Kodi yoyandama chiwerengero mfundo?

Ulaliki kwenikweni (kapena weniweni) manambala, kumene zasungidwa monga mantissa ndipo amalimbikitsa akuyandama manambala mfundo (mwina mfundo monga mwambo m'mayiko Chingelezi). Ngakhale izi, chiwerengero amaperekedwa ndi kuliika molondola wachibale ndi kusintha mtheradi. Chifaniziro chimene ntchito kaŵirikaŵiri, anavomereza muyezo IEEE 754. masamu ntchito kuti ntchito manambala akuyandama-mfundo ndi akuyendera kompyuta machitidwe - onse hardware ndi mapulogalamu.

Point kapena koma

Mndandanda mwatsatanetsatane olekanitsa Decimal limatchula anthu m'mayiko Chingelezi ndi anglofitsirovannye, kumene mbiri ya manambala olekanitsidwa ndi gawo fractional wa mfundo lonse, chifukwa terminology m'mayiko amenewa anatenga dzina akuyandama mfundo - "akuyandama imeneyi". Mu Russian Federation, mbali fractional chonsecho a mwambo, ankasiyana koma, kotero iwo umaimira mfundo yemweyo amene mbiri anazindikira akuti "akuyandama imeneyi". Komabe, lero mu zolembedwa ndi luso mabuku Russian izo amaloledwa options onse.

Mawu akuti "akuyandama mfundo" linachokera ku choona kuti Pamalo chiwerengero chifaniziro ndi koma (decimal labwinobwino kapena bayinare - kompyuta) kuti kulumikiza kulikonse pakati pa manambala mizere. Mbali imeneyi ndi kuonetsetsa kuti amatchula izo payokha. Izi zikutanthauza kuti chifaniziro cha akuyandama manambala mfundo angathe kuonedwa ngati kukhazikitsa kompyuta ya kalembedwe kwakukulu kwambiri. The mwayi wa ntchito chifaniziro ngati wa chifaniziro mtundu atathana-mfundo ndi manambala inteja kuti osiyanasiyana mfundo limakula kwambiri pamene molondola wachibale amakhalabe sichinasinthe.

Mwachitsanzo

Ngati koma chiwerengero cha mapulani ndiye kuutentha ndi mtundu umodzi wokha. Mwachitsanzo, anapatsidwa pang'ono zisanu chiwerengero ndi manambala awiri mu gawo fractional. Izi zikhoza kuchitika kokha motere: 123456,78. Mtundu wa akuyandama manambala mfundo kupereka ukulu wonse kwa Mawu. Mwachitsanzo, chifukwa chomwecho manambala eyiti. Kujambulitsa options akhoza kukhala ngati mapulogalamu sizikupanga ziwiri manambala skimp ntchito m'munda zina, momwe kulemba exponents amene amangoona 10, ndipo kuchokera 0 16, ndi kukha pamene chiwerengero adzakhala khumi 8 + 2.

Ena embodiments ya kujambula, amene amalola kuti mtundu manambala ndi akuyandama mfundo: 12345678000000000000; 0,0000012345678; 123,45678; 1.2345678 ndi zina zotero. Mu mtundu uwu, pali ngakhale gulu la muyeso wa liwiro! M'malo mwake, ntchito ya dongosolo kompyuta amene analemba liwiro limene kompyuta amachita ntchito kumene chifaniziro cha akuyandama manambala mfundo. Machitidwewa amayezedwa mawu a phidigu (ntchito akuyandama-mfundo pa chachiwiri, amene anamasuliridwa kuti chiwerengero cha wotuluka pa chachiwiri ndi mfundo yoyandama). Izi unit zofunika muyeso kompyuta liwiro.

kapangidwe

Lembani chiwerengero mu akuyandama mtundu mfundo n'kofunika motere, kuona ndondomeko ya mbali kuvomerezedwa, chifukwa nkhani imeneyi ndi kwakukulu kwambiri, zomwe zikusonyeza manambala weniweni monga mantissa ndi dongosolo. M'pofunika kuimira manambala waukulu kwambiri ndi chochepa, ali zosavuta kuwerenga. Amafuna mbali: wolembedwa chiwerengero (N), ndi mantissa (M), dongosolo la chizindikiro (p) ndi kuti (n). Mbali yomaliza awiri chizindikiro. Choncho, N = ^M. N ^p. Koteronso kwalembedwa manambala akuyandama-mfundo. Zitsanzo m'ndime yachiwiri.

1. M'pofunika kulemba chiwerengero cha miliyoni, kuti kusochera mu ziro lapansi. 1000000 - ndi zachilendo kujambula, masamu. kompyuta A chiri motere: ^1.0. October ^6. Ndiko kuti, khumi ndi mphamvu chimodzi - zizindikiro zitatu, zomwe ikugwirizana ochuluka monga asanu ndi ziro. Choncho amapezeka chifaniziro cha manambala a amodzi ndi akuyandama poti yomweyo amatha kudziwa kusiyana kalembedwe.

2. Ndipo chotero chiwerengero molimbika ndi 1,435,000,000 (wina biliyoni mazana anayi makumi asanu zikwi) komanso akhoza kulembedwa chabe: ^1.435. September ^10, yekha. Umu ndi chizindikiro chochotsera akhoza kulemba chiwerengero. Ndi zimenezo, ndipo amasiyana mzake ndi chiwerengero cha amodzi ndi akuyandama mfundo.

Koma ndi zina zimene kukhala otsika? Inde, mofulumira.

3. Mwachitsanzo, ngati chizindikiro chimodzi miliyoni? = 0.000001 ^1.0. 10 ^-6. Kwakukulu ntchito ndi manambala kulemba ndi kuwerenga izo.

4. zovuta? mazana asanu ndi makumi chimodzi biliyoni: 0.000000546 = ^546. 10 ^-9. Pano. Osiyanasiyana mfundo akuyandama n'chachikulu kwambiri.

mawonekedwe

Fomu chiwerengero kungakhale labwinobwino kapena dekhetsa. Normal - nthawi zonse amalemekeza mwatsatanetsatane za akuyandama manambala mfundo. Tikumbukenso kuti mantissa mu mawonekedwe, popanda kutenga nkhani chizindikiro, ndi theka la imeneyi 0 1, ndiye 0 ⩽ ndi <1. Osati mu mawonekedwe yachibadwa chiwerengero cha wotaya molondola. The sangathe wa mawonekedwe wabwinobwino ndi manambala ambiri akhoza kulembedwa mosiyanasiyana, kuti ndi osokoneza. CHITSANZO timva zosiyanasiyana za nambalayi: 0 = 0.0001, ^000001. February ¹⁰ = ^0.00001. January ¹⁰ = ^0.0001. 10 ⁰ = ^0.001. 10 ^-1 = ^0.01. 10 ^-2, ndi zina kungakhale kwambiri. N'chifukwa chake kompyuta akugwiritsa ntchito zosiyanasiyana dekhetsa kalembedwe, kumene mantissa decimal amatenga mtengo wa mayunitsi ndi (Ponena), komanso kuti khumi (palibepo), ndi njira yomweyo mantissa bayinare chiwerengero ali ndi phindu pakati (Ponena) awiri (osati Ponena).

Choncho, 1 ⩽ ndi <10 -. Manambala bayinare ndi mfundo akuyandama, ndi mawonekedwe yolemba chiwerengero (kupatula ziro) analanda m'njira yapadera. Koma pali drawback - kulephera kulingalira mtundu uwu wa ziro. Choncho informatics amapereka ntchito manambala wapadera 0 chizindikiro (pang'ono). The inteja gawo la (MSB) wa mantissa mu chiwerengero bayinare kupatula ziro mu mawonekedwe dekhetsa ndi wofanana ndi 1 (silinatchulidwe wagawo). nkhani ntchito muyezo IEEE 754. The Pamalo dongosolo chiwerengero, mmene m'munsi ndi oposa awiri (ternary, quaternary ndi machitidwe ena), katundu uyu si anagula.

reals

manambala weniweni ndi akuyandama mfundo ndi amakhala monga si iye yekha, koma njira yabwino kwambiri kuimira chiwerengero chenicheni, titero, kukondera pakati osiyanasiyana mfundo zolondola. Izi analogous kuti kalembedwe kwakukulu kwambiri, anachita okha pa kompyuta. Akuyandama-mfundo chiwerengero - akonzedwa a Akamva munthu lagawidwa chizindikiro (Chozizwitsacho), kuti (amalimbikitsa) ndi mantissa (mantis). Mtundu ambiri ndi IEEE 754 akuyandama-mfundo chiwerengero ya Akamva kuti encode gawo la mantissa wake, gawo lina - digiri ndi chidutswa chimodzi akusonyeza chizindikiro cha nambala: ziro - ngati ali ndi kachirombo, unit - ngati nambala ndi negative. Ndondomeko lonse lembedwa ndi chiwerengero (kachidindo-kosangalatsa), ndi mantissa - mu mawonekedwe dekhetsa, mbali fractional - mu dongosolo bayinare.

Chizindikiro chirichonse - pang'ono aliwonse amene amasonyeza chizindikiro manambala onse akuyandama-mfundo. Mantissa ndi dongosolo - ndi integers, iwo limodzi ndi chizindikiro ndi kupanga chifaniziro cha akuyandama manambala mfundo. Ndondomeko akhoza kutchedwa kwakukulu kwambiri kapena amalimbikitsa. Osati manambala onse angathe ankaimira mu kompyuta tanthauzo lenileni, enawo anapereka mfundo idzatha. A njira wosalira zambiri - kugonjera ndi chiwerengero chenicheni ndi mfundo mapulani kumene kwenikweni ndi gawo lonse lidzakhala azisiyanitsidwa. Motero n'kutheka kuti inteja gawo nthawi yoikidwayo X Akamva, ndi fractional - Y Akamva. Koma mamangidwe a mapurosesa sadziwa njira yotero, koma chifukwa zokonda zapatsidwa kwa chiwerengero cha mfundo akuyandama.

Kuwonjezera

Kuwonjezera manambala akuyandama mfundo ndi wosavuta. Mogwirizana ndi IEEE 754 muyezo chiwerengero umodzi mwatsatanetsatane ali ambiri Akamva, choncho ndi bwino kusuntha kwa zitsanzo, ndi lingaliro bwino kutenga laling'ono akuyandama-mfundo chiwerengero. Mwachitsanzo, manambala awiri - X ndi Y.

masitepe awa:

a) manambala ayenera akuimira mu mawonekedwe dekhetsa. Ndi bwino munthu chobisika. X = ^1,110. 2 ^2, ndi Y = ^1,000. 2 ^0.

b) Pitirizani ndondomeko zikuchokera zitha mwakufuna ndi aziwonetsero, koma ayenera kulilembanso mtengo wa Y. Iwo zizigwirizana ndi mtengo wa chiwerengero dekhetsa, ngakhale mfundo - unnormalizes.

Kuwerengetsa kusiyana pakati pa exponents wa digirii 2 - 0 = 2. Tsopano kusuntha mantissa azilipira kusintha, ndiye, kuwonjezera 2 kwa index mawu akuti chachiwiri, motero kusuntha ndi koma mayunitsi chobisika pa mfundo ziwiri lamanzere. 0,0100 ^analandira. February ^2. Ichi chidzakhala lofanana ndi phindu yapita Y, ndiye pali kale Y.

c) Tsopano mukufuna kuwonjezera kuchuluka kwa mantissa X ndi Y. zopanda

1,110 + 0,01 = 10,0

Exhibitor akadali ukufanizidwa ndi X chizindikiro, umene uli wofanana 2.

g) Kuchuluka analandira mu sitepe yapita, ankatembenukira ndi normalization wagawo, ndiye muyenera kuloza amalimbikitsa ndalama ndi kubwereza. 10,0 ndi zidutswa ziwiri kumanzere kwa mfundo decimal, chiwerengero ndi zofunikira kuti matenda, mwachitsanzo, sunthani koma lamanzere ndi ina, ndipo amalimbikitsa, motero, chinawonjezeka ndi 1. Iwo likukhalira ^1,000. March ^2.

e) Ndi nthawi kutembenuza yoyandama chiwerengero mfundo dongosolo limodzi-mamvekedwe.

Pomaliza

Monga mukuonera, kuwonjezera chiwerengero ndi chovuta chilichonse chimene amayandama koma. Pokhapokha, ndithudi, kupatula chiwerengero cha amalimbikitsa m'munsi mwa kwambiri (mu Mwachitsanzo pamwambapa, anali Y kuti X), komanso kubwezeretsa kwa zokhazikika, mwachitsanzo nkhani ya malipilo - kusuntha mfundo decimal kumanzere kwa mantissa lapansi. Pamene Kuwonjezera kale ntchito, n'zotheka kwambiri ndipo komabe vuto lina - perenormirovanie ndi truncation pokha ngati chiwerengero chawo sakugwirizana chiwerengero kuimira izo.

chulutsa

dongosolo bayinare amapereka njira ziwiri imene wachulukitsa manambala akuyandama-mfundo. ntchito Izi zikhoza kuchitidwa ndi chulutsa, limene limayamba ndi osachepera Akamva kwambiri ndi limene limayamba ndi Tinthu mwapamwamba mwa multiplier lapansi. Onse milandu muli angapo ntchito sequentially stacking tsankho mankhwala. ntchito izi akulamulidwa ndi Kuwonjezera Akamva multiplier. Choncho, ngati mmodzi wa Akamva multiplier ndi unit, Uwerenge mankhwala tsankho la multiplicand ukukula ndi kosangalatsa lolingana. Ngati manambala a multiplier ndi zitengere ziro, pamene multiplicand si anawonjezera.

Ngati chulutsa imagwiridwa manambala awiri basi, mankhwala a manambala mu kuchuluka yake musalumphe chiwerengero cha manambala ali zinthu, kuposa kawiri, ndi ambiri ndi kwambiri. Ngati kuchulukitsa ndi chiwerengero ena, mankhwala kuopsa sizikugwirizana pa zenera. Chifukwa chiwerengero cha Akamva makina aliyense digito ndi amalire kwambiri, ndipo amakakamiza kuti akunjate munthu pazipita chiwerengero kawiri adders manambala. Ndipo ngati chiwerengero cha malo okha, mu mankhwala n'kogwiritsa atchule zolakwika. Ngati kuchuluka kwa masovedwe waukulu, zolakwa za alipo, ndi chifukwa kumawonjezera kwambiri molondola wonse. Pano, njira - kusonkhanitsa zotsatira chulutsa, ndiye ntchito zonyenga zinali alternating. Pamene chulutsa ntchito, izo zimakhala zotheka kupitirira gululi manambala, koma okhawo wamng'ono, chifukwa pali malire oletsa chiwerengero cha amene akuimira mu mawonekedwe a atathana-mfundo.

ena mafotokozedwe

Bwino tiyambe kuyambira pachiyambi. Ambiri njira kuimira chiwerengero - manambala mzere inteja, komwe koma ndi tanthauzo la mapeto. chingwe Zimenezi zingakhale utali uliwonse, koma koma akuima mu malo oyenera kuziyika izo, kulekanitsa inteja ku gawo fractional za izo. Mtundu wa ulaliki wa dongosolo lokhazikika-mfundo kwenikweni amaika zinthu zina pa malo mfundo decimal. kalembedwe Scientific amagwiritsa muyezo dekhetsa view wa chifaniziro cha manambala. Iwo aqn {\ displaystyle aq ^ {N }} aq N. Kuno {\ displaystyle ^ndi}, ndipo akutchedwa mantissa zingwe. Basi za iwo zanenedwa kuti 0 ⩽ ndi momveka bwino: N {/ displaystyle N} N - ndi inteja amalimbikitsa, ndipo ^Q {/ displaystyle Q} Q - komanso ndi inteja, ndilo maziko a radix ndi (kalata kaŵirikaŵiri 10). Mantissa kusiya koma pambuyo manambala woyamba, omwe si ziro, koma kujambula lina kunditumiza ku nkhani pa mtengo panopa chiwerengero.

Akuyandama-mfundo nambala olembedwa zofanana kwambiri ndi zonse bwino manambala muyezo kulowa okha amalimbikitsa ndi mantissa zinalembedwa payokha. Last ntchito ndiponso mu dekhetsa mtundu - atathana mfundo, amene chokongoletsedwa ndi woyamba manambala kwambiri. Monga akuyandama mfundo ntchito kwenikweni mu kompyuta, ndiko chifaniziro cha pakompyuta kumene dongosolo si decimal ndi bayinare, kumene ngakhale mantissa Denormalize kuwayalanso mfundo - tsopano pamaso pa manambala choyamba, ndiye patsogolo, osati pambuyo kumene inteja gawo mfundo sangakhale. Mwachitsanzo, dongosolo zathu decimal adzapereka dongosolo lake bayinare naini ntchito zosakhalitsa. Ndipo zimene zolembeledwa mantissa ake akuyandama-mfundo monga izi: +1001000 ... 0, ndipo ndi index 0 ... 0100. Koma kachitidwe decimal amalephera kubala kuwerengetsera osiyanasiyana, kumene kungakhale pa bayinare, ntchito mawonekedwe mfundo akuyandama.

masamu yaitali

Makompyuta pakompyuta amanga-mu phukusi mapulogalamu, kumene allocated kwa mantissa ndipo amalimbikitsa kuchuluka kwa kukumbukira mwachindunji mapulogalamu, malire ndi kukula chikumbukiro kompyuta. Ikukhala ngati masamu yaitali, ndiyo ntchito yosavuta pa manambala kuti amachita kompyuta. Ndi chomwecho - wochotsera ndi kuonjedzera, magawano ndi chulutsa, ntchito pulayimale ndi kumanga muzu. Koma chiwerengero cha osiyana kwambiri, mphamvu zawo ndi kwambiri kuposa kutalika kwa mawu makina. Kukhazikitsa ntchito imeneyi si mwa hardware ndi mapulogalamu, koma chimagwiritsidwa ntchito hardware zoyambirira ntchito ndi manambala laling'ono kwambiri malamulo. Pali zambiri ndiponso masamu, kumene manambala kutalika okha okha ndi mphamvu kukumbukira - umasinthasintha mwatsatanetsatane masamu. A masamu yaitali ntchito zosiyanasiyana.

1. kulemba malamulo (mapurosesa, microcontrollers ndi otsika pang'ono kuya - akaundula 10-bit ndi atatu-bit kutalika mawu, sikokwanira kusamalira mfundo analogi ndi digito (analogi ndi digito Converter), choncho sangachite popanda masamu yaitali.

2. komanso masamu yaitali ntchito cryptography, kumene kuli kofunika kuonetsetsa olondola chifukwa cha exponentiation kapena kuchulukitsa kwa ^10.309. Inteja masamu ntchito modulo mamita - lalikulu zachilengedwe moti si wophweka.

3. mapulogalamu kwa zachuma ndi masamu, nayenso, si popanda masamu yaitali, chifukwa njira yokha kutsimikizira zotsatira za kuwerengetsera pa pepala - mothandizidwa ndi makompyuta, kuonetsetsa mkulu lolondola manambala. Akuyandama mfundo iwo china chiwerengero cha kumaliseche yaitali. Koma kuwerengetsera ya zomangamanga ndi ntchito asayansi amafuna kuwerengetsera pulogalamu alowererepo nthawi zonse chifukwa zovuta kuti deta athandizira popanda kulakwitsalakwitsa. iwo amakhala zambiri voluminous kuposa zotsatira nazo.

Nkhondo ndi zolakwika

Chiwerengero cha ntchito imene mfundo akuyandama, n'kovuta kwambiri n'zolondola zotsatira zake. Sizinathe anatulukira kukhutiritsa chiphunzitso onse masamu amene angandithandize kuthetsa nkhaniyi. Koma zolakwa inteja kuunikira mosavuta. Kutheka ndiyotani pakuchotsa zolakwika padziko - monga ntchito kokha chiwerengero cha atathana-mfundo. Mwachitsanzo, pulogalamu ndalama anamanga pa mfundo imeneyi. Komabe, pali chosavuta: chiwerengero chofunika manambala pambuyo mfundo decimal amadziwika pasadakhale.

ntchito zina osati zokhazo, chifukwa inu simungakhoze ntchito ndi mwina manambala ochepa kapena lalikulu kwambiri. Kotero pamene inu ntchito nthawi zonse amaganizira kuti pangakhale zolakwika, ndi chifukwa derivation wa zotsatira m'pofunika chonse. Komanso, basi nazo zambiri kupanda kanthu, choncho nazo limanenedwa mwachindunji. oopsa kwambiri pa nkhani imeneyi, kufanizitsa ntchito. Pali ngakhale amati kuchuluka kwa zolakwa m'tsogolo kovuta.