Kuyini inombolo elintantayo iphuzu?

Ukuziletha yangempela (noma zangempela) izinombolo, lapho zigcinwa njengoba mantissa futhi okungekho kuthiwa elintantayo iphuzu izinombolo (mhlawumbe iphuzu, njengoba kuyisiko emazweni abakhuluma isiNgisi). Naphezu kwakho konke lokhu, nenani inikezwe nge ezihleliwe ukunemba isihlobo nokushintsha ngokuphelele. Ukumelwa esetshenziswa njalo kunazo, evunyiwe IEEE 754. Mathematical imisebenzi ukuthi usebenzisa izinombolo elintantayo-iphuzu ezisetshenziswa Computing izinhlelo - kokubili hardware ne-software.

Point noma ukhefana

Uhlu eningiliziwe isihlukanisi Idesimali ukhombisa lezo amazwe akhuluma isiNgisi futhi anglofitsirovannye, lapho amarekhodi izinombolo ahlukaniswe ingxenye ayingxenye ye lonke iphuzu, ngoba amagama ala mazwe ebizwa ngegama iphuzu elintantayo - "iphuzu ezintantayo". Esikhathini Russian Federation, ingxenye ayingxenye ye wonke yesiko, ahlukaniswe ngekhoma, ngakho-ke limele umqondo ofanayo ngokomlando neyaziwayo igama elithi "iphuzu ezintantayo". Nokho, namuhla kumadokhumenti lobuchwepheshe kanye ezincwadini Russian it ovunyelwe kokubili ongakhetha.

Igama elithi "iphuzu ezintantayo" uvela Iqiniso lokuthi positional inombolo ukumelwa kuyinto ukhefana (idesimali evamile noma kanambambili - ikhompyutha) ukuthi ukwazi ukubona kuphi phakathi emigqeni izinombolo. Lesi sici uqinisekile ugagule ke eceleni. Lokhu kusho ukuthi umfanekiso elintantayo iphuzu izinombolo kungase kubhekwe njengokwelapha ukuqaliswa computer notation exponential. Okuhle ngokusebenzisa umfanekiso ezinjalo ukumelwa Ifomethi elungisiwe-iphuzu futhi inamba izinombolo ziyashiyana yamanani ikhula kakhulu lapho ukuthi ukunemba isihlobo uhlala ingashintshiwe.

Ngokwesibonelo

Uma ukhefana kunombolo nquma ngalesosikhathi awushise kuyinto format eyodwa kuphela. Ngokwesibonelo, unikezwa kancane eziyisithupha inombolo kanye Izinombolo ezimbili kule wamaqhuzu ingxenye. Lokhu kungenziwa kuphela ngale ndlela: 123456,78. Ifomethi elintantayo iphuzu izinombolo akunika okuhilelekile okukhuluma. Ngokwesibonelo, banikezwe amadijithi efanayo eziyisishiyagalombili. ongakhetha Ukuqopha kungenzeka yimuphi uma uhlelo ayenzi zamadijithi amabili a skimp komsebenzi ensimini ezengeziwe, lapho izoqopha exponents uqobo lwazo 10, futhi kusukela 0 kuya 16, nokuphuma esithweni sobulili kuyilapho inani Imininingwane kuyoba eziyishumi 8 + 2.

Ezinye embodiments ukuqopha, okuyinto ikuvumela ukufometha izinombolo nge iphuzu elintantayo: 12345678000000000000; 0,0000012345678; 123,45678; 1.2345678 nokunye. Kulesi sakhiwo, kukhona ngisho iyunithi yokukala ijubane! Kunalokho, ukusebenza ngcondvomshini erekhoda ijubane lapho ikhompyutha wenza imisebenzi lapho kukhona ukumelwa elintantayo iphuzu izinombolo. Lokhu ukusebenza kukalwa ngokuya flops (elintantayo-iphuzu imisebenzi ngomzuzwana, okungama-ngenombolo yemisebenzi ngomzuzwana iphuzu elintantayo). Lokhu lisisakhiwo ngejubane kwesistimu yokulinganisela ikhompyutha.

isakhiwo

inombolo Irekhodi elintantayo iphuzu format kuyadingeka kanje, ogcina ukulandelana izingxenye saziso, ngoba lokhu irekhodi lomchazi, elibonisa izinombolo zangempela njengoba mantissa nokuhleleka. Kuyadingeka ukumela izinombolo ezinkulu kakhulu futhi incane kakhulu, zingabantu lula kakhulu ukufunda. izingxenye Kuyadingeka: inombolo eqoshiwe (N), i-mantissa (M), i-oda uphawu (p) ne-oda (n). Eminyakeni emibili izici zesibonakaliso. Ngakho, N = ^M. n ^p. Ngakho ebhaliwe elintantayo-iphuzu izinombolo. Izibonelo ziyoba nhlobonhlobo.

1. Kuyadingeka alobe inani esigidini, ukuze singathwesi ulahleke amaqanda. 1000000 - kuba evamile ukurekhoda, izibalo. I-computer simiswe ngalendlela lelandzelako: ^1.0. Okthoba ^6. Okungukuthi, eziyishumi ukuze umbuso wezwe wesithupha - izimpawu ezintathu, okuyinto bakwamukele amaningi njengoba eziyisithupha amaqanda. kwenzeka Ngakho Kutsi tinombolo iphuzu esinqunyiwe kanye elintantayo lapho ngokushesha kungathola umehluko isipelingi.

2. Futhi inombolo kanzima esinjalo siyisivikelo 1,435,000,000 (kwezigidi eziyinkulungwane amane namashumi amathathu nanhlanu namakhulu) singasebenza wamane waloba: ^1.435. Septhemba ^10, kuphela. Kunjalo-ke nangobufakazi uphawu lokususa angabhala noma iyiphi inombolo. Yilokho, futhi ihluke nomunye nenombolo iphuzu esinqunyiwe kanye elintantayo.

Kodwa kungcono kanjani ukuba ongaphakeme? Yebo, kalula kakhulu.

3. Isibonelo, njengoba sesigidi omunye uphawu? = 0.000001 ^1.0. 10 ^-6. Kakhulu lula futhi lokubhala izinombolo, nokulifunda.

4. A more xaka? Five lamatshumi amane lesithupha kweziyizigidi: 0.000000546 = ^546. 10 ^-9. Lapha. Ububanzi iphuzu elintantayo ubanzi kakhulu.

ukuma

inombolo Ifomu kungenzeka evamile noma kwesejwayelekile. Okuvamile - ngaso sonke isikhathi sihloniphe ikwazi elintantayo iphuzu izinombolo. Kufanele kuqashelwe ukuthi mantissa kuleli fomu, ngaphandle kucatshangelwa sibonakaliso kwesigamu nalesikhathi 0 1, bese 0 ⩽ a <1. Hhayi ifomu evamile inani ilahlekelwa ukunemba kwayo. Ububi ifomu evamile wukuthi izinombolo eziningi ungalotshwa ngezindlela ezahlukene, ukuthi kuyadida. ISIBONELO amarekhodi ezahlukene inani elifanayo: 0 = 0.0001, ^000001. Februwari ¹⁰ = ^0.00001. Januwari ¹⁰ = ^0.0001. 10 ⁰ = ^0,001. 10 ^-1 = ^0,01. 10 ^-2, futhi kanjalo kungaba okuningi. Yingakho i-computer isebenzisa notation ezahlukene kwesejwayelekile, lapho idesimali mantissa eqala ukubaluleka amayunithi (okufakayo), futhi ngaleyo ndlela kwabayishumi (akufakiwe), futhi ngendlela efanayo mantissa inombolo kanambambili inenani phakathi eyodwa (okufakayo) ezimbili (hhayi okufakayo).

Ngakho, 1 ⩽ a <10 Lokhu -. Izinombolo kanambambili nge iphuzu elintantayo, futhi lolu hlobo ukuqopha noma iyiphi inombolo (ngaphandle zero) ithumba ngendlela eyingqayizivele. Kodwa futhi kukhona ethile - ukungakwazi ukucabanga lolu hlobo zero. Ngakho-ke informatics sihlinzekela ukusetshenziswa izinombolo ezikhethekile 0 uphawu (kancane). I inamba ingxenye (MSB) we mantissa kunombolo kanambambili ngaphandle zero ifomu kwesejwayelekile ilingana 1 (iyunithi ngokuphelele). Leli rekhodi isetshenziswa IEEE 754. I positional uhlelo inombolo, lapho base kuyinto engaphezu kwemibili (ternary, quaternary nezinye izinhlelo), lokhu impahla awathengiwe.

reals

izinombolo Real nge elintantayo iphuzu futhi ngokuvamile njengoba nje akusiyo kuphela, kodwa ngendlela elula kakhulu ukumela inombolo yangempela, kunjengokungathi ukusilela phakathi ububanzi bamanani kanye nokunemba. Lokhu fanekiso ukuba notation exponential, kuphela kwenziwa kuyi-computer. inombolo Floating-iphuzu - iqoqo izingcezu ngabanye sehlukaniswe uphawu (uphawu), ukuze (okungekho) bese mantissa (mantis). Ifomethi ejwayeleke kakhulu kuyinto IEEE inombolo 754 elintantayo-iphuzu njengoba iqoqo ibhithi ukuthi encode ingxenye mantissa bayo, ezinye ingxenye - degree kanye kancane omunye ubonisa uphawu inombolo: zero - uma uthambekele kokuhle, iyunithi - uma inombolo alivumi. Inqubo ephelele kulotshwe ngenombolo (ikhodi-shift), kanye mantissa - ifomu kwesejwayelekile, ingxenye yayo wamaqhuzu - ohlelweni kanambambili.

uphawu ngalunye - kancane olulodwa elikhombisa isibonakaliso zonke izinombolo elintantayo-iphuzu. Mantissa nokuhleleka - kukhona integers, bona, kanye uphawu futhi wenze umfanekiso elintantayo iphuzu izinombolo. Inqubo kungenziwa ngokuthi i lomchazi noma okungekho. Akubona bonke izinombolo zangempela kungenziwa amelwe nekhompyutha ku incazelo yabo ngqo, nabanye ethulwa amagugu eseduze. A option lula kakhulu - ukuhambisa inombolo sangempela iphuzu fixed, lapho yangempela futhi yonke ingxenye izogcinwa ehlukile. Kungenzeka, ukuze inamba ingxenye njalo eyabelwe X izingcezu, futhi ayingxenye - Y izingcezu. Kodwa izakhiwo izilimi abawazi indlela enjalo, kodwa ngenxa kubonelelwa kakhulu isibalo iphuzu elintantayo.

Ngaphezu

Ukwengezwa elintantayo iphuzu izinombolo ulula. Mayelana nomkhosi wokuhlanganisa IEEE 754 ejwayelekile inombolo ngokunemba olulodwa it has a inombolo enkulu izingcezu, ngakho-ke kungcono ukuthi udlulele izibonelo, nombono ongcono ukuthatha kulencane inombolo elintantayo-iphuzu. Ngokwesibonelo, izinombolo ezimbili - X Y.

Izinyathelo injengoba ilandela:

a) nezinombolo kumele amelwe ifomu kwesejwayelekile. Kuyinto kusobala ukuthi enye ezifihliwe. X = ^1,110. 2 ^2, futhi Y = ^1,000. 2 ^0.

b) Qhubeka inqubo Ukwakheka ungenziwa kuphela nokulinganisa umbukiso, kodwa kubaluleke kakhulu ukuba ubhale ukubaluleka Y. Kuyoba zivumelana ukubaluleka izinombolo kwesejwayelekile, nakuba eqinisweni - unnormalizes.

Bala umehluko phakathi exponents idigri 2 - 0 = 2. Manje ukuhambisa mantissa isinxephezeliso lezi zinguquko, okungukuthi, engeza 2 kuya Inkomba kwethemu yesibili, ngaleyo ndlela yokuhamba ukhefana amayunithi ezifihliwe at amaphuzu amabili kuya kwesokunxele. 0,0100 ^{eyatholakala.} Februwari ^2. Lokhu kuyoba okulingana ukubaluleka odlule Y ke kukhona vele Y '.

c) Manje udinga ukwengeza kuze isibalo mantissa X Y. kushintshwe

1,110 + 0,01 = 10,0

Exhibitor namanje emelelwa X ipharamitha, okuyinto ilingana 2.

g) Imali etholwe isinyathelo odlule, lasidedela ukuzinza iyunithi, khona-ke kufanele bayeke isamba exponent bese uphinda. 10.0 amabili ibhithi kwesokunxele iphuzu idesimali, inombolo manje kudingekile ukuze kulesetayelekile, okungukuthi, ukuhambisa ukhefana kuye kwesokunxele ngokuthi iphuzu elilodwa, futhi okungekho, ngokulandelana, kukhuphuke ngo 1. It kuvela ^1,000. Mashi ^2.

e) Sekuyisikhathi ukuguqula elintantayo inombolo iphuzu e single-Byte uhlelo.

isiphetho

Njengoba ubona, engeza lezi zinombolo ayinzima kakhulu, yini sintanta ukhefana. Ngaphandle-ke, ngaphandle ngokuletha inani exponent aphansi phakathi ngaphezulu (in the isibonelo ngenhla, kwaba Y X), kanye nokubuyiselwa isimo esikhona manje, ie udaba isinxephezelo - ukuhambisa iphuzu ledesimali kwesokunxele mantissa. Lapho kwalokho isivele isicelo, kungenzeka kakhulu futhi namanje inkinga eyodwa - perenormirovanie futhi akhronimi kancane uma inombolo yabo ayifani inombolo ukumela ke.

ukubuyabuyelela

uhlelo Binary inikeza izindlela ezimbili by okuyinto esandisa izinombolo elintantayo-iphuzu. Lo msebenzi ungase wenziwe ukubuyabuyelela, oqala ngokuthi izingcezu okungenani abalulekile futhi oqala okusezingeni eliphezulu oda izingcezu in multiplier. Bobabili bavule amacala aqukethe eziningi imisebenzi ngokulandelana emakhiyubhi umkhiqizo esinqunyiwe. Lezi imisebenzi ilawulwa ukwengeza Okuphindaphinda izingcezu. Ngakho, uma omunye ibhithi multiplier uphiko, isamba imikhiqizo olulinganiselwe multiplicand ukhula shift okuhambisanayo. Uma idijithi we Okuphindaphinda sekungene zero, kuyilapho multiplicand wanezela.

Uma ukubuyabuyelela wenziwa izinombolo ezimbili nje, umkhiqizo izinombolo senani ayikwazi ukudlula isibalo kwamadijithi eziqukethwe izici, ezingaphezu kuka kabili, futhi inani elikhulu ngayo kakhulu impela. Uma iphindwe ezinye inombolo, umkhiqizo izingozi kungahlali esikrinini. Ngoba inani ibhithi yimuphi umshini digital ezilinganiselwe kakhulu, futhi iphoqa ukuba afinyelele a esiphezulu kabili isibalo kwamadijithi samabululu. Futhi uma inombolo yezindawo kukhawulwe, umkhiqizo nakanjani ukwethula amaphutha. Uma inani kathisha likhulu, isiphambeko kweqa, futhi ngenxa yalokho kakhulu kwandisa ukunemba jikelele. Lapha, indlela kuphela - elizofinyezwa imiphumela ukubuyabuyelela ke imisebenzi iphutha abangu kushintshana. Lapho ukusebenza ukubuyabuyelela, kuba nokwenzeka okungaphezu igridi kwamadijithi, kodwa yilabo kuphela abasebasha, ngoba kukhona umkhawulo onikezwe eziningana zazo ivezwa ngendlela fixed-iphuzu.

ezinye izincazelo

Kungcono ukuqala kusukela ekuqaleni. Indlela ejwayeleke kakhulu ukumela inombolo - izinombolo umugqa njengenombolo ephakathi, lapho ukhefana kumumethwe kwaze kwaba sekupheleni. Lokhu string kungaba noma ikuphi ubude, kodwa ukhefana umi endaweni efanele uma sikubeka, ihlukanisa inamba kusukela ingxenye ayingxenye yalo. Ifomethi isethulo kohlelo fixed-iphuzu ngempela ubeka izimo ezithile ku indawo iphuzu zamadesimali. notation Scientific isebenzisa ukubuka okuvamile kwesejwayelekile we Kutsi tinombolo. It aqn {\ displaystyle aq ^ {n }} aq n. Lapha {\ displaystyle ^a} a, futhi iyaqhubeka ibizwa ngokuthi nomchilo mantissa. Vele ngakho Kuye kwathiwa 0 ⩽ a kucace: n {/ displaystyle n} n - i-eksponenti inamba, futhi ^q {/ displaystyle q} q - futhi inenombolo, okuyinto ngesisekelo Isisekelo sesistimu yezinombolo (incwadi ngokuvamile 10). Mantissa ushiye ukhefana emva idijithi yokuqala, engesiyo zero, kodwa ukuqopha olunye udluliselwa ulwazi inani lamanje inombolo.

inombolo Floating-iphuzu kulotshiwe okufana kakhulu zonke entry izinombolo ecacile ejwayelekile, kuphela okungekho futhi mantissa elotshiwe ngokwehlukana. Last okufanayo futhi ngefomethi kwesejwayelekile - iphuzu fixed, okuyinto lihlotshiswe idijithi sokuqala esibalulekile. Vele iphuzu elintantayo isetshenziswa ngokuyinhloko computer, okungukuthi, e-ukumelwa electronic lapho uhlelo ngeke idesimali futhi kanambambili, lapho ngisho mantissa Denormalize iphuzu rearranged - manje phambi idijithi kuqala, bese ngaphambi, hhayi ngemuva kokuthi, lapho inamba ingxenye isimiso, akukwazi. Ngokwesibonelo, siqu idesimali uhlelo lwethu ebengakhipha isimiso sakhe ayisishiyagalolunye kanambambili ukusetshenziswa okwesikhashana. Futhi ukuthi izoqopha futhi mantissa yayo elintantayo-iphuzu kanje: +1001000 ... 0, futhi kanye Inkomba 0 ... 0100. Kodwa lesi simiso idesimali awufezi ezifana izibalo eziyinkimbinkimbi, okungase kanambambili, usebenzisa uhlobo iphuzu elintantayo.

izibalo eside

Ngo amakhompyutha electronic baye esakhelwe amaphasela software, lapho sandiswe mantissa futhi okungekho ka inani lememori ecacisiwe isofthiwe, kungagcini kuphela ubukhulu inkumbulo computer. Kubonakala sengathi i-arithmetic eside, okungukuthi, imisebenzi elula ku izinombolo ukuthi wenza ikhompyutha. Konke okufanayo - ukukhupha kanye kwalokho, ukwahlukana futhi ukubuyabuyelela, imisebenzi aphansi kanye nokwakhiwa impande. Kodwa inani ezahlukene kakhulu, emandla ato kakhulu mkhulu kunezinhliziyo ubude izwi emshinini. Ukuqaliswa kwalawa imisebenzi Akukhona hardware ne-software, kodwa sisetshenziswa kabanzi hardware eziyisisekelo ukusebenza ngezinombolo ezincane kakhulu oda. Kukhona okuningi futhi izibalo, lapho izinombolo obuphelele kuphela engavimba wememori - ngokungenasizathu ngobuciko izibalo. A izibalo eside isetshenziswa emikhakheni eminingi.

1. Ukuze ahlanganise ikhodi (izilimi, microcontrollers nge ongaphakeme kancane ukujula - 10-bit amarejista nesishiyagalombili-bit izwi obuphelele, akwanele ukusingatha ulwazi kusuka Analog-to-digital (analog-to-digital Converter), futhi ngaleyo ndlela ngeke wenze ngaphandle izibalo eside.

2. It is futhi izibalo eside isetshenziselwa indlela yokubhala efihla incazelo, lapho kuyadingeka ukuqinisekisa ukunemba umphumela Exponentiation nofana ukubuyabuyelela ukuze ^10.309. izibalo integer isetshenziswa modulo m - inqwaba yezinto zemvelo nangemfundiso awukona ngempela elula.

3. Software bezimali kanye zezibalo, futhi, akuyona ngaphandle izibalo eside, ngoba indlela kuphela ukuqinisekisa imiphumela izibalo ephepheni - ngosizo computer, ukuqinisekisa ukunemba okuphezulu yezinombolo. Floating iphuzu bangakwazi ehilela iyiphi inombolo sokukhishwa eside. Kodwa izibalo zobunjiniyela futhi umsebenzi ososayensi ezidinga ukuthi kungenelelwe hlelo izibalo ngokuvamile kakhulu, ngoba kunzima kakhulu ukwenza idatha okokufaka ngaphandle kokwenza amaphutha. ngokuvamile voluminous okuningi kuka Imiphumela ukuqoqa.

Fight ezinamaphutha

Lapho eziningi imisebenzi lapho iphuzu elintantayo, kunzima kakhulu ukuhlola ukunemba imiphumela. Hhayi okwamanje yasungulwa ngokwanelisa zonke imfundiso yokuziphendukela zezibalo okwakuyosiza ukuxazulula le nkinga. Kodwa inamba ngephutha ukuhlola kalula. The kungenzeka ukususa imibiko enganembile phezu - nje usebenzise kuphela isibalo fixed-iphuzu. Ngokwesibonelo, uhlelo zezimali eyakhelwe zokusebenzisa lesi simiso. Nokho, kukhona lula: inani elidingekayo kwamadijithi emva iphuzu zamadesimali is kusengaphambili ezaziwayo.

Ezinye izinhlelo zokusebenza ayigcini, ngoba awukwazi sisebenze noma izinombolo ezincane kakhulu noma enkulu kakhulu. Ngakho lapho usebenza njalo ucabangela ukuthi kungaba ukungalungi, futhi ngoba bheke ngemiphumela kubalulekile round. Ngaphezu kwalokho, ukuqoqa okuzenzakalelayo ngokuvamile ukuntuleka isinyathelo, ngakho-ke ukuqoqa kuchazwa ngokuqondile. yingozi kulesi sici, ukusebenza ukuqhathanisa kakhulu. Kube ngisho ukulinganisa inani amaphutha esikhathini esizayo kunzima kakhulu.