Into endifuna ukuyenza kulomboniso kukuba ndityelele imibono enikhe nayenza kodwa anayithathela igqalelo sukela
ngeloxesha nanine minyaka eyi3 okanye u4, kodwa ngoku inoba nizakuyibona intsha ezakuthi 3
isincede ukusazisa xasisebenza ngezinye intlobo zamanani. Ke ngoku sine "digit" eziyi u10 kumanani ethu
Ke ngoku sine "digit" eziyi u10 kumanani ethu.Manditsho ndiqalise ukubala. Ke xa ungenanto ndizosebenzisa iphawu u0.
Ndisebenzisa iphawu u1. Yeka ndiyilungise. Ke akhonto, ndibenento, Ndisebenzisa iphawu u1.
Ukuba ndinezinto eziyi u2, ndizo sebenzisa iphawu u2. Ukuba ziyi u2, ndisebenzisa u3. Manditsho ndehlele
phantsi kancinci ukuze ubone. Ukuba ndinezinto eziyi u4, ndizo sebenzisa elaphawu phana. Ukuba ndine
zinto eziyi u5, ndizo sebenzisa eliphawu.Ukuba ndinezinto eziyi u5...masiyizobe kanjeya..ukuba izinto ziyi u6, ndithatha lena
Ukuba ziyi u7, ndisebenzisa oluphawu. Ndiyayazi ukuba lento ingaku xaka kancinci, kodwa yonke
lento inalo ichaphaza. ukuba ndinezinto eziyi u8, ndisebenzisa eliphawu. Ukuba ziyi u9 ndiza
kusebenzisa eliphawu. Ndiphinde ndibene ziyi u10... loluphi uphawu emandilu sebenzise? Seke esebenze onke ayi10, ngoku sina
u10 "systems", siphinde siwasebenzisa kwakhona. Ngoku siphinde sazisa icebo le "number places". Ubuthe ukuba
apha ndino u10 omnye kunye no u1 abayi u0. Ke uthi uno u10 omnye kunye no u1 abayi u0.
...kwaye oo u1 abayi u0. Lona simbiza u1, sithi ukwindawo ka10. Lento ithetha ukuthi u1,
lento ithi"tens" enye, yi "1tens" uyidibanise no u1 abayi u0. Ke lento ithetha ukutsho.
Kodwa bekunga nyanzelekanga siphinde siyisebenzise. Besino vele sibena maphawu aliqela.
Mhlawmbi eli ibiliphawu, endaweni ye, mhlawmbi besenokwenza iphawu elitsha.
Indaweni yoku, sowuyazi, zonke ezi bezinophawu lwazo, endaweni yokuba sisebenzise amadala
phinda senze elinye iphawu layo... mandiye ku11, nditsho ndikhwezele eziko.
Ke ngoku... 2,3,4,5,6,7,8,9,10,11.
Ke, u11 kwi "number system" yethu, sithi ukuba lona ngu10... sithi lena ngu10
...mandiyi bhale ngolu hlobo... u10 omnye. Kwaye nalena, ngu10 omnye, kunye no1 omnye.
...kunye no1 omnye. Ke, ngu10 onye, umdibanise no1 omnye. Ndiyayazi ukuba lento ingaxaka xa uyibona
ngale ndlela, kodwa imele ezizinto zinga. Ukuba besine "base" engu11, ndicinga ukuba besinovele
sithi "base" ka12 we "number system", mhlawmbi besizo kubano phawu lalento
endaweni yokuba siphinde sisebenzise "idigit" ezindala. Mhlawmbi upha belinoba bhetele
... mhlawmbi ibinokuba bubuso obuncumileyo. leyo yinto esiyaziyo. Kwaye ndizakwazisa
ezinkulu i"number base systems", kwimiboniso ezayo apho sibona, amaphawu
asele esetyenzisiwe. Kodwa, into endifuna ukuyenza kulomboniso khawu cinge
ngehlobo esibala ngalo, okanye ngawaphi amaphawu esinoku wasebenzisa
ukuba besine "digit" ezimbalwa, balaseleyo, singenza
njani ukuze sibale i"digits" eziyi u2 qha - ukuba besino
u0 kunye no u1. Okubalulekileyo, sizakuyi cingisisa lento
ukuba sizokuwa misa njani amanani kwi"base" zika u2.
Eyona ndlela yethu ye"number system" ka"base" u10.
Sine "digits" eziyi u10 - u0 uyoqhambuka ku9
Singabala njani kwi"base" ka u2?
Ke, ukuba unezinto eziyi u0, mhlawmbi ungathi
"tshini, ndino u0. Ndingayisebenzisa le 'digit' ka u0."
Ukuba ndinento enye, ndingakwazi ukuthi
"tshini, Apha ndinento enye"... ngoba, sine
'digits' zika u0 nezika u1. Ke, Manditsho ndiyicacise.
Ezi 'digits' apha, i'digits' kwi 'base' zika u2, zingaba ngu u0 okanye
Ukuba ndinento enye, ndingakwazi ukumsebenzisa inani u1
Kodwa, ngoku ngokungxamiseka nje ezizinto ziyi u2 apha,
kwaye ngoku ndilinganiselwe... kwezi 'digits' zimbini phana.
Ke ngoku, lento ndingayi beka njani. Ke, indaweni yokuba
ndibene "ten's place", ndingenza i"two's place".
...kwaye Ndiyayazi ukuba lento ingavakala ngathi ayivakali ncam kodwa ndicinga ukuba uzaku
qhela kancinci kancinci. Ke, apha sine 'base' ka u10, sithi ukuba sino u10 oyi u1 kunye no u0 oyi u1.
Ke ngoku kwi'base' ka u2, kutheni singavele sibeno
1,2 - 1,2 - kunye no u0,1.
Yeka ndicacise lento. Ke, lento ilapha yona ithetha ukuthi
1,2 kunye no0,1.
Ndifuna ukuqinisekisa ukuba uyawuqonda lomzekelo apha.
Kwi isinqu ka u10... mandibhale inani elikhulu apha kwi siqu ka u10...
...kwaye ke ukuba ndibhala elinani u256 kwi 'base' ka u10...
ngoko ke, leyana phana yi'base' ka u10, lento ithetha ukuthini?
Lento ithetha ukuthi u200, ngoku ke, u2 umphinde ngo u100...
okanye, mhlawumbi mandibhale phantsi eligama ukuze ndinga phazamisi amaphawu..
u200 udibanise u5 uphinde ngo... okanye mhlawmbi mandithi u200
umdibanise no u5 ophindwe ngo u10... u200, umdibanise no u5 ophindwe ngo u10, udibanise u6 ophindwe ngo u1.
Lento yilena ndiyibonisayo apha, kwaye ihlobo esiyazi ngayo thina lento kukuba
siyayazi ukuba sibhekela kabini ngasekhohlo, lena yindawo yesi u100
lena yona yindawo yesi u10, lena yona ibeyindawo yesi u1.
Kwaye ukuba uyazazi i"exponents" zakho, lento ilingana no u10 umphinda phinde ngo u10.
Lento apha iyodwa nje ilingana no u10 umphinde kwangaye kanye
kwaye lento iyalingana no10 aziphindaphinde kokwakhw, ndiyathemba
ungayibiza, u0 umphinde.
Okanye, ukuba uyazazi i"exponents" zakho, lento ngu
u10 kwi "power" ka u2, lena yona ngu u10 kwi "power" ka u1,
kwaye lena yona ngu u10 kwi "power" ka u0.
ukuba ubudibanise enye i"digit" apha, lonto
ibizakuba yindawo yesi u1000, ebizakuba ngu
u10 umphinde ngo u10 uphinde kwakhona umphinde ngo u10.
Siza kuphinda senze ngqo kwalento inye kwi "base" ka u2
kodwa, endaweni yokusebenzisa u10, sizaku
kusebenzisa u2.Ngoku Ke lena yindawo ka u2.
Lena apha yindawo ka u2. lena yona yindawo ka u1.
ukuba sidibanisa ezinye i"digits'... manditsho ndiyicacise...
Ke kwi base ka u2... mandibhale
Khumbula, kiwsiqu sika2 ndinga sebenzisa u0 okanye u1.
Ngoko ke, kwisiqu sika2, mhlawumbi ndienani u1010
ngoko ke xa ucinga ngayo ngalendlela, ukuba lento ibinesiqu u10
ungayiza lento ukuba ikwi ndawoye10, kwindawo 100, kwaye kwindawo 1000.
Kodwa, lento ngoku inesiqu u2. ngoko ke mandicacise.
Sisebenzisa imivo eyi2. Ngoko ke kwisiqu u2
lento apha isekwindawo yokuqala
ngoku lento izakuba kwindawo yesibini
khumbula, kwisiqu u10 ibikwindawo ye10, ngoku
lento ikwindawo yesibini.
Ngoku izakuba ngu, kwaye ungenza uqikelelo apha
100 ibingu 10 umphinda-phinde ngo10.
Xa sisiya kabini ngasekunene kwisiqu u2
lento ufenele ukuba ibe ngu 2 umphinda-phinde ngo 2 kwindawo yesibini.
Okanye lento ibekwindawo yesine. Lento ilapha izakuba kwindawo yesibhozo.
Ngoko ke, ukuba ufuna ukucinga ngayo ngendlela
yesiqu esingu 2, lento ngu 1, ngu 18, dibanisa
dibanisa u1 2, dibanisa 0. Dibanisa 0.
Ngoko ke, ukuba ubufuna ukubala lento nganye gqo elinani
kwisiqu u10, ngu 1, 8 dibanisa 1, 2.
ngoko ke kwisiqu esingu 10 lento izakuba ... mandiyibhale phezulu apha...
kwisiqu sia10 izokuba ngu8 umdibanise no2, into ethetha ukuba ngu10
Ngoko ke, lento enisiqu esingu 10. Lento uyibonisa ngoluhlobo
siyazi nggendlela ezininzi- nje ngezinto eziyi10.
Lento uzakuyibonisa ngoluhlobo inesiqu esingu 2.
Lento siyazi ngoluhlobo ukuba ngesiyibonisile inesiqu esingu 10.
Ngoku masiqhubekele phambili apha, ukuqinisekisa ukuba siyaziqonda kakuhle izinto.
Ngoko ke lento ingaveza, kulungile, kwisiqu esingu 2 sino 1...
ukuba ufuna izinto zibe mbini- ngu 1, 2 kunye 0, 1
ngoku xa zintathu izinto zethu izakuba 1,2 dibanisa 1.
Ngoko ke mandiyenze phezulu apha, ngoko ke lento izakuba 1,2
dibanisa 1.
ngoko ke lento zizinto ezontathu ezinesiqu u2.
Ngoku xa sihamba lendlela lento, ngoko ke phezululu apha zizakuba no 1,4...
0,2 kunye 0,1.
Ngoko ke ngoku siya kwindawo yesine.
Ngoba ngokukhawuleza sidibanise yonke into.
Ukuba ziqwalasela ezininzi, kuzakufuneka siye kwindawo ezininzi
nje ngokuba besenzile kwisiqu esingu 10, kodwa ngoku singasebenzisa
imivo u 0 kunye no 1.
Ngoko ke ngoku sizakuba no1 abayi 4, 0 abayi 2, no0 oyi1.
ngoku xa sidibanisa u1 kwakhona, sizakudibanisa u1 kunye nomye u1
ngoko ke, ngoku sino 1 abiyi 4, no0 abayi 2, kunye no1 oyi 1.
kwaye xa ndicacisa, lento zizinto ezininzi.
Lento zizinto ezininzi kwisiqu esingu 2, lento ikwindawo yesine
oo-1 abayi 4 kunye no 1 oyi 1. Ukuba ufuna ukuguqula
lento ibe kwindawo wesishumi, unga khangela
" lona angu 1 no 4, no 0 abayi 2, kunye no 1 oyi 1."
Ngoko ke ukuba uno 4 kunye no1, singaba bhala
ngophawu luka 5 isiqu ibe ngu 10, kodwa
asinaphawu lokulive kwisiqu sethu esingu 2.
Masiye kulento. Ngoko ke, ngoku sizakwandisa onye u1 ngaphezulu.
Ngoko ke, singayibonisa njani lonto kwisiqu esingu 2?
Lento ngokuqinisekileyo, sizakufumana oo-1 abayi 4...
kwaye kwango ko sizakufumana oo-1 abyi 2..kwaye kwango ko
sizakuba no-0 omnye.
Kwaye ukuba siyayigcina ...izakonwabisa ukuyaphambili
kwisiqu u2, uzakuqala kuxhomo lwayo.
Ngoko ke, apha sizakudibanisa u1 no1 kulento ngoko ke si-
funa 1, 1, 1.
Kwaye ngoku xa sifika ku8, akukho
ndlela yokwangeza nayiphi na naka-
ngakanani na, ngoko ke kufuneka sifumane indawo entsha...kufuneka siye
kwindawo yesibhozo. ngoko ke sino 8 omnye...
no0 abayi 4, no 0 abayi 2, kunye no0 omnye.
Lento apha, ingakhangeleka ngathi nje ngo 1000 kuwe
kodwa ibizakuba ngu 1000 ukuba besinesiqu esingu 10.
Kwisiqu esingu 2, lento zizinto ezininzi. Lento zizi eziyi 8 kwisiqu u 2.
Xa sisiya... xa usandisa ku1, siza
kuba nezinto ezininzi, sizakuba no 8 omnye, kwaye kwangoko sizakuba no 1 omnye.
Ngoko ke izakuba ngu 1001.
Kwaye kwangoko, ndizakuohela apha, kulento siyithatha ukuba zizinto ezyi10...
kwisiqu 10, ubungathi uno 8 omnye, kwaye uzakudinga u2 omnye.
ngoko ke oo- 0 abayi 4, kunye no no 1 abangekhoyo.
Ngoko ke, lento apha ngu 10 onesiqu u2.
Lento ngu 10 kwisiqu u 10.
ngethemba lokuba ayinibhidekisi kakhulu.