Chii zvinoyangarara pfungwa nhamba iri?

The mharidzo chaiyo (kana chaiyo) nhamba, apo akachengetwa ave mantissa uye exponent vari zvinoyangarara pfungwa nhamba (zvichida pfungwa, sezvo tsika muna Chirungu vaitaura nyika). Pasinei neizvi, nhamba inopiwa ane wakaiswa hama zvakarurama uye kuchinja neMhedziso. Representation iyo inoshandiswa inonyanyoshandiswa, mvumo mureza IEEE 754. kwemasvomhu akavhiyiwa kuti kushandisa zvinoyangarara-pfungwa nhamba rakatangwa muna kadambari hurongwa - zvose Hardware uye software.

Point kana koma

The ndandanda grade separator rinozivisa avo vaitaura Chirungu nyika uye anglofitsirovannye, apo zvinyorwa nhamba vakaparadzana neboka fractional chikamu yose pfungwa, nokuti mazwi nyika idzi dzakatora zita kuyangarara pfungwa - "zvinoyangarara pfungwa". Mune Russian Federation, ari fractional chikamu yose tsika, akaparadzaniswa ne- koma, saka rinomiririra chete pfungwa yave nhoroondo vakaziva shoko rokuti "zvinoyangarara pfungwa". Zvisinei, nhasi zviri hwokugadzira mapepa uye mumabhuku Russian zviri anobvumirwa zvose zvavanogona.

Shoko rokuti "zvinoyangarara pfungwa" rakabva pakuti munhu positional nhamba Nomufananidzo chinhu koma (kuipa grade kana binary - kombiyuta) kuti anogona kukodzera pose pakati pemitsara nhamba. Nyaya iyi iri chokwadi kuti anoratidza nayo yoga. Izvi zvinoreva kuti mufananidzo zvinoyangarara pfungwa nhamba zvinogona anoonekwa somunhu kombiyuta Implementation pamusoro exponential notation. The mukana kushandisa Nomufananidzo mufananidzo youduku wakaiswa-pfungwa uye integer nhamba kuti siyana netsika dzakadaro chinokura yekudyidzana kana kuti hama zvakarurama anoramba kuzochinja.

muenzaniso

Kana koma kwenhamba wakaiswa, zvino ngaahwuise ndiyo chete nemanyorerwo chete. Somuenzaniso, apa zvishoma ane nhanhatu ari nhamba mbiri digits ari fractional chikamu. Izvi zvinogona kuitwa chete seizvi: 123456,78. Pamanyorerwo zvinoyangarara pfungwa nhamba kupa munyatsonzwisisa kuti mashoko. Somuenzaniso, akapa chete digits masere. Pakunyora nzira kungava chinhu kana programmer hakuiti maviri digit skimp basa mamwe munda, apo zvichaita kunyora exponents kuti vari yemanyorero 10, uye kubvira 0 kusvika 16, uye discharges asi nhamba achava gumi 8 + 2.

Vamwe embodiments of kurekodha, izvo zvinoita kuti Format nhamba pamwe zvinoyangarara pfungwa: 12345678000000000000; 0,0000012345678; 123,45678; 1.2345678 uye zvichingodaro. In nemanyorerwo ichi, hapana kunyange chairema nokuyerwa nokukurumidza! Asi, chokupika yekombiyuta iyo anonyora nokukurumidza panguva iyo kombiyuta anoita akavhiyiwa pane kumiririrwa zvinoyangarara pfungwa nhamba. waivako Izvi hunoyerwa FLOPS (zvinoyangarara-pfungwa kuvhiyiwa por wechipiri, izvo anoshandura neuwandu kwema por yechipiri ine zvinoyangarara pfungwa). Ndicho hweBazi iri kuyerwa yekombiyuta nokukurumidza.

mamiriro

Record nhamba iri zvinoyangarara pfungwa pamanyorerwo zvakakodzera sezvinotevera, vachichengeta kutevedzana kwezviitiko zviri fanira zvikamu, nekuti chinyorwa ichi exponential, iyo inoratidza chaiyo nhamba sechipiriso mantissa uye kurongeka. Zvakakodzera kumirira zvakare makuru uye diki nhamba, vari nyore kuverenga. Raida zvikamu: rakanyorwa nhamba (N), kuti mantissa (M), hurongwa chiratidzo (p) uye hurongwa (n). Okupedzisira zvinhu zviviri chiratidzo. Nokudaro, N = ^M. N ^p. Saka kuchinzi zvinoyangarara-pfungwa nhamba. Mienzaniso zvichabviswa zvakasiyana.

1. Zvakakosha kunyora nhamba miriyoni imwe, kuti arege kurasika ari zeros. 1000000 - ndiwo zvinoitika akarekodwa, svomhu. A kombiyuta iri sezvinotevera: ^1.0. October ^6. Ndiko, gumi rechitanhatu simba - nezviratidzo zvitatu, zvakafanira muna vakawanda nhanhatu zeros. Saka kunoitika kumiririrwa nhamba yatarwa uye zvinoyangarara nguva apo pakarepo anogona kuona kusiyana chiperengo.

2. Zvino nhamba yakadaro nesimba 1,435,000,000 (bhiriyoni mana nemakumi matatu nezvishanu) Uyewo anogona kunyorwa nyore: ^1.435. September ^10, chete. Ndizvo chete kubvisa chiratidzo anogona kunyora chero nhamba. Ndizvozvo, uye vakasiyana mumwe nokuwanda yatarwa uye zvinoyangarara pfungwa.

Asi zviri zvakawanda sei kuva pasi? Chokwadi, zviri nyore.

3. Somuenzaniso, sezvo rimwe millionth chiratidzo? = 0.000001 ^1.0. 10 ^-6. akwanise zvikuru uye nhamba kunyora, uye kuriverenga.

4. Imwe kuoma? mazana mashanu namakumi mana yechitanhatu duku chokupisa: 0.000000546 = ^546. 10 ^-9. Pano. Kuwanda zvinoyangarara pfungwa rakafara chaizvo.

shepi

Form nhamba kungava zvakajairika kana normalized. Normal - nguva dzose kuremekedza zvakarurama kuti kuyangarara pfungwa nhamba. Zvinofanira kucherechedzwa kuti mantissa chimiro ichi, pasina kufungisisa chiratidzo, ndiyo hafu penguva 0 1, ipapo 0 ⩽ munhu <1. Kwete dzose muchimiro uwandu anorasikirwa kururama kwaro. Zvakaipira inowanzotorwa chimiro ndechokuti nhamba dzakawanda zvinogona kunyorwa dzakasiyana, kuti chinoreva zvakawanda. siyana zvinyorwa MUENZANISO zvakafanana nhamba: 0 = 0.0001, ^000001. February ¹⁰ = ^0.00001. January ¹⁰ = ^{0.0001. 10 0} = ^0,001. 10 ^-1 = ^0.01. 10 ^-2, uye naizvozvo anogona kuva zvakawanda. Ndokusaka kombiyuta anoshandisa normalized yakasiyana notation, apo mantissa grade anotora kukosha zviumbu (zvichibatanidzwa), uye saizvozvo gumi (kwete zvaisanganisira), uye saizvozvo ari mantissa binary nhamba ine ukoshi pakati chete (zvichibatanidzwa) maviri (kwete sanganisira).

Saka, 1 ⩽ munhu <10 Izvi -. Binary nhamba pamwe zvinoyangarara pfungwa, uye chimiro ichi pakunyora chero nhamba (kunze razero) rinoburitsa rakasiyana nzira. Asi variko drawback - nekusagona kufungidzira razero mhando iyi. Naizvozvo informatics anopa kushandisa dzinokosha nhamba 0 chiratidzo (chidimbu). The integer chikamu (MSB) zviri mantissa iri binary nhamba kunze razero ari normalized fomu akaenzana 1 (zvakazara chikwata). nhoroondo iyi rinoshandiswa mureza IEEE 754. The positional nhamba hurongwa, sezvamakaropafadzwa nechigadziko kunopfuura maviri (ternary, quaternary nezvimwe hurongwa), pfuma iyi haisi kutengwa.

reals

Real nhamba vane zvinoyangarara pfungwa uye kazhinji sezvariri haasi mumwe chete, asi iri nyore chaizvo nzira kumirira nhamba chaiyo, sokunge, mumwe musarudze pakati kuwanda tsika uye kururama. Izvi zvineringanidzo exponential notation, chete akaita pakombiyuta. Zvinoyangarara-pfungwa nhamba - kuva nomunhu matomu rakakamurwa chiratidzo (chiratidzo), murayiro (exponent) uye mantissa (mantis). The inonyanya Manyorerwo ane IEEE 754 zvinoyangarara-pfungwa nhamba sezvo chine matomu kuti encode chikamu yayo mantissa, chimwe chikamu - ukuru uye mumwe ikakuruma inoratidza chiratidzo nhamba: razero - kana zviri zvakanaka, kuti chikwata - kana nhamba iri kunaka. The yose nzira yakanyorwa ine nhamba (bumbiro-kusuduruka), uye mantissa - ari normalized chimiro, ayo fractional chikamu - munyika binary ino.

Mumwe chiratidzo - ndiwo chete zvishoma kuti inoratidza chiratidzo zvose zvinoyangarara-pfungwa nhamba. Mantissa uye kuti - ndivo integers, ivo, pamwe chiratidzo uye kuti mufananidzo zvinoyangarara pfungwa nhamba. The nzira inogona kunzi exponential kana exponent. Kwete zvose nhamba chaiyo inogona kumiririrwa mu kombiyuta yavo chaicho, vamwe vari akapa anofungidzirwa tsika. A zvikuru nyore kuita - kuzviisa pasi nhamba chaiyo ine wakaiswa nguva, apo chaiye uye yose chikamu ngauitwe unoparadzanisa. Ungangove, saka kuti integer chikamu anogara mugove X matomu, uye fractional - Y matomu. Asi mavakirwo processors havazivi nzira yakadaro, asi nekuti zvatinofarira anopiwa nokuwanda zvinoyangarara pfungwa.

Kuwedzera

Kuwedzera zvinoyangarara pfungwa nhamba iri nyore. Maererano IEEE 754 mureza kuroorwa nemazvo nhamba ine vakawanda matomu, saka zviri nani kuenda pane mienzaniso, pamwe pfungwa iri nani kutora duku zvinoyangarara-pfungwa nhamba. Somuenzaniso, nhamba mbiri - X uye Y.

Matanho ndeinotevera:

a) The nhamba inofanira kumiririrwa mu normalized chimiro. Zviri pachena kuti yakavanzika imwe. X = ^1.110. 2 ^2, uye Y = ^1,000. 2 ^0.

b) Ramba chirongwa nziyo kunogona chete equalize ari exhibitors, asi anofanira nyorazve kukosha Y. Richaita dzinoenderana kukosha normalized nhamba, kunyange chaizvoizvo - unnormalizes.

Ngaaverenge musiyano pakati exponents kuti dhigirii 2 - 0 = 2. Zvino kutamisira mantissa kudzikamisa kuchinja izvi, kureva, wedzera 2 indekisi rechipiri rokuti, nokudaro unomutsa koma yakavanzwa dzakabatana pa mbiri dziri kuruboshwe. 0,0100 ^inotengwa. February ^2. Izvi zvichava yakaenzana rapfuura ukoshi Y, ipapo ichitova Y '.

c) Zvino unofanira kuwedzera kuwanda mantissa X uye Y. kugadziridzwa

1.110 + 0.01 = 10.0

Exhibitor achiri anomiririrwa X parameter, izvo zvakaenzana 2.

g) The mari yakagamuchirwa muzvirevo danho, haachatauri normalization Unit, ipapo unofanira achinakurira exponent Verengai uye kudzokorora. 10.0 pamwechete matomu maviri kuruboshwe ari grade pfungwa, nhamba zvino zvakakodzera kuti normalize, kureva, kufambisa koma kuruboshwe nomumwe pfungwa, uye exponent ukuwo, yakawedzera 1. Zvakaratidza ^1,000. March ^2.

e) Inguva exchange zvinoyangarara pfungwa nhamba imwe iri chete-byte hurongwa.

mhedziso

Sezvaunogona kuona, wedzera nhamba idzi hadzisi kukuomerai, chinhu floats koma. Kutoti Chokwadi, asi kuunza uwandu akaderera exponent pakati zvakawanda (mu muenzaniso pamusoro apa, akanga ari Y kuti X), uyewo kudzorerwa Nezvagara Zviripo, kureva nyaya muripo - kufambisa mashoko grade womuratidza rworuboshwe pamusoro mantissa. Kana Kuwedzera yakatotanga raiswa, zvinokwanisika chaizvo uye achiri mumwe dambudziko - perenormirovanie uye truncation ikakuruma kana nhamba yavo asingadi kuenzaniswa nhamba kumiririra nayo.

chokuwanziridza

Binary maitiro anopa nzira mbiri idzo anowedzera zvinoyangarara-pfungwa nhamba. Basa Izvi zvinogona kuitwa kubudikidza chokuwanziridza, unotanga mudukusa zvinokosha nematomhu uye unotanga murayiro mukuru matomu ari multiplier. Zvose zviitiko zvine nhamba remapazi sequentially kuisira kukwana chigadzirwa. akavhiyiwa aya raitungamirwa kuwedzera multiplier matomu. Saka, kana mumwe nematomhu ari multiplier ari chairema, Verengai rushoma zvibereko multiplicand inokura pamwe runoenzanirana kuchinja. Kana digit pamusoro multiplier chinyararire zero, nepo multiplicand haisi akawedzera.

Kana chokuwanziridza rinoitwa nhamba mbiri chete, nezvibereko zvomunda nhamba chayo haagoni pakuwanda digits zviri zvinhu, kupfuura kaviri, uye nokuda vazhinji kwazvo, zvikuru. Kana vawanda nevamwe nhamba, chigadzirwa ngozi kufanira pamusoro chidzitiro. Nekuti kuwanda nhonga chero digitaalinen muchina iri finite chaizvo, uye simba kuti ndigoisa vaifanira kuti kaviri nhamba nemvumbi digits. Uye kana nhamba panzvimbo iri shoma, zviri chigadzirwa vanotozvikuvadza achasuma zvikanganiso. Kana yakawanda computation riri guru, kukanganisa bindepinde, uye somugumisiro anowedzera zvikuru zvinonyatsorehwa kururama. Pano, nzira bedzi - kuti kumativi chokuwanziridza zvabuda, ipapo kukanganisa mabasa vakanga rakatumbuka. Kana chokuwanziridza oparesheni, zvinovawo zvinobvira kuenda mhiri afoot pamusoro digits, asi bedzi muduku, nokuti pane muganhu kwakaitwa uwandu iyo anomiririrwa muchimiro yakatarwa-pfungwa.

dzimwe tsanangudzo

Zviri nani kutanga kubva pakutanga. The inonyanya nzira kumiririra nhamba - mutsetse nhamba somunhu integer, uko koma iri zvakaburitswa kumagumo. tambo uyu anogona kuva chero kureba, asi koma umire zvakanaka nzvimbo akariisa, mekuparadzanisa integer kubva fractional chikamu. Pamanyorerwo mharidzo yacho yakatarwa-pfungwa hurongwa hazvo anoisa zvimwe zvinhu pamusoro nzvimbo grade pfungwa. Scientific notation anoshandisa mureza normalized maonero mufananidzo nhamba. It aqn {\ displaystyle aq ^ {N }} aq n. Pano {\ displaystyle ^ane} rimwe, uye anonzi mantissa resi. Just nezvazvo zvave akati kuti 0 ⩽ munhu pachena: n {/ displaystyle N} N - ane integer exponent, uye ^Q {/ displaystyle Q} Q - uyewo integer, inova hwaro radix (tsamba kazhinji 10). Mantissa kusiya koma mushure digit wokutanga, zvisina razero, asi mamwe kurekodha iri hwakatamisirwa mashoko aripo kukosha nhamba.

Zvinoyangarara-pfungwa nhamba zvakanyorwa chaizvo zvakafanana zvose zvakajeka mwero kupinda nhamba, asi exponent uye mantissa akanyorwa yoga. Last zvakafanana uye mune normalized pamanyorerwo - wakaiswa pfungwa, izvo yakashongedzwa yokutanga inokosha digit. Just zvinoyangarara nguva rinoshandiswa kureva muna kombiyuta, kureva, iri paindaneti kumiririrwa apo nyika haina grade uye binary, apo kunyange mantissa Denormalize Rearranged pfungwa - zvino kutangira digit, ipapo pamberi, kwete shure, apo integer chikamu pfungwa, haagoni kuva. Somuenzaniso, kwedu grade ezvinhu kupa ake mapfumbamwe binary marongedzero pfupi kushandiswa. Uye kuti zvichaita kunyora yaro mantissa kuyangarara-pfungwa seizvi: +1001000 ... 0, uye uye indekisi 0 ... 0100. Asi grade hurongwa anokundikana kubereka Masvomhu akadaro kunzwisisa, izvo uve binary, vachishandisa chimiro zvinoyangarara pfungwa.

refu svomhu

In zvemagetsi makombiyuta pakuvara Software Mabhokisi, apo dzinounzwa nokuda mantissa uye exponent uwandu ndangariro inotaurwa software, zvakawanda chete kuyeuka kukura kombiyuta. Zvinoita yakaita svomhu refu, ndiko, nyore akavhiyiwa pamusoro nhamba kuti anoita kombiyuta. Zvose zvakafanana - kubvisa uye Uyezve, kupesana uye chokuwanziridza, zvokutanga mabasa uye kuvakwa mudzi. Asi nhamba akasiyana chaizvo, kukwanisa kwavo zviri kupfuura kureba muchina shoko. The Implementation remapazi izvi hazvisi nokuda Hardware uye software, asi chichiri kushandiswa chikuru Hardware kushanda zviduku zvikuru nhamba mirairo. Pane zvakawanda uye svomhu, apo nhamba urefu chete parinoperera ndangariro vanokwanisa - zvemasanga nemazvo svomhu. A refu svomhu inoshandiswa zhinji minda.

1. Kuti kuronga bumbiro remitemo (processors, microcontrollers pamwe yakaderera ikakuruma udzamu - 10-ikakuruma evoruzhinji masere-yati shoko kureba, hazvina kukwana kugadzirisa mashoko kubva Analog-kuti-digitaalinen (analoginen-to-digitaalinen convert), uye saka kuita pasina refu svomhu.

2. zvakare kwenguva svomhu rinoshandiswa kuti cryptography, apo zvakakodzera kuitira rakarurama mugumisiro Exponentiation kana chokuwanziridza kuti ^10.309. Integer svomhu rinoshandiswa modulo M - huru dzinongoitika nhamba, uye hachisi nyore.

3. Software nokuti mari uye mathematicians, zvakare, haisi pasina refu svomhu, nokuti chete nzira kuti ritsigire migumisiro Masvomhu papepa - tichibatsirwa pakombiyuta, kuona yakakwirira rakarurama nhamba. Zvinoyangarara pfungwa vanogona inosanganisira chero nhamba refu buditsa. Asi injiniya Masvomhu uye basa masayendisiti inoda kupindira chirongwa Masvomhu kakawanda, nekuti zvakaoma chaizvo kuti mazano Data pasina kukanganisa. Kazhinji ndivo zvikuru voluminous pane rounding results.

Fight nokukanganisa

Kana nhamba remapazi apo zvinoyangarara pfungwa, zvakaoma chaizvo kuongorora rakarurama nemigumisiro. Asati akagadzira ndokugutisa zvose akarongeka dzidziso izvo zvaizobatsira kugadzirisa nyaya iyi. Asi kukanganisa integer vaongorore nyore. Mukana ndichiva kubvisa mashoko okuti panyika - chete kushandisa chete kuwanda yakatarwa-pfungwa. Somuenzaniso, purogiramu zvemari yakavakwa pamusoro musimboti ichi. Zvisinei, pane nyore: runodiwa uwandu digits mushure grade pfungwa anozivikanwa pachine.

Dzimwe nyaya dzacho hakugumiri, nekuti haugoni kushanda pamwe kana vashomashoma kana huru chaizvo nhamba. Saka kana iwe kushanda nguva dzose inorangarira kuti pangava mashoko okuti, uye nokuti Kunyange zvazvo kwakabva zvabuda zvakafanira denderedzwa. Uyezve, otomatiki rounding kazhinji kushayikwa chiito, uye naizvozvo rounding kunotsanangurwa zvakananga. Very ngozi nokuremekedza ichi, fananidzo oparesheni. Pane kunyange kufungidzira uwandu zvikanganiso ramangwana riri zvakaoma.