E hoohalike ai o nā helu i loko o ke kamepiula. E hoohalike ai o integers a me maoli loa i loko o ke kamepiula paʻa

Mea i loa manao ma koʻu ola ana, e lilo i ka "pros" a me ka luna hoʻomalu o ka'ōnaehana pūnaewele, ai wale e kuhikihi ana i ka hailona i kamepiula enehana, ka ike e pili ana i ana i ka hoohalike o ka helu ma ke kamepiula iaiyoe, i loa nō. Ma hope o nā mea a pau, ma muli o kēia haʻahaʻa-ʻilikai iaaiey 'ōlelo e like me Assembler. Nolaila, i keia la, ua noonoo i ka hoohalike o ka helu ma ke kamepiula, a waiho ia mau mea i loko o ka iaiyoe keena.

notation

Inā 'oe i kēia' atikala heluhelu, oe paha ua ike no ia, akā, i ke kumukuai o hou. Allʻikepili ma kekahi 'aoʻao pilikino kamepiula e waiho i loko o ka aeaie helu nenoaiu. Kēia 'o ia hoʻi i kekahi helu oe e waiho i ka palapala kūpono, i ua haku o ka' Aʻohe hualoaʻa a me ka mea uuku.

I mea e hoolilo a kohu pono no mākou kekimala nui i ke ano maopopo lolouila, e pono e hoʻohana i ka algorithm i ho'ākāka 'ia ma lalo nei. Aia nō i hana kūikawā m'kini helu.

No laila, ma ka mea e kau i ka helu i loko o ka aeaie'ōnaehana, e pono e lawe mākou i waeʻia waiwai, a puunaue ia ma 2. Ma hope iho o ia, e hele mākou i ka hopena, a me ka poe i koe (0 a 1). Hopena 2 hou e puunaue me ka hoʻopaʻanaʻau koena. Kēia kaʻina hana e e hai like loa me ka hopena i e e 0 a 1. A laila, e kakau i ka waiwai hope loa, a me ka i koe iho i loko o ka aʻe mea, e like me mākou i loaa ia lakou.

Ia mea me kēia mea, ke ahaʻia ana ma ke kamepiula e hoohalike ai o ka helu. Kekahi helu waiho i loko o aeaie palapala, a laila, lawe i ka iaiyoe aeea.

paʻa

Me oe e ike mua i ka 'ike o ka mokuna palena iki o 1 pihoihoi. E like me mākou i ike, o ka hoohalike o ka helu ma ke kamepiula i wahi i loko o aeaie format. Penei, kēlā wahi o ka iaiyoe ua ku e kekahi waiwai o - 1 'ole 0.

No ka pūnaewele o ka nui loa i hoʻohana aeea. Kēlā me kēia pa alima he 8'āpana o ka 'ike. Nolaila, ua hiki ke manao nei makou, o ka palena iki cia i loko o kēlā me kēia iaiyoe Hoʻohana i e 1 ole ia heʻewalu-ʻai aeaie helu.

holoʻokoʻa

Hope mākou i loaʻa ai i ka pololei i hoʻokomo o kaʻikepili ma ke kamepiula. E like me ka olelo, ka mea mua loa i ka unu lawelawe translates ka 'ike i loko o ka aeaie waihona, a wale laila allocates ka iaiyoe.

Na Google e hoʻomaka me ka simplest koho, i mea e hoohalike ai i ke ana o integers ma ke kamepiula. PC paʻa ua anao? Aou no ke kaʻina mea ridiculously uuku helu o aeee - wale kekahi. Penei, he i kā mākou no kekahi kau e ia i ka waiwai mai ka 0 a hiki i 11111111. E ka unuhi i ka i kā mākou helu o nā 'ikamu i loko o ka mau palapala.
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 .

Ano, ke ike ia i loko o kekahi iaiyoe aeea hiki e hoʻonoho mai 0 a hiki i 255. naʻe, ua pili wale nō i 'ole-io helu. Inā ke kamepiula, e pono ai i ka palapala i ka io waiwai, na mea a pau e hele ai ka apana uuku na okoa.

hopena maikaʻi 'helu

Ano, e ka ike ana i ka hoohalike o ka helu ana ma ka lolouila, ina ka mea, e io. No ka kākau i kekahi waiwai a mea emi o Aʻohe, ia mau iaiyoe keena, a me 16'āpana o ka 'ike. Pela 15 e hele ma lalo o ka helu ia iho, a ua haawiia mai ka mua (leftmost) iki ma ka AYEIE mark.

Inā ka huahelu mea io, ka mea, ua kākau, "1", ina 'oluʻolu, laila, "0". No ka nanea o ka memorization, e hiki ke kikoo aku i ke kēia analogy: ina ka hoailona mea, alaila, i 1 ina ia mea ole, alaila, e olelo iki mai (0).

Ke koe 15'āpana o ka 'ike i ia i ka helu. Like me ia i ka mua neo, e hiki ke kau i ka i kā mākou o ka umikumamalima huahelu i loko o ia mau mea. It E e hoʻomaopopo i ke komoʻana o ka hopena maikaʻi a me ka maikaʻi nui mea me ka nui loa okoa mai kekahi i kekahi.

I mea e lawa i ka 2 iaiyoe keena, ua oi aku ma mua o 'Aʻohe a ua like no, he ai-kapaia pololei kivila. Keia hana ua hana ia ma ke ano hookahi me ia i ho'ākāka 'ia ma luna, a me ka i kā mākou A = 32766, hoʻohana' ana i ka wā kekimala notation. Pono makemake e hoailona oukou ia ia ma keia hihia, "0" pili ia i ka maikaʻi.

examples

E hoohalike ai o integers ma kamepiula iaiyoe mea,ʻaʻole ia he pilikia hana. ʻOiai ka mea, O ka iki hou huikau ka wā e hele mai ai i ka io nui. E palapala i ka helu o ka i mea emi o Aʻohe, ka hoʻohana 'ana i ka hou kivila.

E kiʻi ia, ka mīkini produces ka helu o nā kākoʻo hana.

1. Mua modulus o ka hopena maikaʻi helu i loko o aeaie notation kākau. Ia mea, ke kamepiula hoʻomanaʻo i ka like akā maikaʻi.
2. A laila, he hoʻomanaʻo hulu kēlā me kēia pihoihoi. No keia mea, e UAIAaIN e 'Aʻohe hualoaʻa a me ka Hope versa a pau huahelu.
3. E hookui i ka "1" a hiki i ka hopena. Kēia e ia i ka hou kivila.

Eia ka he vivid laʻana. Ina mākou i ka helu o X = - 131. First, loaa i ka modulus | X | = 131 Ua laila hoohuliia mai i loko o ka aeaie kahua, a me ka moolelo o ka 16 aeee. E loaa X = 0000000010000011. Ma hope hulu X = 1111111101111100. Ohui ia "1", a loaa iho la i ka inverse kuhi X = 1111111101111101. No ka kākau i kekahi 16-iki iaiyoe aeea o ka palena iki helu o X = - (2 ¹⁵⁾ = - 32767.

ka loihi o

E like me 'oe ke ike, i ka hoohalike o maoli loa i loko o ke kamepiula mea ole ia pilikia. Naʻe, i ole e lawa no ka hapanui ana kūkākūkā o ka laulā. No laila, i mea e lawa nui nui o ka kamepiula allocates iaiyoe aeea 4, a me 32'āpana.

Ke hoʻopaʻa kaʻina Aʻole i oko mai ia imua o luna. No laila mākou e hāʻawi aku i ka laulā o ka helu i hiki ke waiho i loko o kēiaʻano.

X _max = 2.147.483.647.

X _min = - 2147483648.

ʻIkepili aiee i loko o ka hapanui manawa kupono e palapala a me ka hana ana ma luna o nā ikepili.

E hoohalike ai o maoli loa i loko o ke kamepiula i kona pono a me keakea. Ma ka kekahi lima, i kēia iaoia mea hiki pono o ka hana ana ma waena o ka helu waiwai, a nui ka mämä holo i ka unu lawelawe. Ma ka kekahi lima, keia laulā mea,ʻaʻole i lawa ke hoʻoponopono i ka hapanui pilikia ma ka 'aoʻao hoʻokele waiwai, ke kālaikūlohea, makemakika a me nā sciences. No laila, e nānā mākou i kekahi papa hana no ka sverhvelichin.

lana wahi

'O kēia ka hope mea e pono ai, e ike e pili ana i ka hoohalike o ka nui loa i loko o ke kamepiula. No ka mea, he pilikia i maopopo ai i ka oihana o ka comma i loko o ia mau mea, e lawa na nui i loko o ke kamepiula hoʻohanaʻia ka exponential palapala ka wā kākau hapa.

Kekahi helu hiki ke poe ma ke kēia 'ano X pa = ka m * ^n. Where ka m - i ka helu o ka mantissa, pa - radix a me N - i ka mea helu.

E standardize i ka hoʻopaʻa lana wahi helu hoʻohana i kēia kūlana, e like me a ka mantissa Module e kela aku kona nui ma mua o paha e like me 1 / N a emi o 1.

ua haawiia mai e mākou helu 666,66. E hāʻawi mai ia iā mākou i ka exponential ano. I ka m = 0.66666 * ¹⁰ March. P = 10 a me N = 3.

Ma waho pūnaewele o lana wahi loina pele anao? Aou 4 a 8 nāʻai (32'āpana a me 64). Ma ka hihia mua ka mea, ua kapaʻia ka helu o hookahi-miomio, oiai o ka lua - he papalua miomio.

O ka 4 nāʻai anao? Aou no ka papaa o ka helu, 1 (8'āpana) haawi ia ma lalo nei ma ke kaʻina hanaʻikepili a me kona hoailona, a me 3 nāʻai (24'āpana) no ka ho'āhu ka mantissa haʻalele kona hoailona, a ma luna o ka mea like me nā loina like no me ka helu loina. Ike keia, ua hiki e kekahi poe noonoo ole ho.

ʻO kā mākou waiwai o ka n = ^{2 1111111} 127 = ^10. Ma muli o ka mea, ua hiki ke kiʻi i ka i kā mākou dala o ka helu i hiki ke waiho i loko o kamepiula iaiyoe. X = ^2127. Ano, ua hiki e huli i ka i kā mākou hiki mantissa. Ka mea, e like me 2 ²³ - 1 ≥ 2 ²³ = 2 ^{(10 × 2,3)} ≥ 1000 ^2.3 = 10 ^{(3 × 2,3)} ≥ 10 ^7th. E like me ka hopena, ua loaa i ka He kokekau wale waiwai.

Ano, ina ua hui pu iho la laua no ka i ka ho omaulia, ua loaa i ka waiwai e hiki e waiho waho me ka poho o ka 4 nāʻai o ka iaiyoe. Ka mea, e like no X = 1.701411 * 10 ^38. Ka i koe, huahelu i kāpaeʻia, no ka mea, e leie aku oe ia i ka miomio o ke ano o ka hoʻopaʻa.

papalua miomio

No nā helu i ua pena, a wehewehe i loko o ka mua paukū,ʻaneʻi mākou e haʻi aku 'oe a pau loa koke. No ka papalua miomio helu i ana anao? Aou 11'āpana no ka mea a me kona hoailona, a me 53'āpana no ke mantissa.

1111111111 N = ² 1023 = ^10.

M = ^{52 -1 = 2 2 (10 *} 5.2) = 1000 5.2 = 10 15.6 . Ua hoʻokōʻia, a loaa i ka i kā mākou helu = 2 X ¹⁰²³ mai ai i "ka m".

Mākou manaʻolana i ka 'ike e pili ana i ka hoohalike o integers a me maoli loa ma ke kamepiula, ua hoomakaukau mākou, e mea pono ia oe ma ka aʻo, a, e ia i kona wahi clearer ma mua o ka mea ana i kākau i loko o nā puke.