Inkqubo nani lokugqibela: kwisiseko, imizekelo, kunye translation kwezinye anenkqubo

Ukusuka umntu mzuzu waqonda kuqala ngokwaso into azimeleyo ehlabathini, wajonga, waphula isangqa zikhohlakeleyo ukusinda kucinga, waqalisa ukufunda. Wakhangela, xa kuthelekiswa, Ndaziqiqa iziphumo wenza. Kuyinto kwezi zenzo ezibonakala eziziziqalelo ngoku phantsi ngamandla umntwana waza waqalisa ukwakha yinzululwazi yale mihla.

Yintoni eya kusebenza?

Okokuqala kufuneka ukuba imisele ukuba ngokubanzi limela inkqubo inani. Lo mgaqo amanani irekhodi enemiqathango, ukumelwa kwabo ezibonwayo, leyo lula inkqubo kwingqiqo. Bebodwa, amanani musa ayisekho (kusixolela nathi Pythagoras, kholwa inani ngokwesiseko wendalo). Oku nje into nje ukuba unalo isiseko ebonakalayo yobalo, umlinganiselo yokuqala. Amanani - izinto apho inani amacandelo.

ekuqaleni

Okokuqala kwaziswa enxibe umlinganiswa kakhulu kwakudala. Ngoku ibizwa ngokuba inkqubo inani nonpositional. Ukuziqhelisa, oko inani apho indawo lweziqalelo enqila semxholweni. Ngokomzekelo, imivalo eziqhelekileyo, nganye lihambisana into ethile ezintathu elilingana yabantu |||. Njengalo okanye hayi, imivalo ezintathu - ukuba zonke oodwi mathathu. Ukuba uthatha umzekelo sisondela, Novgorod amandulo kwi-akhawunti ye-Slavic alphabet. Xa kufuneka ukwaba kuyo inani kwileta ~ kuzala nje. Kwakhona alfabhethi inkqubo inani yabanjwa sixabise phakathi ngamaRoma amandulo, apho amanani - oku kwakhona oonobumba, kodwa sele fanele ku oonobumba Latin.

Ngenxa ngabodwa kwamagunya yamandulo, iyileyo liqulunqe inzululwazi yabo, ngubani na kakhulu. Eyona nto iphawulekayo kukuba inkqubo enye wokugqibela libekiwe nkqu amaYiputa. Nangona kunjalo, i "isihlobo" ingcamango eqhelekileyo kuthi ke asikwazi ozakuthathwa siseko ukubala eyahlukileyo: abantu waseYiputa basebenzisa inani ezilishumi njengesiseko, ngokwalo izidanga.

kwabakho imfuneko ukuqaqambisa khupha ngophuhliso nokuntsonkotha nokuqonda inkqubo yehlabathi. Masithi kufuneka ulungise ngandlel ubungakanani umkhosi karhulumente, leyo ulinganiswa amawaka (kakuhle). Kulungile ngoku angenakulinganiswa amisele uneentonga? Ngenxa yoku, abaphengululi bamaSumeri kwaloo minyaka ziye zachongwa inkqubo amanani, apho kwindawo umlinganiswa kwakubangelwa ekubhobhozeni kwakhe. Kwakhona, umzekelo: amanani 789 no 987 babe "isakhiwo" efanayo, kodwa ngenxa amanani indawo utshintsho, owesibini inkulu kakhulu.

Yintoni na - inkqubo inani lokugqibela? izizathu

Kakade ke, ukuma kunye ipateni wayengekho efanayo kuzo zonke iindlela yokubala. Umzekelo, eBhabhiloni wenza inombolo isiseko 60, eGrisi - kwinkqubo yokubhala (inani zezincwadi). Kuyabonakala ukuba indlela yokubala abemi baseBhabheli, uphile unanamhla - wafumana indawo yakhe ngeenkwenkwezi.

Noko ke, oko wabanjwa yaye isasazeka ukuba apho radix - elinesibini, oluchazwa frank ngaxeshanye kunye iminwe wezandla zabantu. Ngumgwebi ngokwakho - khosi ngokugoba iminwe nakubalwa phantse kwi-iseti ongapheliyo.

Imvelaphi yale nkqubo yaqala ngo-India, apho wabonakala nangoko ngokusekelwe "10". Formation of the amanani lwamagama mbini - umzekelo, 18 akwazi igama yaye "elinesibhozo" kwaye njenge "ezingamashumi amabini anesibini ngaphandle." Kwakhona, kuba i izazinzulu Indian ziye kwakuthe into efana "zero", kungarekhodishwa ngokusesikweni imbonakalo yayo kwinkulungwane IX. Oku eli nyathelo iye ibalulekileyo ekubunjweni kwenkqubo yamandulo inani ngokokuma, ngokuba zero, nangona ufuzisela yanto, akukho nto iyakwazi ukuxhasa inombolo bit, ukuba akukho ilahlekelwe intsingiselo yalo. Umzekelo: 100000 kunye 1. Inani lokuqala luquka amanani 6, lokuqala apho - iyunithi, nabokugqibela ezintlanu amele into engento, engekho, kwaye inani lesibini - nje omnye. Ngokusengqiqweni, kufuneka alingane, kodwa kusenziwa njalo. Amaqanda angu ku 100000 abonisa phambi kwabo iphiko, nto leyo ke inani lesibini apho. Apha ukuba "akukho nto".

modernity

Inkqubo inani lokugqibela wenziwa amanani ukusuka kwiqanda ukuya ezisithoba. Amanani azotywe ngaphakathi kwayo, zisekelwe kumgaqo ilandelayo:

digit abaninzi bomtya ibonisa yunithi, ukuhambisa inyathelo elinye ukuya ngasekhohlo - ufumana ishumi, elinye inyathelo ukuya ekhohlo - ikhulu, njalo njalo. Nzima? Into enjalo! Enyanisweni, imizekelo inkqubo wokugqibela Unganikezela ebonakalayo kakhulu, ukuba ubuncinane 666. iqulathe amanani amathathu 6, ngalinye olumele udidi. Ngaphezu koko, le yindlela yokubhala inciphisiwe. Ukuba ufuna ukugxininisa ngoko kanye inani ekuthethwa, kuqashwe ibe oko, bendise ngokubhala ukuba "ovakalisa" ilizwi lakho elingaphakathi ixesha nganye ubona inani - "omathandathu anamanci mathandathu anesithandathu". yokubhala ezingeyomfuneko kuquka zonke kwabo efanayo, amashumi nabamakhulu, oko kukuthi, isikhundla idijithi nganye liphindaphindwe ethile ngamandla inani 10. Le fom eyandisiweyo i ndlela ilandelayo:

6x10 = 666 ₁₀ ^{2 + 6 * 10 1 + 6} * 10 0 = 600 + 60 + 6 .

ezinye zangoku

Okwesibini ezithandwa emva kokuba inkqubo inani lokugqibela usemtsha ngokwaneleyo ezahlukeneyo - lokubini (kabini). Kubonakele Bulelani ikuyo Leibniz, ababekholelwa ukuba kwiimeko ezinzima ekufundeni thiyori amanani okubini kuya kuba lula ngakumbi lemivo elishumi. ubukhulu babo, lafumana kunye nophuhliso lwetheknoloji yedijithali, njengoko anayo isiseko inombolo 2, kwaye izinto kulo ziyaqokelelwa kumanani-1 no-2. Coding ulwazi kwenzeka kule nkqubo, ukususela-1 - ubukho umqondiso 0 - akukho. Ngokusekelwe kulo mgaqo, sinokubonisa embalwa mizekelo ibonisa imifanekiso ukubonisa transfer inkqubo wokugqibela.

Ekuhambeni kwexesha, iinkqubo ezinxulumene senkqubo waba nobunzima kakhulu, ngoko anenkqubo iindlela amanani yokubhala apho balala esisekweni 8 no 16. Kutheni na ke? Okokuqala, inani loonobumba ngakumbi, kwaye ke inani ngokwayo iya kuba elifutshane, yaye okwesibini - zisekelwe amandla ababini. inkqubo Octal iqulathe amanani 0-7, kunye elinekona ezintandathu eziphela kwishumi - lala manani manye ukuba wokugqibela iileta plus ukusuka A ku F.

Siseko kunye neendlela translation

Guqulela inkqubo wokugqibela nje ngokwaneleyo ukuba zilandele ngqo umgaqo ilandelayo: inani yokuqala ibhalwe njenge polynomial, nto leyo ubunjwe izibalo imveliso yenani ngalinye kwi ngokusekelwe "2" ephakanyiswe ukuya kwinqanaba elifanelekileyo bit.

Le ndlela yokubala esisiseko yokubala:

x2 = y k 2 k-1 + y k-2 k-1 2 + y 2 k-2 k-3 + ... + y 2 + y 1 2 1 2 0.

imizekelo translation

Ukuqinisa ingqalelo amazwi ezininzi:

101111 ₂ = (1x2 ⁵⁾ + (0x2 ⁴⁾ + (1x2 ³⁾ + (1x2 ²⁾ + (1x2 ¹⁾ + (1x2 ^{0) = 32 + 8 + 4} + 2 + 1 = 47 10 .

Nzima ingxaki, ngokuba le nkqubo ibandakanya amanani translation and iqhezu, kuba oku, sicinga ngokwahlukeneyo lilonke inxalenye iqhezu ngokwahlukeneyo - 111,110.11 _2. Ngoko ke:

111110.11 ₂ = (1x2 ⁵⁾ + (1x2 ⁴⁾ + (1x2 ³⁾ + (1x2 ²⁾ + (1x2 ¹⁾ + (0x2 ^{0) = 32 + 16 + 8} + 4 + 2 = 62 10 ;

Novemba ₂ = 2 ^-1 x1 + 2 ^-2 x1 = 1/2 + 1/4 = 0,75 _10.

Ngenxa yoko, siyabona ukuba ₂ = 62.75 111,110.11 _10.

isiphelo

Phezu kwayo yonke i "kudala", inkqubo inani lokugqibela, imizekelo esifunde ngazo ngasentla, kwaba sekunjalo: "ngehashe", kwaye ukutsala kuyo le ngxelo, akukho mfuneko. Ukuba iba isiseko zemathematika esikolweni, umzekelo layo bayazi imithetho ekuqiqeni zezibalo, ababonisa ukukwazi ukwakha ubuhlobo iqinisekisiwe. Ewe, ukuba kukho - phantse ihlabathi lonke usebenzisa le nkqubo ethile, atyhafe yi awungeni yakhe. Isizathu sokuba lo: kulula. Enyanisweni, isiseko ukurhoxisa nayiphi na iakhawunti, uyakwazi, ukuba kukho imfuneko, kuya kuba i-apile, kodwa kutheni nzima izinto? Ngokugqibeleleyo-yalungisa inani lamasuntswana, ukuba kuyimfuneko, unokuthenjwa ngeminwe.