He aha mea he lana wahi helu?

ʻO ka hōʻike o maoli ( 'ole maoli) nui, kahi a lakou i waiho ai me ka mantissa a me ka exponent e lana wahi helu (paha wahi, e like me ke ano mua i loko o ka' ōlelo Pelekānia-olelo ana'āina). I loko nō o kēia, ua hoomakaukau i ka helu a me ka paa pili pololei a me ka hoʻololi loa. E hoohalike ai i ua hoʻohana 'loa pinepine, i aponoia maʻamau IEEE 754. makemakika hana i hana lana-wahi nui i hoʻokō i ka Me nenoai - nā lako e pono ai.

Point ole comma

Ka piha papa o kekimala separator e hōʻike ana i ka poe English-olelo ana aina a me ka anglofitsirovannye, ma ka mooolelo o ka helu hookaawale ae ma kekahi fractional hapa o ka mea a pau wahi, no ka mea, o ka terminology o kēia mau'āina aponoia i ka inoa lana wahi - "lana wahi". Ma ka Russian Hui, ka fractional hapa o ka pau o ka moolelo, kaawale ma ke comma, pela no ka mea, ho i ka ia manaʻo i Hawaiʻi nei ike i ka manawa "lana wahi". Naʻe, i kēia lā i loko o ka oaoieei-nā moʻolelo, a ma ka Russian moʻokalaleo ka mea, ua ae nā koho.

Kaʻia "lana wahi" originated mai i ka mea ana i positional helu e hoohalike ai i ke comma (maʻamau kekimala a aeaie - he kamepiula) i hiki pono anywhere i waena o ka laina helu. Kēia hiʻona Heʻoiaʻiʻo, e stipulate mea kaawale. Kēia 'o ia hoʻi i ka mea e hoohalike ai o ka lana wahi helu hiki e manao like i kekahi kamepiula manaʻo o exponential notation. I ka lanakila o ka hoʻohana 'ia o ka hoohalike o ka hoohalike ai waihona paa-wahi a me ka helu helu i ka laulā o nā loina ulu me ka nui loa ia i pili pololei koe ua hoʻololiʻia.

Eia kekahi laʻana

Inā ka comma i loko o ka helu o ka paa, alaila, e puhi ia mea wale nō hoʻokahi format. No ka laʻana, haawi mai i ka wahi o ka eono ma ka helu a me nā huahelu ma ka fractional hapa. Ua hiki ke hana wale ia ma keia aoao. 123456,78. I ka waihona o ka lana wahi helu haawi piha laulā no ka hōʻike. No ka laʻana, haawi mai i ka ia ewalu huahelu. Kākau i nā koho e ia i kekahi ina ka programmer aʻole ole e huahelu elua-he skimp hana i nā mahinaʻai, ma ka mea e hoʻopaʻa i nā exponents i mea nō kāu 10, a mai ka 0 a hiki i 16, a me ka hookuuia ana o ka huina helu e e he umi 8 + 2.

Kekahi mau nā kinolau o ka hoʻopaʻa, a leie aku oe i ka waihona nui me ka lana wahi: 12345678000000000000; 0,0000012345678; 123,45678; 1.2345678 a no laila, ma luna o. Ma keia waihona, he mea hiki i ka pa alima o ka ana o ka holo! Kaupalena naʻe, i ka hana ana o kekahi kamepiula'ōnaehana i na mooolelo i ka mämä holo i i ke kamepiula hanaʻia ana kahi mea e hoohalike ai no lana wahi helu. Keia hana ana ua ana i ka hua'ōlelo o FLOPS (lana-wahi ana no kekona, a translates i ka helu o ka hana no kekona me ka lana wahi). 'O kēia ke kumu o ka mokuna i loko o ke ana kamepiula'ōnaehana holo.

'ole

E palapala i ka helu ma ka lana wahi waihona mea pono e like me ia mahope iho, ka malama ana i ke kaʻina o ka OAXA māhele, no ka mea, keia mooolelo mea exponential, a hōʻike mai i ka helu maoli me ka mantissa a me ka pono. He mea pono e kū no hoi nui a me ka loa ka nui, ka mea, ua ikaika nui ae maʻalahi ka heluhelu. Koi 'ia māhele: ka mea kākau helu (N), ka mantissa (M), i ka mea o ka hoailona (P), a me ka mea (N). Ka hope mau hiʻona o ka hoailona. Nolaila, N = ^M. N ^p. No laila, i kākau lana-wahi helu. Ano he kumu hoʻohālike e e e lauwili.

1. He mea pono i ka palapala i ka helu ana o kekahi miliona, no laila, like ole no ka nalowale i loko o ka 'Aʻohe hualoaʻa. 1000000 - ia mea he maʻamau i hoʻopaʻa 'ia, makemakika. A kamepiula Ua like penei: ^1.0. October ^6. Ia mea, he umi i ka ono o ka mana - ekolu hoailona, i kupono i ka poe a pau eono 'Aʻohe hualoaʻa. Ke'ōlelo mai ia lŘlŘ e hoohalike ai o ka loa o ka paʻa a me ka lana wahi kahi koke hiki huai ae oko ao ma ka pela.

2. A ua ka paakiki helu o 1,435,000,000 (hoʻokahi piliona,ʻehā haneri a me ke kanakolu-kumamalima tausani) i hiki ke kākau wale: ^1.435. September ^10, wale. Pela ia mea me ka hua hoʻolawe ke kākau i kekahi helu. ʻO ia ka mea, a oko mai kekahi i kekahi me ka helu o ka paʻa a me ka lana wahi.

Akā, he oi o pehea e e haʻahaʻa? Ae, he hiki wawe ka.

3. No ka laʻana, e like me ka kekahi millionth mark? = 0.000001 ^1.0. 10 ^-6. Nui kōkua ai i nā a me ke kākau nui, a me ka heluhelu ia.

4. A oi huikau? Five haneri a me kanaha-ono billionth: 0.000000546 = ^546. 10 ^-9. Here. I ka laulā o ka lana wahi ka loa ka laula.

shape

Palapala helu i e maʻamau paha normalized. Normal - mau mahalo i ka miomio o lana wahi helu. It E e hoʻomaopopo i ka mantissa ma keia palapala, me ka lawe i ka mooolelo o ka hoailona, ka hapalua o ka wā mawaena 0 1, laila 0 ⩽ ka <1. 'Aʻole i loko o ka maʻamau ano o ka helu o ke haalele i kona pololei. Ke keakea ana o ka mea maʻamau palapala nei i na huahelu hiki ke kākau i loko o naʻano likeʻole, i mea kekahi henua. Kumu kekahi mau mooolelo o na ia helu: 0 = 0.0001, ^000001. February ¹⁰ = ^0.00001. January ¹⁰ = ^0.0001. 10 ⁰ = ^{0.001. 10 -1} = ^0,01. 10 ^-2, a no laila, hiki e nui aku. Ia mea ke kumu o ka kamepiula hoʻohana he okoa normalized notation, ma ka mantissa kekimala kuhi i ka waiwai o ka huahelu (aupuni), a pela i ka umi (i hui pū), a ma ka like o ka mantissa aeaie helu i ka waiwai ma waena o kekahi (aupuni) i elua (i kauoha aupuni).

No laila, 1 ⩽ he <10 He -. Aeaie helu me ka lana wahi, a me keia ano o ke kākau i kekahi helu (koe Aʻohe) ka hopuʻia kekahi hanana ala. Akā, ua koe mai kekahi drawback - ka hikiʻole, e hoi i noonoo ai i kēiaʻano o ka 'Aʻohe. No laila, informatics eaaaony no ka pono o kūikawā helu 0 ka hoailona (iki). Ka helu wahi o (MSB) o ka mantissa i loko o ka aeaie helu koe Aʻohe i loko o ka normalized palapala Ua like no 1 (implicit pa alima). Keia mooolelo Ua hoʻohana 'maʻamau IEEE 754. Na positional helu'ōnaehana, kahi o ka waihona ipu, ua oi aku mamua o elua (ternary, quaternary a me nā nenoai), keia waiwai ua i ho'ōla pānaʻi ai.

maoli

Real helu me ka lana wahi, a ua IeAUPIIe, IAa IO e like me ka mea mea ole ka mea wale kekahi, akā, he o ia ho i kekahi maoli helu loa kupono ala, me he mea la, heʻae like hoʻokuʻu ma kahai ma waena o ka laulā o nā loina a me ka pololei. Kēia mea analogous i exponential notation, wale hana ma ke kamepiula. Lana-wahi helu - he lākou o kanaka'āpana ua puunaueia i ka hoailona (hoailona), mea (exponent) a me ka mantissa (mantis). Ka loa, he pono ole waihona mea he IEEE 754 lana-wahi helu like me ka lākou o nā'āpana i encode i kekahi hapa o kona mantissa, ka kekahi hapa - ka degere, a me ka kekahi iki Hōʻike i ka hoailona o ka helu. Aʻohe - ina ia mea 'oluʻolu, ka mokuna - ina ka helu mea io. Ke kaʻina hana holoʻokoʻa ua palapalaʻia ka helu (kuhi-naeaeaa), a me ka mantissa - i loko o ka normalized palapala, kona fractional hapa - i loko o ka aeaie nenoaiu.

Kēlā me kēia hōʻailona - mea he hookahi iki i Hōʻike ka hoailona no nā mea a pau e lana-wahi helu. Mantissa a me ka mea - i integers, mea, a me ka hoailona, a e ka e hoohalike ai o ka lana wahi helu. Ke kaʻina hana hiki ke kapaia he exponential paha exponent. 'Aʻole i pau ka makemake nui e hoʻokū' ia ma ke kamepiula i loko o kā lākou mau hua'ōleloʻano, e hōʻike mai iā ia i nā mea e ae He kokekau wale nā loina. A nui simpler hōʻoia - e waiho i kekahi maoli helu me ka paa wahi, ma ka oiaio a me ka mea a pau loa, e e mālama ana. Loa paha, no laila, i ka helu 'ana ua mau haawiia X'āpana, a me ka fractional - Y i nā kānaka. Akā, ke kuhikuhipuʻuone o nā unu lawelawe iʻaʻoleʻike nōʻo ia ia i kekahi papa hana, akā, ua hāʻawiʻia mai i ka helu o ka lana wahi, no ka mea koho.

Eia hou kekahi

Hou o ka lana wahi helu mea he mea. I e pili ana me ka IEEE 754 maʻamau hookahi miomio helu ia mai he nui helu o nā'āpana, no laila ia mea maikaʻi, e neʻe ana i nā hōʻailona, a me ka maikaʻi manaʻo e lawe i ka mea uuku lana-wahi helu. No ka laʻana, ka mea mau helu - X a me Y.

Nāʻanuʻu e like penei:

i) ka helu pono e na poe i normalized palapala. He maopopo he huna kekahi. X = ^1,110. 2 ^2, a me Y = ^1,000. 2 ^0.

b) E hoomau i ke kaʻina hana o ka haku mele 'hiki wale equalize na exhibitors, akā, ka mea pono, e rewrite i ke kumukuai o Y. It, e hoʻopili like i ka waiwai o ka normalized helu, koe ma ka mea - unnormalizes.

E huli i ka likeʻole ma waena o nā exponents o ke degere 2 - 0 = 2. Ano, hoʻoneʻe i ka mantissa e compensate no kēia mau loli,ʻo ia hoʻi, hui 2 a hiki i ka Papa kuhikuhi o ka lua o ka makahiki, pela e neʻe i ka comma huna huahelu ma nā wahi ma ka hema. 0,0100 ua ^loaa. Pepeluali ^2. Kēia e ia i ka like o ka mea mua cia Y, alaila, he mea ano he Y '.

c) Ano, e pono e hoonui i ka helu o ka mantissa X a me Y. like

1,110 + 0,01 = 10,0

Exhibitor nō ua poe e ka X aiao, i mea like me 2.

g) ke dala i loaa i loko o ka mua ka anu u, 'oni iki ka normalization pa alima, a laila, e pono e hoʻololi i ka exponent huina a me' oe. 10,0 a me nā'āpana a hiki i ka hema o ka kekimala wahi, i ka helu mea e pono e normalize, 'o ia hoʻi, neʻe i ka comma a hiki i ka lima hema ma kekahi wahi, a me ka exponent, pakahi, mahuahua ma 1. Ua huli mai ^1,000. March ^2.

e) He manawa, e hoohuli i ka lana wahi helu i loko o hookahi-ʻai nenoaiu.

ka hopena

E like me 'oe ke ike, hui mau helu i ole pohihihi, i kekahi mea e lana comma. Ināʻaʻole, o ka papa, koe wale no ka lawe ana i ka helu o lalo, exponent i waena o oi (i loko o ka luna kumu hoʻohālike, ka mea, ua ka Y i ka X), e like me ka hoihoi hou ia ana o ke kūlana quo, oa ke kahe o ka uku - hoʻoneʻe i nā kekimalaʻoi ana i ka hema o ka mantissa. I ka wa a ka poe koa hou i mua, ua noi ia, ia mea loa e hiki, a no kekahi pilikia - perenormirovanie a me ka truncation iki ina lākou helu 'aʻole i like loa me ka helu, e ko ia.

multiplication

Aeaie'ōnaehana kaumaha ana i mau ki ina hana like ana i multiplies ka lana-wahi helu. Kēia hana i hanaʻia nō ia ma ka multiplication, i hoʻomaka me ka mea uuku nui'āpana, a i hoʻomaka me ke kiʻekiʻe'āpana mea i loko o ka multiplier. He mau hihia iloko o ka helu o nā hana sequentially stacking hapa huahana. Mau hana i noho mana ana ma ka hou o ka multiplier i nā kānaka. No laila, ina kekahi o nā'āpana o ke multiplier mea he pa alima, ka huina o ka helehelena huahana o ka multiplicand ulu me ka AYEIE naeaeaa. Inā he huahelu o ka multiplier kokolo Aʻohe, oiai i ka multiplicand ua hou.

Inā multiplication ua hana pono mau helu, i ka huina hoonui o ka loa i loko o kona dala hiki ole oi aku i ka helu o nā huahelu na i loko o nā kumumea, oi ma mua o palua, a no ka nui loa ia ka loa, loa nui. Inā hoonuiia e kekahi helu, ka huina hoonui ka pilikia i pono ma luna o ka pale. No ka mea, o ka helu o nā'āpana o kekahi mīkini mīkini ka loa finite, a me ia poe koa, e hoopaa i kekahi i kā mākou o ka palua o ka helu ana o adders huahelu. A ina o ka helu o nā wahi ua kaupalena, i loko o ka huina hoonui e inevitably mai i ka wahaheʻe. Inā i ka nui o ka computation mea nui, i ka hewa o ke ano, a me ka hopena nui maoli ka pono pololei. Eia, ka mea wale ala - e hoopoepoe i ka multiplication hualoaʻa, alaila, o ka hewa hana i alternating. I ka wā o ka multiplication ana, e lilo ia i hiki ke hele aku ma kēlāʻaoʻao o ka maka aha o nā huahelu, akā, wale ma ke kaikaina, no ka mea, ke kali kau ma luna o ka helu o i i na poe ma ke ano o ka haka-wahi.

kekahi mau wehewehe

Maikaʻi, e hoʻomaka mai ke kinohi. Ka loa, he pono ole ala o ia ho i ka helu - laina helu me ka helu, ma ka comma ua ua hoʻohuʻuʻia i loko o ka mea hope. Kēia kaula hiki e kekahi lōʻihi, akā, he comma ku ma ka akau, wahi, e waiho aku ia mea, e hoʻokēʻai i ka helu, mai ka fractional hapa o ia. I ka waihona o ka hōʻike o ka haka-wahi'ōnaehana pono e ukuhi i kekahi rula ma luna o ka wahi o ka kekimala wahi. ʻepekema notation hoʻohana i ka hae normalized nānaina o ka hoohalike o ka helu. It aqn, \ displaystyle aq ^ {N }} aq n. Eia kekahi, \ displaystyle ^he} i kekahi, a me ka mea, ua kapaia ka mantissa kaula. Anna no ka mea, ua olelo mai ia 0 ⩽ he hala ole: N, / displaystyle N} N - he helu exponent, a me ka ^Q {/ displaystyle Q} Q - i ka helu, i mea ke kumu o ka radix (i ka palapala o pinepine 10). Mantissa waiho i kekahi comma ma hope o ka huahelu mua, i mea ole 'Aʻohe, akā, ua hoolilo hou i hoʻopaʻa' ana i ka 'ike ma luna o ka makana waiwai o ka helu.

Lana-wahi helu ua palapala mea i like loa me nā mea a pau maopopo maʻamau komo helu, wale ka exponent a me ka mantissa i kakauia kaawale. Hope a hiki i ka ia, a me ka normalized waihona - paa wahi, a ua hoʻonaniʻia me ka mea mua nui huahelu. Anna lana wahi ua hoʻohana 'kuhikuhi ana ma ka lolouila, e mea, ma ka lolouila e hoohalike ai o kahi o ka'ōnaehana ua ole kekimala a me ka aeaie, kahi hoi mantissa Denormalize pūʻali wahi - kēia manawa ia mea ma mua o ka huahelu mua, a laila, ma mua,ʻaʻole ma hope o ka mea, ma ka helu hapa ma ka rula, hiki ole e. No ka laʻana, mākou iho kekimala'ōnaehana e haawi mai i kona eiwa aeaie nenoaiu no? Aiaiiuie ana. A me ka mea e palapala a me kona mantissa lana-wahi me keia: +1001000 ... 0, a me ka ia, a me ka 'inideka 0 ... 0100. Akā, me nā kekimala'ōnaehana 'aʻole e paka i na luna' ho, a i e ka aeaie, ka hoʻohana 'ana i ka palapala o ko lana wahi.

lōʻihi makemakika

Ma lolouila kamepiula 'ē aʻe i kūkulu aʻe nei-ma ka lako polokalamu pūʻolo helu, kahi anao? Aou no ka mantissa a me exponent o ka nui o ka iaiyoe hoakaka ia lako polokalamu, kaupalena wale ma ka hoomanao nui o ke kamepiula. Ua nana e like me ka lōʻihi makemakika, i mea, na mea ana i helu i hanaʻia kamepiula. O nā mea a pau i ka ia - subtraction a me ka hou, mahele a me ka multiplication, kula haʻahaʻaa oihana, a me ka hana ana o ke kumu. Akā, i ka helu o ka loa okoa, i kā lākou kākoʻo mea me ka nui loa oi aku ma mua o ka lōʻihi o ka mīkini olelo. I ka manaʻo o kēia mau hana mea,ʻaʻole ma ka lako e pono ai, akā, ka mea, ua hoʻomano hoʻohana kumu o lako e, e hana me ka liʻiliʻi loa o nā kauoha. Aia mea hou a me ka makemakika, kahi helu lōʻihi wale kaupalena 'ia e iaiyoe nona iho - ākeʻakeʻa kumu miomio makemakika. A lōʻihi makemakika ua hoʻohana 'ia i loko o na kula.

1. No i hoʻouluulu i ka code (nā unu lawelawe, microcontrollers me ka haahaa iki hohonu - 10-iki? Aaeno? A ewalu-iki hua'ōlelo lōʻihi, ia mea,ʻaʻole i lawa ke lawelawe i ka 'ike mai ka Analog-i-kikohoʻe (Analog-i-kikohoʻe mīkini hoʻololi), a nolaila, hiki ole ke hana me ka lōʻihi makemakika.

2. Ua Ua hoi Ua hoʻohana i ka lōʻihi makemakika no cryptography, kahi ia mea e pono ke hoʻopaʻa i ka pololei o ka hopena o ka exponentiation paha multiplication i ka ^10.309. Helu makemakika ua hoʻohana 'modulo ka m - he nui maoli ka helu, a me ka mea i pono mea.

3. Nokia no financiers a me mathematicians, he, mea,ʻaʻole me ka lōʻihi makemakika, no ka mea, ka mea wale ala e hōʻoia i ka hopena o ka helu ma ka pepa - me ke kōkua o ke kamepiula, kaulike kiʻekiʻe pololei o ka helu. Lana wahi ka mea, hiki pū i kekahi helu o ka lōʻihi hookuuia. Akā, i ka 'enekinia, helu, a me ka hana ana o kānakaʻepekema koi' uao polokalamu ho loa pinepine, no ka mea, he mea paʻakikī e e ka hoʻokomo oʻikepili me ka hana ana i hewa. ka mea, ua IeAUPIIe, IAa IO nui oi voluminous ma mua o kēia polopelema hualoaʻa.

Kaua aku me ka wahaheʻe

A i ka helu o ke ana ma i ka lana wahi, ia ka loa paakiki e Loiloi i ka pololei o ka hopena. 'Aʻole i invented satisfying a pau i ka makemakika kumumanaʻo i makemake kōkua i ka hoʻonā i kēia pukana. Akā, i ka hewa helu loiloi wale. I ka manawa kūpono o ka noho pakele o inaccuracies ma luna o ka ili honua - wale i ka helu o ka haka-wahi e hoʻohana 'ia. No ka laʻana, he polokalamu kālā kukulu ma keia rula. Eia naʻe, loaʻa nō simpler: na koi 'ia ka helu o nā huahelu ma hope o ka kekimala wahi ua ikea keia ma ka mua.

Other noi ka mea, i kaupalena 'ia, no ka mea, hiki ole e hana i kekahi meaʻuʻuku a me ka loa nui helu. Nolaila, i ka wa e hana mau mea i loko o ka mooolelo i loaʻa i e inaccuracies, a no ka mea, o ka derivation o nā hualoaʻa ia mea pono i ka poepoe. A, 'akomi polopelema He pinepine ka nele o ka hana, a no ia mea, polopelema ua ho'ākāka' ia ua hōʻike hewa. Loa pilikia i loko o kēia mau mea, i ka hoʻohālike hana. Aia Ka hiki manaʻo i ka nui o ka wā e hiki mai ka wahaheʻe mea paʻakikī loa.