Tau-rua: pūnaha ā-rua

tau-rua - ko te maha o-rua pūnaha tau, he turanga 2. Kei te whakatinana te reira i tika i roto i te hikohiko mamati, whakamahia te i roto i te nuinga o ngā pūrere rorohiko hou, tae atu ki ngā rorohiko, waea pūkoro me nga mea katoa o pūoko. Ka taea e tatou te mea i hanga katoa o to tatou hangarau wā i runga i tau ā-rua.

tau record

Tetahi maha, noa'tu te rahi e ko te reira, i roto i tuhia i te pūnaha ā-rua e te tikanga o e rua ngā tohu: 0 me 1. Hei tauira ahua 5 o te pūnaha ira maheni katoa i roto i te rua te māngai rite 101. tau-rua kia whakaritea e te kuhimua 0b amapehana ranei (&) hei tauira: & 101.
I roto i ngā pūnaha tau katoa, hāunga te ira, e lau nga pūāhua tetahi i tetahi, tangohia e te rite te tauira 101 te tai'o rite "kotahi kore tetahi".

Whakawhiti i te pūnaha tetahi ki tetahi

Kei te tonu te mahi hötaka ki te pūnaha pūtakerua i runga i te haere e taea tahuri tau ā-rua ki te ira. tino taea te mahi i tēnei, kahore tetahi tātai, rawa ki te he tangata he whakaaro o te āhua o te mahi i te reira ko te wahi iti rawa o te rorohiko "roro" - paraire.

Ko te tau kore i te mea he 0, me te tokomaha tetahi i roto i te pūnaha ā-rua, ka waiho ano he wae, engari aha ki te mahi ina rere i te tau? Kei te "karangatia" te pūnaha ira ki te tomo i roto i te take i taua, ko te wā "tekau", me i roto i te pūnaha ā-rua, ka e huaina a reira "haupara".

Ki te 0 Ko 0 ° (amapehana - pūnaha momotuhi ā-rua) 1 = k 1, ka tuku i te reira ki rite 2 & 10. Ko te runga e toru e taea hoki te tuhituhi i roto i rua mati, ka waiho i te reira o te puka & 11, e ko te taurite me te wae kotahi. Kua pau nga ngā taea, a i roto i te pūnaha ira whakaurua rau i tenei wā, me i roto i te-rua - "wha". Wha - reira & 100, rima - & 101, e ono - & 110, e whitu - & 111. Next, he wae nui o pūkete - waru he ahua.

Ka taea te kï hoki āhuatanga: ki te e whakanuia nga mati-ira e tekau (1, 10, 100, 1000, me te pera i runga i), i roto i te rua, aua, ki e rua: 2, 4, 8, 16, 32. hāngai tenei ki te rahi o kāri mahara flash me ētahi atu puku whakamahia i roto i rorohiko, me te tahi atu pūrere.

He aha te mea te waehere ā-rua

Ko te tau e whakaaturia i roto i te pūnaha ā-rua, e mohiotia ana ko-rua, engari i roto i tenei puka e taea te aroaro me te uara tau (pūāhua me ngā tohu). Ko te kupu, ko reira taea ki te whakawaehere te kupu me ngā tuhinga i roto i tau, ahakoa ka whai ratou i te tirohanga kore pera tau, no te mea ki te tuhituhi tetahi anake reta Me etahi ngā kore, me te hunga.

Ko pehea rorohiko whakahaere ki te pānui i kia nui ngā kōrero? I roto i te meka, he māmā atu te mea te reira mea katoa. Iwi waia ki te pūnaha ira, te tuatahi tahuri tau ā-rua i roto i te maheni ake, a ka meinga ratou tetahi whawhe, me arorau e hāngai ana-rorohiko, ko te pūnaha tau tuatahi rua. Unit i roto i te toi hāngai ki te ngaohiko tiketike, me te kore - he iti, ranei te ngaohiko mo te waeine ko, a ki te kore e ngaro.

tau-rua i roto i te ahurea

Ko te hapa ko te ki amo e te pūnaha ā-rua - ko reira he paetae o pāngarau hou. Ahakoa he mahu'inga i roto i to tatou hangarau wa tau ā-rua, me te, kua kua whakamahia ratou mo te wa roa, me te i roto i ngā wāhanga rerekē o te ao. Whakamahia te rārangi roa (kōwae) me taratahi waru pūāhua (kore) whakawaehere, te tikanga e waru huānga: te rangi, te whenua, te whatitiri, te wai, maunga, hau, he ahi me te wai (te wai taimaha). Tenei tairitenga o tau moka-3 whakaahuatia i roto i te kuputuhi matarohia o te Buka o Changes. Trigrams ko Hexagrams 64 (tau bit-6), te raupapa i roto i i kua i te rēhita kua Kei huringa i roto i runga i te tau ā-rua i 0 ki te 63.

hanga tenei tikanga i roto i te tekau ma tahi rau akonga Hainamana Shao Yong, ahakoa kahore he taunakitanga e matau tino ia te pūnaha tau ā-rua rite te katoa.

I roto i India, ara i mua i te whakamahia to tatou era hoki tau ā-rua i roto i te pūtake pāngarau mo te whakaahuatanga o te rotarota, mathematician titoa Pingala.

whakaaro nodular tuhituhi Inca (wuru) ko te tauira o pātengi raraunga hou. Ko te wā tuatahi kua whakamahia ratou tau-rua e kore anake, engari e kore e te tāurunga tau i roto i te pūnaha ā-rua. reta kono pēre taviri tuatahi, me te atu e kore anake āhuatanga, engari te whakamahi i tau tū whakawaeheretia te whakamahi i tae, me te raupapa raraunga o aua (huringa). Inky te tuatahi ki te whakamahi i te tikanga o te kaute i huaina urunga-rua.

Ko te tuatahi o nga hötaka

pūnaha pūtakerua i runga i nga tau 0 me te 1, ka whakaahuatia te pūtaiao rongonui, ahupūngao me te mathematician Gotfrid Vilgelm Leybnits. ko aroha o te ahurea Hainamana tawhito, me te ako i te tuhinga tuku iho o te Buka o Huringa ia, hexagrams rite kitea tau ā-rua i 0 ki te 111111. whakamoemititia ia i te taunakitanga o taua ahunga whakamua i roto i te rapunga whakaaro me te pāngarau i te wa. Leibniz kia whakahuatia ai tuatahi o hötaka me pūkenga mōhiohio. Ko ia te tangata e kitea e te mea e tuhituhi tatou te rōpū o ngā tau ā-rua poutū (tetahi i runga i te tahi atu), ka e kia korerotia wā nga pou poutū hua o tau ngā kore, me te hunga. ka karanga te reira ia ki te whakaaro e reira kia waiho he ture pāngarau rawa hou.

matau Lejbnits me e he tino pai mō te whakamahi i roto i rehe nga tau pūtakerua, te pūtake o e kia he huringa huringa hāngū me te kaha. Ko te iari i roto i te rau tau 17, me te kaipūtaiao nui whakaaro he mīhini tātai i roto i te pepa, mahi i runga i te pūtake o ana ngā āhuatanga hou, engari hohoro mohio e kore i e ano tae te ao taua whanaketanga hangarau, a i roto i tona wa, e kore e taea te hanga o te mīhini taua.