Umelo amanani kwikhompyutha. Umelo integers neenombolo yokwenene kwimemori computer

Nabani na okhe wacinga ebomini bam ukuba ukuba i "kwizazi" okanye Umphathi wendlela, okanye nje ukunxibelelanisa iqashiso kunye nobuchwepheshe computer, ulwazi malunga nendlela ukumelwa amanani kwinkumbulo yekhomputha, nakanjani. Ngapha koko, ezisekelwe phezu kweli-kwinqanaba elisezantsi lwimi iinkqubo ezifana Assembler. Ngoko ke, namhlanje sicinga ukumelwa amanani kwi computer kwaye ukuwabeka iiseli kwinkumbulo.

notation

Ukuba ufunda eli nqaku, mhlawumbi sele uyazi, kodwa kubalulekile ukuzisebenzisa. Yonke idatha ikhompyutha siqu zigcinwa kwi binary kwinkqubo inani. Oku kuthetha ukuba naliphi na inani kufuneka angenise ifomu efanelekileyo, ukuba ubunjwe amaqanda kunye nabo.

Ukuze akhuphele ukusoloko kuthi amanani lokugqibela ukuba uhlobo yekhompyutha eqondakalayo, kufuneka usebenzise algorithm echazwe ngezantsi. Kukho kwakhona izibali ezizodwa.

Ngoko ke, ukuze ukubeka inani kwinkqubo yokubini, kufuneka uthathe ixabiso lethu ezikhethiweyo kwaye ulahlule 2. Emva koko, sifumana iziphumo kwaye intsalela (0 okanye 1). Isiphumo 2 kwakhona yahlula ukunkqaya abaseleyo. Le nkqubo kufuneka iphindwe elide ngenxa nayo iya kuba 0 okanye 1. Emva koko bhala ixabiso lokugqibela isidumbu umyalelo reverse, njengoko samkelayo kubo.

Yiloo nto kanye eyenzekayo xa ukumelwa yekhompyutha lwamanani. Naliphi na inani agcinwa ifomu yokubini, uze emva koko uthabathe iseli memory.

memory

Njengoko kufuneka sele uyazi iyunithi ulwazi elinganiselwe 1 bit. Njengoko sele sibonile, ukumelwa amanani kwi computer kwenzeka ayofomati yokuphindwe kabini. Ngenxa yoko, bit ngalinye imemori kuhlala kwenye ixabiso - 1 okanye 0.

Kuba yokugcina amanani amakhulu wasebenzisa iseli. unit nganye iqulethe 8 wayemana. Ngoko ke, sinokugqiba ukuba ixabiso isezantsi kwicandelo memory nganye-1 okanye inani yebhayinari byte ezisibhozo-.

lonke

Ekugqibeleni sifika nokubekwa ngqo kwedatha kwikhompyutha. Njengoko kukhankanyiwe, into yokuqala kumqhubekekisi litolika iinkcukacha ayofomati yokuphindwe kabini, uze kuphela sokunikela inkumbulo.

Siza ukuqala nge khetho kwecacileyo, nto leyo ukumelwa integers kwi computer. imemori PC yabelwe le nkqubo aphakame kakhulu inani elincinane iiseli - nje omnye. Ngaloo ndlela, a ubuninzi indawo yokubeka into inokuba ixabiso ukusuka ku-0 ukuya 11111111. Makhe ukuguqulela inani eliphezulu yobhaliso nefom.
X = 1 × 2 ⁷ + 1 × 2 ⁶ + 1 × 2 ⁵ + 1 × 2 ⁴ + 1 × 2 ³ + 1 × 2 ² + 1 × 2 ¹ + 1 × 2 ⁰ = 1 × 2 ⁸ - 1 = 255 .

Ngoku siyabona ukuba kwinkumbulo iseli kwenye indawo kwi-0 ukuya 255. Noko ke, oku kusebenza kuphela inani elipheleleyo engasiyiyo-. Ukuba ikhompyutha kuya kufuneka ukuba ubhale esinentlawulo engenaxabiso, yonke into ihamba kancinci eyahlukileyo.

amanani akhabayo

Ngoku makhe sibone indlela ukumelwa amanani kwi computer, ukuba awunayo. Zokubhala ixabiso elingaphantsi kwama-zero, eyabelwe iiseli ezimbini inkumbulo, okanye amasuntswana-16 yolwazi. Ngaloo 15 hamba phantsi kwinani ngokwawo, kunye (esekhohlo) bit yokuqala anikwa amanqaku ahambelanayo.

Ukuba lo mzobo lelikhabayo, kubhaliwe, "1", ukuba HIV, ngoko "0". Kuba lula ukuwakhumbula, unako ukuzoba lo mzekeliso: ukuba uphawu, ngoko wabeka 1 Ukuba akunjalo, ngoko akukho (0).

Eziseleyo amasuntswana 15 lolwazi wabelwe inani. Ngokufanayo kwityala elidlulileyo, uyakwazi ukubeka ezona iiyunithi ezilishumi elinesihlanu kuyo. Kufuneka kuqatshelwe ukuba ukungena amanani ezimbi nezilungileyo yahlukile kakhulu enye kwenye.

Ukwenzela ukulungiselela le-2 memory iiseli mkhulu zero okanye iyalingana, ebizwa ngokuba ikhowudi ngqo. Olu sebenziso lwenziwa ngendlela efanayo njengoko kuchaziwe apha ngasentla, kwaye ubuninzi A = 32766, xa kusetyenziswa ubhalo lokugqibela. bafuna nje ukuba uqaphele ukuba kulo mzekelo, "0" libhekisela ezakhayo.

izibonelo

Umelo integers kwinkumbulo yekhomputha ayikho umsebenzi olunzima njengolu. Nangona isuntswana nzima ngakumbi xa kufikwa engenaxabiso. Ukuze ubhale inani leyo libengaphantsi kunonothi, usebenzisa ikhowudi olongezelelweyo.

Ukuze uyifumane, umatshini uvelisa iqela imisebenzi abancedisayo.

1. Okokuqala kwabhalwa modulus kwenani embi ngokwe yokubini. Oko kukuthi, ikhompyutha ukhumbula into efanayo kodwa ezintle.
2. Emva koko, a memory inverting bit nganye. Ukulungiselela le njongo, zonke iiyunithi indawo amaqanda kunye vice versa.
3. Siya ufaka "1" umphumo. Oku kuya kuba ikhowudi olongezelelweyo.

Nanku umzekelo ocacileyo. Masithi kufuneka eziliqela X = - 131. Okokuqala, ukufumana modulus | X | = 131 ithotyiweyo aze ke atshintshelwe yaba inkqubo yokubini kunye nerekhodi iiseli 16. Thina ukufumana X = 0000000010000011. Emva inverting X = 1111111101111100. Ukongeza koku "1" kwaye afumane eguqulweyo ngokubaxwa i ikhowudi X = 1111111101111101. Kuba urekhoda ekhethekileyo eziibhithi ezingama-16 imemori iseli linani Ubuncinane X = - (2 ¹⁵⁾ = - 32767.

ulangazelela

Njengoko ubona, ukumelwa amanani ngokwenene ngekhompyutha ayikho nzima. Noko ke, ingxoxo uluhlu inokuba ezaneleyo ukwenzela imisebenzi ezininzi. Ngoko ke, ukuze ukulungiselela amanani amakhulu khompyutha yabela memory iseli 4, okanye amasuntswana 32.

Inkqubo yokurekhoda ayahlukanga kuloo uchazwe apha ngasentla. Ngoko ke sinike nje uluhlu lwamanani anokuthi agcinwe kolu hlobo.

X _max = 2.147.483.647.

X _min = - 2147483648.

amaxabiso Data kwiimeko ezininzi ngokwaneleyo ukubhala nokwenza imisebenzi le data.

Umelo amanani ngokwenene kwikhompyutha iye alungileyo kwakunye nangalunganga. Kwelinye icala, le ndlela yenza kube lula ukwenza imisebenzi phakathi amaxabiso elipheleleyo, leyo ikhawulezisa kakhulu kumqhubekekisi. Kwelinye icala, kwalomqolo akwanelanga ukuba ukusombulula iingxaki ezininzi kakhulu Economics, physics, izibalo kunye nezinye izifundo zesayensi. Ngoko ke sijonga enye indlela ye sverhvelichin.

lencopho equkuqelayo

Nantsi into yokugqibela kufuneka wazi malunga nokumelwa amanani kwikhompyutha. Ekubeni kukho ingxaki kujongwa indawo isiphumlisi kubo, ukulungiselela amanani olunjalo ikhompyutha esetyenziswa yi ifomu bomtya xa ubhala amaqhezu.

Naliphi na inani angamelwa ngohlobo X p = m * ^{n elilandelayo.} Apho m - linani mantissa, p - radix kunye n - nenombolo odolo.

Ngokusesikweni amanani indawo yokurekhoda engenasigxina kusetyenziswa olandelayo imeko, njengoko apho imodyuli mantissa kufuneka ibe inkulu kune okanye ilingana-1 / n ne ngaphantsi kwe-1.

Makhe inombolo 666,66 sinikwe. Makhe niyinike kwifom bomtya. Xa x = 0.66666 * ¹⁰ Matshi. P = 10 kunye n = 3.

On ukugcinwa ngendlela lwamaxabiso encopho equkuqelayo ngokuqhelekileyo abelwe bytes 4 okanye 8 (amasuntswana 32 okanye 64). Kwimeko yokuqala ibizwa ngokuba inani elinye-ngqo, ngoxa yesibini - a ngendlela kabini.

Le bytes-4 zabelwe yokugcina amanani, 1 (8 amasuntswana) zinikwe apha ngezantsi phezu iinkcukacha ngenkqubo kunye umqondiso yayo, kunye bytes-3 (24 amasuntswana) okugcina i mantissa ushiye uphawu wayo kwimigaqo ngokufanayo amaxabiso elipheleleyo. Ukwazi oku, sinako ukwenza izibalo ezilula.

Elona xabiso liphezulu n = ^{2 1111111} 127 = ^10. Ngokusekelwe kuwo, singafumana zesixa amanani ezinokuthi lugcinwe kwinkumbulo yekhomputha. X = ^2127. Ngoku sinako ukubala mantissa eliphezulu kunokwenzeka. Kuya kuba ezilinganayo ezi-2 ²³ - 1 ≥ 2 ²³ = 2 ^{(10 × 2,3)} ≥ 1000 ^2.3 = 10 ^{(3 × 2,3)} ≥ 10 ^7. Ngenxa yoko, nathi bafumana sentengo.

Ngoku, xa sidibanisa zombini ekubaleni, sifumana ixabiso ukuba igcinwe ngaphandle ilahleko bytes 4 kwinkumbulo. Kuya kuba kulingana X = 1.701411 * 10 ^38. Imivo eseleyo alahlwa, kuba likuvumela ukuba ikwazi indlela yokurekhoda.

ngobuciko double

Ekubeni zonke izibalo ziye zipeyintwe kwaye kucaciswe kumhlathi ongaphambili, apha ke ndithi kuni nonke kamsinya kakhulu. Kuba amanani ngobuciko kabini ngokuqhelekileyo zabelwe amasuntswana 11 umyalelo kunye umqondiso zalo kwakunye amasuntswana 53 ukuze mantissa.

1111111111 n = ² 1023 = ^10.

M = ^{2 52 -1 = 2 (10 *} 5.2) = 1000 5.2 = 10 15.6 . Ajikelezayo kwaye bafumane inani eliphezulu = 2 X ¹⁰²³ ukuya ku "m".

Sinethemba ulwazi malunga nokumelwa integers neenombolo yokwenene kwi computer, siye kubonelelwa, akukho luncedo kuwe uqeqesho kwaye kuya kuba kancinci icace ngaphezu koko ngokuqhelekileyo kubhaliweyo kule ncwadi zezifundo.