Representation o tau i roto i te rorohiko. Māngai o tau tōpū me ngā tau tūturu i roto i te mahara rorohiko

Tangata e kua tonu whakaaro i roto i toku ora e ki riro i te "AtAKi" kaiwhakahaere pūnaha ranei, noa ki te hono i te rota ki ranei hangarau rorohiko, mōhiotanga e pā ana ki te āhua o te kanohi o tau i roto i te mahara rorohiko, he tino tika. I muri i te katoa, i runga i tenei reo hōtaka taumata-iti pērā i Assembler. Na reira, i tenei ra whakaaro tatou te kanohi o tau i roto i te rorohiko me te whakatakoto a ratou i roto i te pūtau mahara.

reo tohu

Ki te kei te pānui koe i tenei tuhinga, koe pea kua mohio e pā ana ki reira, engari he utu tukurua. E penapena raraunga katoa i roto i te rorohiko whaiaro i roto i te ā-rua pūnaha tau. tikanga o tēnei e me te tuku i tetahi tau koe te puka e tika ana, tito e te o ngā kore, me te hunga.

I roto i te tikanga ki te whakawhiti ritenga mo tatou tau ira ki te rorohiko mahinongofua puka, me te whakamahi koe i te hātepe papatono whakaahuatia i raro nei. He hoki tātaitai motuhake.

Na, i roto i te tikanga ki te hoatu i te tokomaha i roto i te pūnaha ā-rua, e hiahia ana koe ki te tango i to matou uara whiriwhiri a wehe ai i te 2. I muri i taua, tiki matou te hua me te toenga (0 ranei 1). Hua 2 ano wehe me te tamau aau i te toenga. kia tenei tukanga kia korerotia rite te roa rite te hua ka waiho ano 0 1. ranei Na ka tuhituhi i te uara whakamutunga me te toenga i roto i te raupapa whakamuri, rite kua riro matou ratou.

Ko rite te mea kei te tupu i roto i te kanohi rorohiko o tau. Tetahi tau rongoa i roto i te puka takirua, a ka tango i te pūtau mahara.

pūmahara

Ka rite ki kia mohio kē koe i te wae mōhiohio iti ko 1 moka. Ka rite ki te mea kua kite tatou i te kanohi o tau i roto i te rorohiko, e wahi i roto i te hōputu takirua. Ko te kupu, nohoia ia wahi o te mahara e tetahi uara o - 1 0 ranei.

Hoki te rokiroki o tau nui whakamahia pūtau. Ia kōwae 8 paraire o ngā mōhiohio kei roto. Na reira, e nehenehe tatou e faaoti e te uara iti i roto i ia wāhanga mahara ai kia 1 ranei kia he tau-rua waru-paita.

katoa

I te pae hopea ka matou ki te whakanohonga tika o ngā raraunga i roto i te rorohiko. Ka rite ki whakahuatia, te mea tuatahi i te pūtukatuka whakawhiti i te mōhiohio ki te hōputu-rua, a ka anake tukuna te mahara.

Ka tīmata tatou ki te kōwhiringa māmā, i te mea te kanohi o tau tōpū i roto i te rorohiko. Kei te tohaina mahara PC mo te tukanga ko ridiculously maha iti o ngā pūtau - tika kotahi. Ko te kupu, he mōrahi o tetahi mokamoka pea he uara i 0 ki te 11111111. Kia iriti o te tau mōrahi o ngā tāurunga i roto i te puka mua.
X = 1 x 2 ⁷ + 1 x 2 ⁶ + 1 x 2 ⁵ + 1 × 2 ⁴ + 1 x 2 ³ + 1 × 2 ² + 1 x 2 ¹ + 1 × 2 ⁰ = 1 x 2 ⁸ - 1 = 255 .

Na kite tatou e i roto i te kotahi pūtau mahara taea te tūnga i 0 ki te 255. Heoi, pā tenei ki tau tōpū kore-kino anake. Ki te ka hiahia ki te tuhi i te uara tōraro te rorohiko, rerekē katoa haere te iti.

tau tōraro

Na kia kite a e founga te kanohi o tau i roto i te rorohiko, ki te he tōraro ratou. Hoki te tuhi i te uara i te mea iti iho i te kore, whakaritea rua pūtau mahara, 16 paraire o ngā mōhiohio ranei. Ko te kupu 15 haere i raro i te tau iho, ka hoatu te tuatahi bit (mauīmai) e te tohu hāngai.

Ki te he kino te ahua, kua tuhia reira, "1", ki te pai, ka "0". Hoki te māmā o te aauraa, ka taea e koe te utu i te faaauraa e whai ake nei: ki te ko te tohu, ka hoatu 1 ki te kahore he reira, na tetahi mea (0).

Kua whakaritea te toe 15 paraire o ngā mōhiohio i te tau. Waihoki ki te take o mua, ka taea e hoatu e koe he mōrahi o rima wae i roto ia ratou. Me kï reira e ko tino rerekē i ia atu te tomokanga o ngā tau tōraro, me te pai.

I roto i te tikanga ki te hāngai te 2 ngā pūtau mahara he nui ake i te kore ranei e rite ana ki, he waehere tika pera-ka karanga. whakamana ana tēnei mahi i roto i te tikanga ano rite whakaahuatia ana i runga, me te mōrahi A = 32766, ka whakamahi i momotuhi ira. hiahia Just ki te mōhio e i roto i tenei take, "0" e pā ana ki te pai.

tauira

e kore te mea he taua mahi uaua Representation o tau tōpū i roto i te mahara rorohiko. Ahakoa te reira atu uaua te bit, ina tae mai te reira ki te uara tōraro. Hei tuhi i te tau, ko te iti iho i te kore o nei, te whakamahi i te waehere atu.

Ki te tiki i te reira, te mīhini hua he maha o ngā mahi ngaahi houalotú.

1. tuhia Tuatahi uara tawhiti o te tau tōraro i roto i momotuhi takirua. Ko, mahara he rite engari pai te rorohiko.
2. Na, he mahara faatahuriraa ia moka. Hoki tenei whakaaro, e whakakapi e ngā kore, me te te hurihia wae katoa.
3. tāpiri tatou he "1" ki te hua. Tenei ka waiho i te waehere atu.

Ko te tauira oraora Here. Pea to tatou he maha o X = - 131. Tuatahi, whiwhi i te uara tawhiti | X | = 131 te ka tahuri ki te pūnaha ā-rua, me te lekooti o 16 pūtau. whiwhi tatou X = 0000000010000011. muri fulihi X = 1111111101111100. Tāpiri atu ki "1" me te whiwhi i te waehere kōaro X = 1111111101111101. Hoki tuhi i te pūtau mahara moka-16 Ko te maha mōkito o X = - (2 ¹⁵⁾ = - 32767.

hiahia

Ka rite ki a koutou e taea te kite, e kore te mea e uaua te kanohi o tau tūturu i roto i te rorohiko. Heoi, e kore ai e ranea mo te nuinga ngā mahi kōrero o te awhe. Na reira, i roto i te tikanga ki te whakanoho tau nui o rorohiko tukuna mahara pūtau 4, 32 paraire ranei.

Ko te tukanga tuhi e kore e rere ke i taua aroaro i runga ake. Na hoatu noa e matou i te whānuitanga o ngā tau e taea te rongoa i roto i tenei momo.

X _max = 2.147.483.647.

X _min = - 2147483648.

uara Raraunga i roto i nuinga o te wā nui ki te tuhi me te ki te mahi i ngā mahi i runga i te raraunga.

He ona huapai me ngā huakore Representation o tau tūturu i roto i te rorohiko. I runga i te ringa kotahi, hanga tenei tikanga māmā ki te mahi i ngā mahi i waenganui i te uara tōpū, e nui tere ake te pūtukatuka. I te tahi atu te ringa, e kore he nui ki te whakaoti te nuinga raruraru i roto i te ohaoha, te ahupūngao, tauhanga me ētahi atu pūtaiao tenei awhe. Na titiro tatou i teie nei i te tahi atu tikanga mo te sverhvelichin.

ira māngi

Ko te mea whakamutunga e hiahia ana koe ki te mohio e pā ana ki te kanohi o tau i roto i te rorohiko tenei. Mai i reira he he raruraru whakatau i te tūranga o te piko i roto ia ratou, ki te whakanoho i taua tau i roto i te rorohiko e whakamahia ana e te puka taupūtanga, ka tuhi hautau.

Ka taea te māngai Tetahi tokomaha i roto i te puka X p = m * ^{n whai.} Kei hea m - ko te maha o mantissa, p - pakiaka, me te n - te tau kia.

Hei whakakotahi te tau ira tuhi tere whakamahia whai huru, rite tonu ki nei kia nui atu rite ki te 1 / n ranei me iti iho i te 1 te kōwae mantissa.

Kia tatou tau 666,66 homai te. Kia tatou e hoatu a reira ki te puka taupūtanga. I roto i te x = 0.66666 * ¹⁰ Maehe. P = 10, me te n = 3.

I te rokiroki o tere uara ira te tikanga tohaina 4 8 ranei paita (32 paraire ranei 64). I roto i te take tuatahi i huaina ai ko te maha o kotahi-pū, i te tuarua - te pū rua.

O te paita 4 tohaina mo te rokiroki o ngā tau, 1 (8 paraire) hoatu i raro nei i runga i nga raraunga tukanga me tona tohu, me 3 bytes (24 paraire) mo rokiroki i te mantissa waiho tona tohu me i te taua parau tumu rite mo te uara tau tōpū. E matau ana tenei, e taea te hanga matou i te tahi mau tātai ohie.

Ko te uara mōrahi o te n = ² 1111111 127 = ^10. I runga i taua mea, ka taea e te tiki tatou te nui mōrahi o tau e taea te rongoa i roto i te mahara rorohiko. X = ^2127. Na ka taea e tatou tātai i te mantissa taea mōrahi. Ka riro te reira rite ki te 2 ²³ - 1 ≥ 2 ²³ = 2 ^{(10 × 2.3)} ≥ 1000 ^2.3 = 10 ^{(3 × 2.3)} ≥ 10 ^7. Ka rite ki te hua, whiwhi tatou he uara tata.

Na, ki te mea te whakakotahi tatou e rua o te tātai, te tiki matou te uara e taea te rongoa, kahore mate o 4 paita o mahara. Ka riro te reira rite ki X = 1.701411 * 10 ^38. E whiua ana te toe mati, no te mea taea reira ki a koe i te pū o te tikanga o te tuhi.

pū rua

Mai kua peitatia tātaitanga katoa a faataa i roto i te paratarafa o mua, i konei korero matou ki a koutou katoa rawa tata. Hoki tau hanga pū rua e te nuinga o tohaina 11 paraire mo te tikanga, me tona tohu me te 53 paraire mo te mantissa.

1111111111 n = ² 1023 = ^10.

M = ^{2 52 -1 = 2 (10 *} 5.2) = 1000 5.2 = 10 15.6 . Moremore, me te whiwhi i te tau mōrahi = 2 X ¹⁰²³ ki runga ki "m".

Te ti'aturi nei tatou i te mōhiohio e pā ana ki te kanohi o tau tōpū me ngā tau tūturu i roto i te rorohiko, kua whakaratohia matou, he mea pai ki a koutou i roto i te whakangungu, me te ka waiho he iti bit mārama atu te mea te nuinga o te wā i tuhituhia i roto i te pukapuka.