Ukumelwa izinombolo ikhompyutha. Ukumelwa of integers nezinombolo yangempela imemori ikhompyutha

Noma ubani oke waba wacabanga empilweni yami ukuthi babe "kochwepheshe" noma wesistimu noma umane ukuxhumanisa okuningi nge ubuchwepheshe bama-computer, ulwazi mayelana nendlela umfanekiso Izinombolo inkumbulo computer, kuyadingeka. Ngemva kwakho konke, kuncike kule eliphansi izilimi izinhlelo ezifana Assembler. Ngakho-ke, namuhla sicabangela Kutsi tinombolo ku computer futhi okuwenza aqondane kumaseli inkumbulo.

notation

Uma ufunda lesi sihloko, kungenzeka usuyazazi kakade ngakho, kodwa kuwufanele ukuphinda. Yonke idatha ku kwikhompyutha siqu zigcinwa kanambambili inombolo system. Lokhu kusho ukuthi noma iyiphi inombolo kumelwe ugcwalise ifomu elifanele, ukuthi sakhiwa amaqanda futhi abathandekayo.

Ukuze uthumele komkhuba kithi izinombolo ledesimali ifomu ikhompyutha kuyaqondakala, kumele usebenzise i-algorithm kuchaziwe ngezansi. Kukhona futhi yokubala ezikhethekile.

Ngakho, ukuze ubeke inombolo ohlelweni kanambambili, udinga ukuthatha ukubaluleka kwethu abakhethiwe ulwahlukanise by 2. Ngemva kwalokho, sithola yi bese kuthi (0 noma 1). Umphumela 2 futhi uhlukanise futhi ngekhanda ezisalayo. Le nqubo kufanele ziphindwe uma nje umphumela futhi kuyoba 0 noma 1. Bese ubhala ukubaluleka kokugcina nezinsalela ezihlaba kule oda reverse, njengoba sesamukele kubo.

Yilokho kanye okwenzeka ukumelwa ikhompyutha izinombolo. Noma iyiphi inombolo elondolozwe ezihamba ngakubili, bese uthatha cell inkumbulo.

inkumbulo

Njengoba kufanele kakade esiphansi Imininingwane Phiko 1 kancane. Njengoba sesibonile, umfanekiso wanoma Izinombolo ikhompyutha yenzeka ifomethi kanambambili. Ngakho, kancane imemori ngamunye kuhlala omunye ukubaluleka - 1 noma 0.

Ukuze isitoreji izinombolo ezinkulu kusetshenziswe cell. iyunithi ngasinye siqukethe 8 ibhithi ulwazi. Ngakho-ke, singaphetha ngokuthi inani eliphansi inkumbulo esinye nesinye kungenzeka 1 noma kube ayisishiyagalombili-Byte inombolo kanambambili.

wonke

Ekugcineni sifika ukubekwa ngqo idatha ku-khompuyutha. Njengoba kushiwo, into yokuqala wokugaya uhumusha ulwazi ibe ifomethi kanambambili, bese kuphela inike imemori.

Sizoqala inketho elula, okuyinto umfanekiso integers kule khompyutha. inkumbulo PC zibekelwe nqubo aweve inani elincane lamaseli - eyodwa nje. Ngakho, inani eliphezulu elilodwa slot kungaba value kusuka 0 kuya 11111111. Ake ukuhumusha inombolo enkulu okufakwe ifomu evamile.
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 .

Manje siyabona ukuthi kwelinye inkumbulo cell ingabekwa kusuka 0 kuya 255. Nokho, lokhu kwenzeka kuphela kubantu inamba non-negative. Uma ikhompyutha uzodinga ukuqopha ukubaluleka negative, yonke into ihamba ngendlela ehlukile kancane.

izinombolo engemihle

Manje ake sibone ukuthi umfanekiso izinombolo computer, uma omubi. Kute bakwati kubhala i-value okuyinto esingaphansi zero, kunikezelwe amaseli ezimbili inkumbulo, noma 16 ibhithi ulwazi. Ngakho 15 ukuya ngaphansi inombolo uqobo, futhi owokuqala (ezikwesokunxele) kancane enikezwa uphawu okuhambisanayo.

Uma lesi sibalo alivumi, silotshwe, "1", uma omuhle ke "0". Ukuze kube lula futhi ukuwakhumbula, ungakwazi ukufinyelela kwesakho ngalo mzekeliso: uma uphawu, wayesezibeka 1 uma kungenjalo, khona-ke (0) lutho.

Labo abasele abanga-15 ibhithi nolwazi inikezwa inamba. Ngokufanayo ngecala odlule, ungafaka esiphezulu amayunithi nanhlanu kuzo. Kufanele kuqashelwe ukuthi ukungena izinombolo engemihle futhi omuhle sihluke kakhulu komunye nomunye.

Ukuze ihlanganise inkumbulo amaseli 2 ngaphezu kuka-zero noma ilingane, okuthiwa ikhodi oqondile. Lo msebenzi wenziwa ngendlela efanayo njengoba kuchaziwe ngenhla, futhi esiphezulu A = 32766, uma usebenzisa inotheshini yedesimali. Ufuna nje uqaphele ukuthi kuleli cala, "0" libhekisela omuhle.

izibonelo

Ukumelwa of integers kumemori ikhompyutha akuyona umsebenzi onzima kangaka. Nakuba kungcono kancane more xaka uma kuziwa value ezimbi. Ukurekhoda inani okuyinto esingaphansi zero, usebenzisa ikhodi eyengeziwe.

Ukuze uthole it, umshini ukhiqiza eziningi imisebenzi asizayo.

1. Okokuqala eqoshiwe wemfihlo yenombolo ongathandeki notation kanambambili. Okungukuthi, abangabantwana ikhompyutha ukhumbula efanayo kodwa omuhle.
2. Khona-ke, inkumbulo inverting kancane ngamunye. Ngenxa yale njongo, wonke amayunithi esikhundleni amaqanda, noHezekeli.
3. Thina ungeze "1" kumphumela. Lokhu kuyoba ikhodi eyengeziwe.

Nasi sibonelo esigqamile. Ake sithi ube nenani X = - 131. Okokuqala, ukuthola wemfihlo | X | = 131 is ke iguqulwe ibe ohlelweni kanambambili futhi irekhodi amaseli 16. We ukuthola X = 0000000010000011. Ngemva inverting X = 1111111101111100. Ukungeza nalokho "1" futhi ukuthola ikhodi ephambene X = 1111111101111101. Ukuze uqopha-16-bit inkumbulo cell inombolo ubuncane X = - (2 ¹⁵⁾ = - 32767.

ufisa

Njengoba ubona, umfanekiso wanoma izinombolo yangempela ikhompyutha akuyona ukuthi kunzima. Nokho, ingxoxo senhlobo elingenele imisebenzi kakhulu. Ngakho-ke, ukuze ihlanganise isibalo esikhulu computer inike inkumbulo iseli 4, noma u-32 izingcezu.

Inqubo ukuqoshwa akahlukile ukuthi ethulwa ngenhla. Ngakho nje ukunikeza uhla lwezinombolo zingagcinwa kulolu hlobo.

X _max = 2.147.483.647.

X _imiz = - 2147483648.

Idatha amagugu ezimweni eziningi ngokwanele ukuba alobe futhi ukwenza imisebenzi kwi-data.

Ukumelwa izinombolo yangempela ikhompyutha kunezinzuzo zako kanye nebubi. Ngakolunye uhlangothi, le ndlela kwenza kube lula ukwenza imisebenzi phakathi kwezindinganiso inamba, okuyinto igijimisa kakhulu kuze wokugaya. Ngakolunye uhlangothi, kuleli banga akwanele ukuxazulula eziningi izinkinga kwezomnotho, i-physics, i-arithmetic kanye neminye imikhakha yesayensi. Ngakho manje sibheka enye indlela sverhvelichin.

iphuzu elintantayo

Le yinto yokugcina odinga ukukwazi mayelana Kutsi tinombolo ku-khompuyutha. Njengoba kunenkinga sokunquma isikhundla ukhefana kuzo, ukuze ihlanganise izinombolo onjalo kwikhompyutha esetshenziswa ifomu lomchazi lapho ebhalela izingxenyana zaso.

Noma iyiphi inombolo kungenziwa amelwe elandelayo ifomu X p = m * ^n. Lapho m - inombolo mantissa, p - Isisekelo sesistimu yezinombolo kanye n - inombolo oda.

Elifanele ukuqopha elintantayo iphuzu izinombolo esetshenziswa olulandelayo isimo, owawuthi module mantissa Kufanele libe likhulu noma lilingane no-1 / n encane kuno-1.

Ake inombolo 666,66 kunikezwa. Ake lona ifomu lomchazi. Ngo x = 0.66666 * ¹⁰ Mashi. P = 10 kanye n = 3.

On isitoreji iphuzu elintantayo amagugu ngokuvamile zabelwe 4 noma 8 amabhayithi (izingcezu 32 noma 64). Esimweni sokuqala-ke kubizwa ngokuthi isibalo esisodwa-ngokunemba, kanti eyesibili - ngokunemba double.

Kulaba amabhayithi 4 abelwe isitoreji izinombolo, 1 (8 izingcezu) ngezansi ku idatha inqubo kanye uphawu yayo, futhi 3 amabhayithi (24 izingcezu) ukugcina lo mantissa ushiye izibazi futhi izimiso ezifanayo ngoba amagugu inamba. Ukwazi lokhu, singakwazi ukwenza ezinye izibalo ezilula.

Inani esiphezulu n = ^{2 1111111} 127 = ^10. Kususelwa ke, singathola inani eliphezulu lwezinombolo ingagcinwa enkumbulweni ikhompyutha. X = ^2127. Manje singakwazi ukubala esiphezulu mantissa kungenzeka. Kuzoba elilingana 2 ²³ - 1 ≥ 2 ²³ = 2 ^{(10 × 2,3)} ≥ ¹⁰⁰⁰ 2,3 = 10 ^{(3 × 2,3)} ≥ 10 ^7th. Ngenxa yalokho, sithola i value eseduze.

Manje, uma sihlanganisa kokubili ukubala, sithola ukubaluleka ukuthi ingagcinwa ngaphandle kokulahleka 4 amabhayithi yimemori. Kuzoba elilingana X = 1.701411 * 10 ^38. Izinombolo asele ayalahlwa, ngoba ikuvumela ukuba abe ikwazi indlela yokuqopha.

ngokunemba double

Njengoba zonke izibalo ziye zaveza futhi wachaza esigabeni esandulele, lapha esikutsho kuwe zonke ngokushesha kakhulu. Ukuze double ngokunemba zinombolo ngokuvamile zabelwe 11 izingcezu sokuba umyalelo kanye uphawu yayo kanye 53 izingcezu ukuze mantissa.

1111111111 n = ² 1023 = ^10.

M = ^{52 -1 = 2 2 (10 *} 5.2) = 1000 5.2 = 10 15.6 . inombolo Oyindilinga futhi ukuthola esiphezulu = 2 X ¹⁰²³ kuze kube "m".

Sithemba ulwazi mayelana umfanekiso integers nezinombolo yangempela computer, sinikeze, kuyasiza kuwe ukuqeqeshwa kuyoba kancane kusobala kakhulu ukuthi Ivame kubhalwa izincwadi.