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[Powered by Google Translate] Nate HARDISON: Nyuma wakati wewe kujifunza jinsi ya kusoma na kuandika

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namba, wewe kujifunza kuhusu tarakimu 0-9.

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Kuandika idadi kubwa kuliko yote 9, wewe kujifunza kwamba wote

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mnatakiwa kufanya mara kutumia baadhi ya macho ya tarakimu hizi,

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kama katika 52 na 437.

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Hivyo njia hii ya kuandika namba ina jina, decimal nukuu.

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>> Mbona decimal?

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Naam, mizizi ya Kilatini ya decimal, "decem," maana yake ni 10.

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Na wakati una tarakimu 10 katika nukuu mfumo wako, 10

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inakuwa idadi badala maalum.

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Hebu tuangalie idadi 437 yaliyoandikwa katika nukuu decimal kwa

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kuelewa nini.

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Tunaweza kwanza kuvunja 437 400 plus 30 katika plus 7.

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>> Tunaweza kuchukua ni mbali zaidi hata hivyo kwamba sisi tumepewa mara 4 100

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plus 3 mara 10 plus mara 7 1.

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Kumbuka kujifunza kuhusu mahali ndio, mahali makumi,

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mahali mamia, na kadhalika?

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Hii ni hasa ambapo kwamba linatokana.

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Na hatimaye, tunaweza kuona jinsi sisi tumepewa rundo la nguvu za

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10 iliyoingia katika hapa.

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Sisi tumepewa mara 4 10-2 plus mara 3 10-1 plus

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7 nyakati 10-0.

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Hivyo sasa unaweza kuona kwa nini 10 ni maalum

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idadi katika nukuu decimal.

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Kwa kweli, sisi tumepewa jina kwa ajili yake, ni kuitwa wigo tangu

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ni msingi wa exponent katika hesabu yetu hapa.

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>> Nukuu decimal si njia pekee ya kuwakilisha idadi.

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Kwa kweli, hata kama sisi kujikwamua digits 2 kupitia 9, tunaweza

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bado kuwakilisha yote ya namba ambazo

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tunaweza pamoja na decimal.

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Hivyo sasa kwamba tuna tarakimu mbili, 0 na 1, 2 ni wetu

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maalum idadi, msingi wa nukuu mfumo wetu.

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jina la mfumo huu nukuu inaitwa binary, tangu

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kiambishi awali "bi" ina maana mbili.

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Hivyo badala ya sasa kuwa na mahali ndio na makumi mahali na

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kadhalika, sasa tuna nafasi ndio, mahali wawiliwawili, fours

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mahali, na kadhalika, kwenda kwa nguvu ya mbili.

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Basi hebu angalia hili na kufanya baadhi ya kuhesabu kura.

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Hivyo 0 0 bado, na 1 bado ni 1.

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>> Hata hivyo, sasa kwamba sisi tumepewa mahali wawili-wawili badala ya makumi

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mahali, 10 inawakilisha idadi 2.

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Ili kupata 3, sisi kuongeza 1 kwa kuwa na kupata 11.

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4, tangu sasa kuna mahali fours, ni kuwakilishwa na 100.

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Tano ni 101.

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6 ni 110.

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7 ni 111.

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8, tena, ina nafasi yake mwenyewe, hivyo ni 1000.

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Na nadhani wewe kupata uhakika.

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Hebu kumchoma katika kusoma kubwa binary idadi na

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kumwelekeza nyuma katika nukuu decimal, tangu kwamba ni nini

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tuliyoizoea.

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Idadi hii, katika binary, anayesoma 101,110,011.

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>> Kufikiri uwakilishi wake decimal, hebu kuanza kwa

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kuandika maeneo chini ya kila tarakimu.

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Kuanza, tuna 2 mahali zeros juu ya haki ya mbali,

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ikifuatiwa na 2 mahali ndio, 2 kwa mahali wawiliwawili, 2

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watatu, 2 hadi nne, 2 hadi tano, 2 hadi sita, 2

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hadi saba, na hatimaye, njia yote hadi 2 hadi nane.

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Sasa kama sisi kufanya math, hiyo ni mahali ndio, wawili-wawili

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mahali, mahali fours, mahali eights, mahali 16ths,

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Mahali 32nds, 64ths mahali, 128ths mahali, na hatimaye

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256ths mahali.

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Whew.

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Hivyo sasa, kama tunataka kuanza kuzidisha kila kitu

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pamoja, tunaona tuna 1 mara mara 256 plus 1 64 plus

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1 mara 32 plus 1 mara 16 plus 1 2 nyakati na nyakati 1 1.

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>> Hivyo kama sisi jumla yote ya kwamba pamoja, sisi kupata 256 plus

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64 plus 32 plus 16 plus plus 2 1, wote kwa

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grand jumla ya 371.

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Utafsiri kutoka nukuu decimal kwa nukuu binary ni

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kiasi fulani gumu, tangu tunahitaji kwenda kutoka idadi hiyo ni

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msingi juu ya nguvu ya 10 kwa moja hiyo kwa kuzingatia uwezo wa 2.

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Hebu kutoa ni kwenda.

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Hapa tuna idadi 237 katika nukuu decimal.

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Kutafsiri katika nukuu binary, mimi kuanza kwa kutafuta

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nguvu kubwa ya 2 kwamba ndogo zaidi, ambayo ni 128.

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Mimi kuweka 1 katika mahali 100/28 chini hapa

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katika binary namba yangu.

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Na kisha mimi Ondoa 128 kutoka 237, na mimi kupata 109.

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Kisha mimi tu kurudia utaratibu.

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nguvu kubwa ya 2 kwamba ni ndogo kuliko 109 64, hivyo mimi

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kuweka 1 katika mahali 64ths na Ondoa 64

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kutoka 109 kwa kupata 45.

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Tena, nguvu kubwa zaidi ya 2 kwamba chini ya 45 ni 32, hivyo

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kuweka 1 katika yanayopangwa sahihi na Ondoa 32 -

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Mimi naenda hoja juu hapa -

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kupata 13.

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>> Kuhama, mimi kupata 8 kama nguvu kubwa

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2 ya sasa, si 16.

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Basi, mimi kuweka 0 katika mahali 16S, 1 katika mahali 8s,

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Ondoa, na kupata 5.

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Kisha 4 ni nguvu kubwa ya 2.

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Mimi Ondoa na kupata 1.

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Sasa naweza kumaliza mbali tafsiri urahisi.

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Mimi kuweka 0 katika mahali wawiliwawili, na kuweka 1 katika mahali ndio.

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Matokeo yake, 11,101,101.

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>> Jambo moja unaweza kuwa inatarajiwa ni kwamba wote

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algorithms wewe kujifunza na kuongeza, Ondoa, kuzidisha, kugawanya na

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katika decimal nukuu kazi katika nukuu binary pia.

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Tutaweza kufanya mfano wa nyongeza.

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Hapa sisi tumepewa 1101101 plus 1,010,110.

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Tu kama katika kuongeza decimal, tutaweza kuanza kutoka kulia na

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kazi njia yetu kwa upande wa kushoto.

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Tofauti tu ni kwamba sisi kubeba 1 kama tarakimu mbili

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sisi ni kuongeza kuwa Jumla mkuu zaidi kuliko 1, badala ya

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jumla zaidi kuliko 9, kama katika decimal.

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Hivyo juu ya haki, tuna 1 plus 0, 1.

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>> Kusonga wa kushoto, tuna 0 plus 1, tena 1.

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Kusonga kushoto tena, tuna 1 plus 1, sisi kuandika 0,

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na sisi kubeba 1.

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Basi tuna 1, 1, 0, hivyo tuna 0, kubeba 1.

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Kisha 1, 0, 1, tena 0, kubeba 1.

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1, 1, 0, 0 tena, kubeba 1 ya mwisho.

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>> Na hatimaye, 1, 1, 1, hivyo tuna 1 na

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mwisho 1 upande wa kushoto.

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Matokeo yake, 11,000,011.

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Na kwamba anahitimisha haraka wetu

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kuanzishwa kwa nukuu binary.

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>> Jina langu ni Nate Hardison, na hii ni CS 50.