Pūnaha Tau Rua
Ko te pūnaha tau rua tētahi o ngā ariā tino taketake o te rorohiko o ēnei rā. Tata ki ngā taputapu matihiko katoa e whakamahia ana e tātou i ia rā—mai i ngā waea pūkoro me ngā rorohiko ki ngā ATM me ngā taputapu Ipurangi o ngā Mea—ka tukatuka i ngā raraunga i roto i te āhua rua. Ahakoa te āhua tūturu o te pūnaha ira tekau (pūtake 10) ki te tangata nā te mea kua taunga tātou ki te tatau me ngā mati tekau (0–9), he pai ake te whakamahi a ngā rorohiko i ngā āhua māmā e rua: 0 me te 1. Ka hangaia ngā mōhiohio matihiko katoa mai i ēnei tohu e rua.
Te mārama ki te pūnaha tau rua
Ko te pūnaha tau rua he pūnaha tau e whakamahi ana i te pūtake o te 2. Ko te tikanga o tēnei, e rua noa ngā mati o te tau rua: 0 me te 1. Kāore i rite ki te pūnaha ira tekau, he pūtake o te 10 me te tekau mati (0–9), ka tohu te tau rua i ngā uara mā te whakamahi i ngā huinga o ēnei mati e rua. He uara tūnga tō ia tūranga mati i roto i te tau rua, he mana o te 2, ehara i te mana o te 10.
Hei tauira, e whā ngā mati o te tau rua 1011. Ko ō rātou uara tūnga mai i te matau ki te maui ko:
– 2⁰ (1)
– 2¹ (2)
– 2² (4)
– 2³ (8)
Nō reira, ko te tau 1011 (rua) he ōrite ki:
(1×8) + (0×4) + (1×2) + (1×1) = 8 + 0 + 2 + 1 = 11 (ira).
He aha i whakamahia ai e ngā rorohiko ngā pūnaha rua?
Ko te take matua e whakamahia ai e ngā rorohiko te pūnaha rua, he mea e tino ōrite ana ki te mahi a ngā taputapu hiko. Ko ngā wāhanga taketake o ngā ara iahiko matihiko, pērā i ngā transistors, ka taea te wehewehe i roto i ngā āhua e rua: te whakakā/te whakaweto, te teitei/te iti, te ngaohiko/te kore ngaohiko rānei. Ka taea te mahere tika i ēnei āhua e rua ki te 1 me te 0.
Hei tāpiritanga, he painga anō hoki tō te pūnaha rua mō:
1. Te pono o te tohu: he nui ake te pumau o te wehewehe i ngā taumata ngaohiko e rua i te wehewehe i ngā taumata maha i te wā kotahi.
2. He hoahoa ara iahiko māmā ake: ka mahi noa ngā kēti arorau pēnei i a AND, OR, NOT me ngā uara e rua.
3. Te whai huatanga o te tukatuka: ka taea te whakatinana i ngā mahi tātai me ngā mahi arorau mā roto i ngā ara iahiko tino māmā.
Te ariā o ngā moka me ngā paita
I roto i te horopaki rua, ka kiia he mati kotahi, 0, 1 rānei, he moka (mati rua). Ko te moka te waeine raraunga iti rawa i roto i te rorohiko. Heoi, i roto i te mahi, he onge te tukatuka raraunga i roto i te moka kotahi anake. Ko ngā moka ka whakarōpūhia ki ngā waeine nui ake, hei tauira:
– 4 ngā moka = ngaungau
– 8 ngā moka = 1 paita
– 1024 paita ≈ 1 kiropaita (KB) (ko te tikanga 1 KiB = 1024 paita)
Mā te 8 bits (1 byte), ka taea e tātou te hanga i te 2⁸ = 256 uara pea (0 ki te 255). Koinei te mea e taea ai e ngā rorohiko te penapena i ngā momo raraunga: ngā tau, ngā reta, ngā tae, me ngā tohutohu hōtaka—e whakaatuhia ana katoa hei huinga o ngā 0 me ngā 1.
Me pēhea te huri i te rua ki te ira tekau
Hei huri i tētahi tau rua ki te tau ira, ka tāpirihia e tātou te hua o te whakarea i ia mati ki tōna uara tūnga (mana o te rua).
Tauira: 11010 (rua)
Uara tūnga: 16, 8, 4, 2, 1
Hitungan:
(1×16) + (1×8) + (0×4) + (1×2) + (0×1)
= 16 + 8 + 0 + 2 + 0
= 26 (ira)
He mea tino nui tēnei tikanga nā te mea ka āwhina i a tātou ki te mārama ki te tikanga o ngā tau rua e rongoa ana i roto i te mahara.
Me pēhea te huri i te ira tekau ki te rua
Hei huri i te tau ira-ira ki te tau rua, ko te tikanga tino noa ko te wehewehe anō i te 2, kātahi ka pānui i te toenga mai i raro ki runga.
Tauira: tahurihia te 19 (ira-tekau) ki te rua:
– 19 ÷ 2 = 9 toenga 1
– 9 ÷ 2 = 4 toenga 1
– 4 ÷ 2 = 2 toenga 0
– 2 ÷ 2 = 1 toenga 0
– 1 ÷ 2 = 0 toenga 1
Pānuihia te toenga mai i raro ki runga: 10011
Nō reira, 19 (ira-ā-ira) = 10011 (rua-ā-ira).
Ngā mahi pāngarau i roto i te rua
Ka tautokohia hoki e te pūnaha rua ngā mahi pāngarau pēnei i te tāpiri, te tango, te whakarea, me te wehewehe. Ko te tāpiri rua te mea tino taketake, ā, he rite ki te tāpiri ira, engari ko ngā mati he 0 me te 1 anake.
Ngā ture tāpiri rua:
– 0 + 0 = 0
– 0 + 1 = 1
– 1 + 0 = 1
– 1 + 1 = 10 (hua 0, pupuri i te kawe 1)
Tauira: 1011 + 0110
""
1011
+ 0110
-
10001
""
Ko te hua ko 10001 (rua) = 17 (ira). Koinei te kaupapa o te tāpiri a ngā rorohiko i ngā tau ki roto i te CPU.
Te whakaaturanga raraunga: mai i ngā tau ki te tuhinga
Ehara i te mea ko te pūnaha rua anake te mea hei penapena tau. I runga i ngā rorohiko, ka whakakōwaeatia hoki te tuhinga ki roto i te pūnaha rua mā te whakamahi i ētahi paerewa. Ko ngā tauira rongonui ko te ASCII me te Unicode.
– I roto i te ASCII, ko te reta 'A' e tohuhia ana ko te tau ira 65, arā, i roto i te rua ko te 01000001.
– I roto i te Unicode (hei tauira, UTF‑8), ka taea te whakaatu i ngā pūāhua mā te whakamahi i tētahi, neke atu rānei o ngā paita, ā, ka taea te whakamahi i ngā momo reo me ngā tohu.
Haunga te tuhinga, ka whakaatuhia hoki ngā whakaahua me ngā oro i roto i te reo rua. He mea tito ngā whakaahua matihiko i ngā pika, ā, he uara tae motuhake kei ia pika kua rongoatia hei reo rua. Ka tuhia te oro hei tauira whānui, ka hurihia hoki ki ngā uara rua.
Te whanaungatanga o te pūnaha tau rua me ētahi atu pūnaha tau
I roto i te hōtaka rorohiko me te hangarau, he maha ngā wā ka honoa te rua ki ētahi atu pūnaha tau pēnei i:
– Octal (turanga 8): e whakamahi ana i ngā mati 0–7
– Hexadecimal (turanga 16): e whakamahi ana i ngā mati 0–9 me A–F
He tino rongonui te ira-ā-ira he iti ake i te tuhi i ngā ira-rua. Hei tauira, ka taea te whakaatu i ngā ira-rua e 8 mā te whakamahi i ngā mati ira-ā-ira e 2. Hei tauira: ira-rua 11111111 = FF (ira-ā-ira). Mā tēnei ka māmā ake te pānui i ngā wāhitau mahara, ngā waehere tae (hei tauira, FF00FF), tae atu ki ngā kaupapa patuiro.
Te tūranga o te rua i roto i te ao hou
Ahakoa te āhua māmā noa iho o te pūnaha rua, he hohonu rawa tōna mahi. Ko ngā arorau tukatuka rorohiko katoa, mai i ngā mahi pāngarau me te rokiroki kōnae ki ngā whakawhitiwhitinga whatunga me te whakamunatanga haumarutanga, he mea hanga i runga i te whakahaere i ngā moka rua. Ina tuku karere tātou, ina mātaki ataata rere, ina mahi rānei i ngā tauwhitinga matihiko, kei te neke me te tukatuka tātou i ngā aho roa o te 0 me te 1.
Ahakoa ngā ariā matatau pēnei i te kōpeketanga raraunga, te mātauranga horihori, me te tukatuka tohu mamati, kei te pūtake tonu i te whakaaturanga rua. Arā, ko te mārama ki te pūnaha tau rua he taahiraa tuatahi nui ki te māramatanga hohonu ake ki te mahi a te hangarau mōhiohio.
Whakamutunga
Ko te pūnaha tau rua he pūnaha turanga-2 e whakamahi ana i ngā mati e rua anake: 0 me te 1. Ahakoa tōna māmā, ko te rua te tūāpapa o ngā taputapu matihiko katoa nā te mea e ōrite ana ki ngā āhuatanga hiko o ngā ara iahiko hiko. Mā te whakamahi i te ariā o ngā moka me ngā paita, ka taea e te rua te tohu i ngā momo raraunga - ngā tau, ngā tuhinga, ngā whakaahua, me te oro - ā, e tautoko ana i ngā mahi tātai me ngā mahi arorau kei te ngākau o te tukatuka rorohiko. Ko te mārama ki te rua ehara i te mea ka āwhina noa i te ako pāngarau me ngā rorohiko, engari ka whakatuwhera hoki i ngā māramatanga ki te mahi a te hangarau hou i muri i ngā whakaaturanga.
