibisa chokuwanziridza pamusoro polynomials.

Panyaya weboka, mutoo iri Roman nhamba maitiro uchiri rakaoma zvikuru. Zvadaro shandisa hwakawanda yekare yeRoma - Mushosho. Kushanda naye zvikurukuru vakadzidziswa vanhu (uye kwete munhu wose akakwanisa kudzidza science).

Zvinokanganiswa nepozitsionnyh nehurongwa

Sezvataurwa pamusoro apa, pane zvainovhiringidzawo, nechinouya kushandiswa nepozitsionnyh nhamba enyika. Unary riri nyore kuti nhoroondo nyore, asi svomhu uye Masvomhu yakaoma, haumanikidzwi zvachose.

MuRoma hapana zvakafanana mitemo paumbwe vazhinji uye pane nyangarara, uye zvakaoma chaizvo kuita Masvomhu. Uyezve, vakawanda nhamba huru, iyo inogona zvakanyorwa nevaRoma tichibatsirwa nzira yake, akanga 100,000.