He aha te he tau ira tere?

Ko te whakaaturanga o tūturu (tūturu ranei) tau, kei hea e rongoa ratou rite te mantissa me taupū e tere tau ira (pea ira, rite he tikanga i roto i te whenua Ingarihi-korero). Ahakoa tenei, whakaratohia te maha kei te ki te tika whanaunga whakaritea, me te huri pūmau. Kanohi whakamahia nei te tino auau, whakaaetia paerewa IEEE 754. Mathematical ngā mahi e whakamahi tau māngi-ira e whakatinanatia i roto i te rorohiko pūnaha - e rua pūmārō me te pūmanawa.

Point te piko ranei

Ko te rārangi taipitopito o te Whakawehe ā-ira tāutu aua whenua English-korero me te anglofitsirovannye, te wahi i nga pūkete o tau wehea e te wahi hautanga o te pūwāhi katoa, no te mea ka tangohia te kupu o enei whenua te ingoa māngi ira - "tētē ira". I roto i te Russian Federation, te wahi hautanga o te katoa o te iho, wehea e te piko, na tohu reira kua mua mohio te taua ariā te wā "tētē ira". Heoi, i tenei ra i roto i te tuhinga hangarau me i roto i te tuhinga Russian te whakaaetia reira kōwhiringa e rua.

Ko te wā "tētē ira" ahu i te meka e te kanohi tau tū ko te piko (ira noa ranei ā-rua - he rorohiko) e taea uru ki hea i roto i te tau rārangi. Tēnei āhuatanga he tino ki te stipulate reira motuhake. tikanga o tēnei e taea te i titiro te kanohi o tere tau ira rite te whakatinanatanga rorohiko o momotuhi taupūtanga. tupu te painga o te whakamahi i te kanohi taua o te hōputu kanohi whakaritea-ira me tau tōpū e ngā o ngā uara tino ina tonu taua tika whanaunga tonu.

tauira

Ki te te piko i roto i te maha o whakaritea, ka tahu he reira hōputu kotahi anake. Hei tauira, i homai he wahi o te ono i roto i te maha, me te rua mati i roto i te wahi hautanga. Ka taea te mahi i tēnei anake i roto i tenei ara: 123456,78. Ko te hōputu o tere tau ira hoatu hōkai tonu mō te faaiteraa. Hei tauira, hoatu te waru mati taua. kia i tetahi kōwhiringa tuhi ki te kore e te kaihātepe hanga he rua-mati nohopuku ohipa mara atu, te wahi e tuhi ai te taupū e Ko te tikanga he 10, me i te 0 ki te 16, me tukunga ia ka waiho i te tau tapeke tekau 8 + 2.

Ētahi taatou o te tuhi, e taea ai e koe te whakahōputu tau ki mata tere: 12345678000000000000; 0,0000012345678; 123,45678; 1.2345678 a na i runga i. I roto i tenei hōputu, i reira he ara he wae o te inenga o te tere! Engari, ko te mahi o te pūnaha rorohiko e tuhi te tere i nei mahi ngā mahi i te rorohiko wahi i reira he kanohi o tere tau ira. whanganga ana tēnei mahi i roto i ngā o flops (ngā mahi māngi-ira ia tuarua, e whakawhiti ki te maha o ngā whakawhitinga ia rua ki te wāhi tere). Ko te kōwae taketake i roto i te tere pūnaha rorohiko inenga tenei.

hanganga

tau Tuhia i roto i te hōputu mata māngi he tika e whai ake, te mātakitaki i te raupapa o nga wahi whakahauanga, no te mea he taupū tenei lekooti, e whakaatu ana i nga tau tūturu rite te mantissa kia me. he tika ki te tohu i ngā tau nui rawa, me te iti rawa i te reira, e nui māmā ki te pānui i ratou. wahi e hiahiatia ana: ko te tokomaha tuhia (N), te mantissa (M), te tikanga o te tohu (p) me te raupapa (n). Ko te āhuatanga whakamutunga e rua o te tohu. No reira, N = ^M. n ^p. Heoi tuhituhia tau māngi-ira. Ka kia kehekehe tauira.

1. He mea tika ki te tuhi i te maha o tetahi miriona, kia rite kore ki te kia ngaro i roto i nga ngā kore. 1000000 - Ko reira he tuhi noa, tauhanga. He rorohiko Ko e whai ake: ^1.0. Nuku ^6. Ko, kotahi tekau ki te ono o nga mana - e toru nga tohu, e uru i roto i te hunga i rite ono ngā kore. Ko te kupu puta kanohi o tau o pūwāhi pūmau, me te tere te wahi tonu e taea te kitea ngā rerekētanga i roto i te takikupu.

2. A he tokomaha pakeke taua he 1,435,000,000 (kotahi piriona wha rau e toru tekau-rima mano) e taea te tuhituhi hoki noa: ^1.435. Mahuru ^10, anake. Na ko reira ki te tohu tango e taea tuhituhi i tetahi tau. Ko te reira, a ka rerekē i ia atu ki te maha o te pūwāhi pūmau, me te tere.

Ko te reira atu o te āhua o ki te kia iti? Ae, ngāwari rawa.

3. Hei tauira, rite te tohu kotahi te milioniraa? = 0.000001 ^1.0. 10 ^-6. Nui ngä me tau tuhituhi, a pānui reira.

4. He uaua ake? E rima rau me te wha tekau-ono o milia: 0.000000546 = ^546. 10 ^-9. Here. Ko te tino whānui te whānuitanga o te pūwāhi tere.

āhua

pea tau Puka noa tonu o ranei. Pūnoa - faatura tonu te pū o tere tau ira. Me kï reira e te mantissa i tenei puka, kahore tango ki pūkete te tohu, he hawhe o te wā 0 1, ka 0 ⩽ he <1. E kore i roto i te puka noa o te maha o te ngaro tona tika. Ko te ngoikoretanga o te puka noa ko e taea te tuhituhi maha tau i roto i te ara rerekē, e he rangirua. TAUIRA pūkete rerekē o te tau kotahi: 0 = 0.0001, ^000001. February ¹⁰ = ^0.00001. January ¹⁰ = ^0.0001. 10 ⁰ = ^0.001. 10 ^-1 = ^0.01. 10 ^-2, a kia taea e nui ake. Ko Ko te aha whakamahi te rorohiko he momotuhi tonu o rerekē, te wahi riro te ira mantissa te uara o nga wae (urutomo), a ko te kupu ki tekau (e kore e whakaurua), me i te ara ano te tau ā-rua mantissa he uara i waenganui i tetahi (urutomo) ki e rua (e kore e urutomo).

Na, 1 ⩽ he <10 tenei -. Tau ā-rua hopu ki te mata tere, me tenei ahua o tuhi i tetahi tau (kore anake) he ara ahurei. Ko ano hoki i reira ko te drawback - te ngoikore ki te whakaaro tenei ahua o te kore. Na reira whakarato Informatics mo te whakamahi o ngā tau motuhake 0 tohu (moka). He rite ki te 1 (wae paruhi) te wāhanga tau tōpū o (MSB) o te mantissa i roto i te tau ā-rua te kore anake i roto i te puka tonu o. whakamahia tēnei lekooti te paerewa IEEE 754. Ko te pūnaha tau tū, ai ko te turanga ake atu i te rua (ternary, quaternary me ētahi atu pūnaha), e kore te tenei taonga hokona.

reals

tau tūturu me tere ira, me te he te nuinga o tika rite kore ko reira te kotahi anake, engari he huarahi tino watea ki te tohu i te tau tūturu, me te mea, he ngātahitia i waenganui i te whānuitanga o ngā uara, me te tika. Ko e ngákaunuitia ki momotuhi taupūtanga tenei, anake whakamana i runga i te rorohiko. tau Māngi-ira - he huinga o nga paraire takitahi e wehea ki te tohu (tohu), kia (taupū) me mantissa (eia). Ko te hōputu tino noa ko te IEEE tau 754 tere-ira rite te huinga o nga paraire e whakawaehere he wahi o ona mantissa, te tahi atu wahi - te tohu, me te kotahi wahi tohu te tohu o te tau: kore - ki te he reira pai, te wae - ki te he kino te tau. tuhia te tukanga katoa e te maha (code-neke), me te mantissa - i roto i te puka tonu o, tona wahi hautanga - i roto i te pūnaha ā-rua.

Ia tohu - ko te bit kotahi e tohu te tohu mō ngā tau māngi-ira katoa. Mantissa kia me - he tau tōpu, ratou, me ki te tohu, me te hanga i te kanohi o tere tau ira. Ka taea te huaina e te tukanga he taupūtanga taupū ranei. E kore e taea e tūturu tau katoa kia kanohi i roto i te rorohiko i roto i to ratou auraa tangohia, e nga ētahi atu aroaro uara āwhiwhiwhi. He kōwhiringa nui ohie - ki te tuku i te tau tūturu me te wāhi i whakaritea, i reira te mau me te wahi katoa, ka pupuri i te motuhake. Te nuinga pea, kia e te wahi te wahi tōpū tonu paraire X, me te hautanga - paraire Y. Ko te hoahoanga o pūtukatuka kore e mōhio o te tikanga taua, engari kua hoatu hoki hiahia ki te maha o te pūwāhi tere.

tua

Addition o tere tau ira, ko te tino ohie. I roto i te hononga ki te IEEE 754 tau pū kotahi paerewa he maha nui o paraire kua reira, na he pai ki te neke i runga i ki nga tauira, me te whakaaro pai ki te tango i te iti rawa te maha māngi-ira. Hei tauira, te tau e rua - X me Y.

Ko nga kaupae e whai ake:

he) Me māngai te tau i roto i te puka tonu o. Ko reira mārama he tetahi huna. X = ^1,110. 2 ^2, a Y = ^1,000. 2 ^0.

b) A tamau i te tukanga o te hanganga e taea anake whakaōrite i te exhibitors, engari me te reira ki te tuhituhi anō i te uara o Y. e hāngai reira ki te uara o nga tau tonu o, ahakoa i roto i te meka - unnormalizes.

Tātaihia te rerekētanga i waenganui i te taupū o te tohu 2 - 0 = 2. Na neke te mantissa ki utu mo enei huringa, e ko, tāpiri 2 ki te taupū o te wā tuarua, ko te kupu neke i te piko wae huna i rua ngā ki te maui. 0,0100 te ^whiwhi. 2 ^2. Tenei ka te ōrite o te uara o mua Y, na reira he kē he Y '.

c) Na e hiahia ana koe ki te tāpiri i ake te maha o mantissa X me Y. whakaritea

1.110 + 0.01 = 10.0

tonu kanohi Exhibitor e te tawhā X, i te mea rite ki te 2.

g) Ko te moni riro i roto i te taahiraa o mua, neke te wae māori, ka hiahia koe ki te nuku i te moni taupū me te faahiti. 10.0 ki e rua paraire ki te maui o te ira, te tau, ko te inaianei tika ki te haerenga, arā, neke te piko ki te mahue i tetahi ira, me te taupū, aua, nui haere e 1. Huri i te reira i roto i ^1,000. 2 ^3.

e) Ko te wa ki te tahuri i te tau ira tētē i roto i te pūnaha kotahi-paita.

mutunga

Ka rite ki a koutou e taea e kite, te tāpiri i kore e pakeke rawa enei tau, tetahi e taritari piko. Te kore, o te akoranga, ki te kahore hoki mau mai i te maha o te taupū raro i roto atu (i roto i te tauira i runga ake, ko reira te Y ki X), kia rite ki te pai kia rite ki te faaho'iraa mai o te tatūtangā, arā, te take o te utu - neke te ira ki te maui o te mantissa. A, no te mea kua oti tono te tua, ko reira rawa e taea, me te tonu tetahi raruraru - perenormirovanie me te poporetanga moka, ki te kore ratou tokomaha e ōrite te maha ki te tohu i te reira.

whakareatanga

pūnaha ā-rua tuku e rua ngā tikanga i ai whakamahatia nga tau māngi-ira. kia tenei mahi e whakamana i te whakareatanga, i haamata ki te iti rawa nui paraire me e haamata ki te paraire kia tiketike i roto i te whakanui. he maha o ngā mahi raupapa tāpae hua wāhanga i roto i take rua. E whakahaeretia e te tua o paraire whakanui enei ngā mahi. Na, ki te mea ko te waeine kotahi o nga paraire o te whakanui, tupu te moni o ngā hua wāhanga o te multiplicand ki te neke hāngai. Ki te tomo te mati o te whakanui kore, i te kore e te multiplicand tāpiri.

Ki te whakamana i whakareatanga te rua noa ngā tau, e kore te hua o te tau i roto i tona nui e taea nui te maha o ngā mati i roto i roto i te āhuatanga, neke atu i te rua, ka hoki tau nui ko reira rawa, rawa nui. Ki te whakanuia e etahi maha, e kore mōrea te hua pai i runga i te mata. No te mea ko te tino fakataimí te maha o nga paraire o tetahi mīhini mamati, a taruke ana e ia ki te haapa'o noa i te he mōrahi o te maha rua o te neke mati. A ki te iti te maha o nga wahi e, i roto i te hua, ka te taniwha, whakamōhio hapa. Ki te he nui te nui o te tätaitanga, te hapa o te inaki, ka rite ki te hua nui ake te tika whānui. Here, te ara anake - ki tawhio nga hua whakareatanga, ka i tauutuutu i te mahi hapa. A, no te he mahi whakareatanga, riro te reira taea ki te haere ki tua atu i te tukutuku o ngā mati, engari anake i te teina, no te mea i reira te mea he rohe utaina ki runga ki te maha o tei faahoho'ahia i roto i te puka o whakaritea-ira.

etahi whakamārama

He pai ki te tīmata i te timatanga. Ko te ara tino noa ki te tohu i te maha - tau raina hei tōpū, te wahi Poiete te piko te i roto i te mutunga rawa. Ka taea e tēnei string e tetahi roa, engari he piko tu i roto i te wahi e tika ana ki te hoatu i te reira, wehe i te tau tōpū i te wahi hautanga o reira. Ko te hōputu o te whakaaturanga o te pūnaha whakaritea-ira tika e etahi tikanga i runga i te wāhi o te tekauira. whakamahi momotuhi Scientific te tirohanga tonu o paerewa o te kanohi o tau. Te reira i aqn {\ displaystyle aq ^ {n }} aq n. Here he {\ displaystyle ^he} he, a ka huaina te mea te miro mantissa. kua Just e pā ana ki reira kua mea e 0 ⩽ he mārama: n {/ displaystyle n} n - he taupū tau tōpū, me te ^q {/ q displaystyle} q - ano he tau tōpū, e ko te pūtake o te pakiaka (ko maha he reta 10). Mantissa waiho te piko i muri i te mati tuatahi, e kore he nei kore, engari kua whakawhiti tuhi atu ki te kōrero i runga i te uara hakari o te tau.

tau Māngi-ira te tuhituhi te tino rite ki mārama tau urunga paerewa katoa, te taupū me te mantissa anake kua oti te tuhituhi motuhake. Last ki te taua, me te i roto i te hōputu tonu o - ira whakaritea, te whakapaipai nei ki te nui mati tuatahi. Just tere ira whakamahia te matua i roto i te rorohiko, e ko, i roto i te kanohi hiko o te wahi e kore e ira te pūnaha, me te-rua, te wahi noa mantissa Denormalize wāhi anō - inaianei ko reira te aroaro o te mati tuatahi, na i mua, e kore i muri i reira, i reira te wahi tōpū i roto i te parau tumu, e kore e taea e. Hei tauira, e homai i to tatou iho pūnaha ira tona pūnaha ā-rua iwa hoki te whakamahi rangitahi. A ka tuhi e me tona mantissa tere-ira rite tenei: +1001000 ... 0, a reira me te taupū 0 ... 0100. Ko kore te pūnaha ira ki te whakaputa i taua tātai uaua, e ai kia i pūtakerua, te whakamahi i te puka o te pūwāhi tere.

tauhanga roa

I roto i te rorohiko hiko kua hanga-i roto i te pōkai pūmanawa, te wahi tohaina hoki te mantissa me taupū o te nui o te mahara tohua pūmanawa, iti anake e te rahi mahara o te rorohiko. rite te tauhanga roa, e ko, ngā mahi ohie i runga i ngā tau e mahi rorohiko titiro te reira. Ko te te taua katoa - tangohanga me te tua, wehenga me te whakarea, mahi timatanga me te hanga o te pakiaka. Ko te maha o te tino rerekē, he tino nui atu te roa o te kupu mīhini ratou kaha. E kore te mea te whakatinanatanga o enei ngā mahi i te taputapu me ngā pūmanawa, engari kua whakamahia whānuitia reira pūmārō taketake ki te mahi ki tau nui iti o whakahau. He he ake me tātai, tau roa anake iti te wahi i te kaha mahara - te noho tauhanga pū. whakamahia te tauhanga roa i roto i mara maha.

1. Ki te whakahiato i te waehere (pūtukatuka, microcontrollers ki hohonu moka iti - rēhita moka-10 me te roa kupu moka-waru, e kore i te mea nui ki te hapai i te mōhiohio i te Analog-ki-mamati (tairitenga-ki-mamati pūtahuri), a na reira e kore e taea te mahi i waho i te tauhanga roa.

2. Kei te hoki te whakamahia te reira i te tauhanga roa mō te tuhiwhakamuna, kei hea he mea e tika ana ki te whakarite i te tika o te hua o te mana rea whakareatanga ranei ki ^10.309. whakamahia tauhanga tōpū te modulo m - he tau tūturu nui, a kahore he tika ohie.

3. Pūmanawa mō financiers me mathematicians, rawa kore ko, kahore he tauhanga roa, no te mea ki anake te ara manatoko i te hua o te tātaitanga i runga i te pepa - ki te awhina o te rorohiko, te whakarite tika tiketike o nga tau. Māngi wāhi e taea e ratou ngā tetahi maha o rere roa. Ko te tātaitanga engineering me te mahi o pūtaiao rapu wawaotanga tātaitanga hōtaka rawa maha, no te mea he tino uaua ki te hanga i te raraunga tāuru kahore hanga hape. Ko te nuinga o ratou nui atu whakaemi atu i ngā hua whakaawhiwhi.

Whawhai ki hapa

A, no te ki te maha o ngā mahi i roto i nei te wāhi tere, he reira tino uaua te aromatawai i te tika o nga hua. Ehara i ano whakaaro makona i te ariā pāngarau katoa e pai te āwhina ki te whakatau i tēnei take. Ko te tau tōpū hapa arotake ngāwari. Ko te taea o te pae whakakahoretia o haupūtanga i runga i te mata - te whakamahi tika i te maha anake o whakaritea-ira. Hei tauira, hanga he hōtaka pūtea i runga i tenei parau tumu. Heoi, i reira e ngāwari: mohiotia te tau e hiahiatia ana o ngā mati i muri i te ira i roto i mua.

e kore e Ētahi atu tono iti ki, no te mea e kore koutou e taea e te mahi ki rānei tau iti rawa ranei rawa nui. Na ka mahi koutou e nga wa katoa ki te pūkete e reira kia haupūtanga, a no te mea te piripiri ore o te hua, ko te mea e tika ana ki te a tawhio. Ano, he whakaawhiwhi aunoa maha he kore o te mahi, a na reira te whakaawhiwhi tautuhi te āta. Tino kino tenei faatura, te mahi whakarite i roto i. He ngā ara whakatau tata i te nui o ngā hapa heke mai ko te tino uaua.