WEBVTT Kind: captions Language: xh 00:00:00.000 --> 00:00:04.981 Into endifuna ukuyenza kulomboniso kukuba ndityelele imibono enikhe nayenza kodwa anayithathela igqalelo sukela 00:00:04.981 --> 00:00:10.638 ngeloxesha nanine minyaka eyi3 okanye u4, kodwa ngoku inoba nizakuyibona intsha ezakuthi 3 00:00:10.638 --> 00:00:14.402 isincede ukusazisa xasisebenza ngezinye intlobo zamanani. Ke ngoku sine "digit" eziyi u10 kumanani ethu 00:00:14.402 --> 00:00:22.804 Ke ngoku sine "digit" eziyi u10 kumanani ethu.Manditsho ndiqalise ukubala. Ke xa ungenanto ndizosebenzisa iphawu u0. 00:00:22.813 --> 00:00:27.669 Ndisebenzisa iphawu u1. Yeka ndiyilungise. Ke akhonto, ndibenento, Ndisebenzisa iphawu u1. 00:00:27.669 --> 00:00:34.387 Ukuba ndinezinto eziyi u2, ndizo sebenzisa iphawu u2. Ukuba ziyi u2, ndisebenzisa u3. Manditsho ndehlele 00:00:34.387 --> 00:00:40.566 phantsi kancinci ukuze ubone. Ukuba ndinezinto eziyi u4, ndizo sebenzisa elaphawu phana. Ukuba ndine 00:00:40.597 --> 00:00:50.922 zinto eziyi u5, ndizo sebenzisa eliphawu.Ukuba ndinezinto eziyi u5...masiyizobe kanjeya..ukuba izinto ziyi u6, ndithatha lena 00:00:50.922 --> 00:00:57.740 Ukuba ziyi u7, ndisebenzisa oluphawu. Ndiyayazi ukuba lento ingaku xaka kancinci, kodwa yonke 00:00:57.740 --> 00:01:04.676 lento inalo ichaphaza. ukuba ndinezinto eziyi u8, ndisebenzisa eliphawu. Ukuba ziyi u9 ndiza 00:01:04.676 --> 00:01:23.314 kusebenzisa eliphawu. Ndiphinde ndibene ziyi u10... loluphi uphawu emandilu sebenzise? Seke esebenze onke ayi10, ngoku sina 00:01:27.037 --> 00:01:30.698 u10 "systems", siphinde siwasebenzisa kwakhona. Ngoku siphinde sazisa icebo le "number places". Ubuthe ukuba 00:01:30.698 --> 00:01:38.654 apha ndino u10 omnye kunye no u1 abayi u0. Ke uthi uno u10 omnye kunye no u1 abayi u0. 00:01:38.654 --> 00:01:45.898 ...kwaye oo u1 abayi u0. Lona simbiza u1, sithi ukwindawo ka10. Lento ithetha ukuthi u1, 00:01:45.898 --> 00:01:55.837 lento ithi"tens" enye, yi "1tens" uyidibanise no u1 abayi u0. Ke lento ithetha ukutsho. 00:01:55.837 --> 00:01:59.629 Kodwa bekunga nyanzelekanga siphinde siyisebenzise. Besino vele sibena maphawu aliqela. 00:01:59.629 --> 00:02:02.974 Mhlawmbi eli ibiliphawu, endaweni ye, mhlawmbi besenokwenza iphawu elitsha. 00:02:03.035 --> 00:02:06.982 Indaweni yoku, sowuyazi, zonke ezi bezinophawu lwazo, endaweni yokuba sisebenzise amadala 00:02:06.982 --> 00:02:13.231 Indaweni yoku, sowuyazi, zonke ezi bezinophawu lwazo, endaweni yokuba sisebenzise amadala 00:02:13.231 --> 00:02:17.021 phinda senze elinye iphawu layo... mandiye ku11, nditsho ndikhwezele eziko. 00:02:17.021 --> 00:02:21.946 Ke ngoku... 2,3,4,5,6,7,8,9,10,11. 00:02:21.946 --> 00:02:26.619 Ke, u11 kwi "number system" yethu, sithi ukuba lona ngu10... sithi lena ngu10 00:02:26.619 --> 00:02:35.071 ...mandiyi bhale ngolu hlobo... u10 omnye. Kwaye nalena, ngu10 omnye, kunye no1 omnye. 00:02:35.071 --> 00:02:43.001 ...kunye no1 omnye. Ke, ngu10 onye, umdibanise no1 omnye. Ndiyayazi ukuba lento ingaxaka xa uyibona 00:02:43.001 --> 00:02:49.121 ngale ndlela, kodwa imele ezizinto zinga. Ukuba besine "base" engu11, ndicinga ukuba besinovele 00:02:49.151 --> 00:02:51.813 sithi "base" ka12 we "number system", mhlawmbi besizo kubano phawu lalento 00:02:51.813 --> 00:02:55.544 endaweni yokuba siphinde sisebenzise "idigit" ezindala. Mhlawmbi upha belinoba bhetele 00:02:55.544 --> 00:02:59.464 ... mhlawmbi ibinokuba bubuso obuncumileyo. leyo yinto esiyaziyo. Kwaye ndizakwazisa 00:02:59.464 --> 00:03:05.206 ezinkulu i"number base systems", kwimiboniso ezayo apho sibona, amaphawu 00:03:05.206 --> 00:03:09.115 asele esetyenzisiwe. Kodwa, into endifuna ukuyenza kulomboniso khawu cinge 00:03:09.115 --> 00:03:12.270 ngehlobo esibala ngalo, okanye ngawaphi amaphawu esinoku wasebenzisa 00:03:12.270 --> 00:03:16.152 ukuba besine "digit" ezimbalwa, balaseleyo, singenza 00:03:16.152 --> 00:03:19.530 njani ukuze sibale i"digits" eziyi u2 qha - ukuba besino 00:03:19.530 --> 00:03:23.973 u0 kunye no u1. Okubalulekileyo, sizakuyi cingisisa lento 00:03:23.973 --> 00:03:27.457 ukuba sizokuwa misa njani amanani kwi"base" zika u2. 00:03:27.457 --> 00:03:30.695 Eyona ndlela yethu ye"number system" ka"base" u10. 00:03:30.695 --> 00:03:33.523 Sine "digits" eziyi u10 - u0 uyoqhambuka ku9 00:03:33.523 --> 00:03:35.877 Singabala njani kwi"base" ka u2? 00:03:35.877 --> 00:03:38.531 Ke, ukuba unezinto eziyi u0, mhlawmbi ungathi 00:03:38.531 --> 00:03:41.295 "tshini, ndino u0. Ndingayisebenzisa le 'digit' ka u0." 00:03:41.295 --> 00:03:43.540 Ukuba ndinento enye, ndingakwazi ukuthi 00:03:43.540 --> 00:03:45.800 "tshini, Apha ndinento enye"... ngoba, sine 00:03:45.800 --> 00:03:47.874 'digits' zika u0 nezika u1. Ke, Manditsho ndiyicacise. 00:03:47.935 --> 00:03:54.809 Ezi 'digits' apha, i'digits' kwi 'base' zika u2, zingaba ngu u0 okanye 00:03:54.809 --> 00:03:58.477 Ukuba ndinento enye, ndingakwazi ukumsebenzisa inani u1 00:03:58.492 --> 00:04:02.115 Kodwa, ngoku ngokungxamiseka nje ezizinto ziyi u2 apha, 00:04:02.123 --> 00:04:07.153 kwaye ngoku ndilinganiselwe... kwezi 'digits' zimbini phana. 00:04:07.184 --> 00:04:09.844 Ke ngoku, lento ndingayi beka njani. Ke, indaweni yokuba 00:04:09.844 --> 00:04:13.415 ndibene "ten's place", ndingenza i"two's place". 00:04:13.415 --> 00:04:16.218 ...kwaye Ndiyayazi ukuba lento ingavakala ngathi ayivakali ncam kodwa ndicinga ukuba uzaku 00:04:16.218 --> 00:04:22.718 qhela kancinci kancinci. Ke, apha sine 'base' ka u10, sithi ukuba sino u10 oyi u1 kunye no u0 oyi u1. 00:04:22.718 --> 00:04:25.722 Ke ngoku kwi'base' ka u2, kutheni singavele sibeno 00:04:25.722 --> 00:04:30.041 1,2 - 1,2 - kunye no u0,1. 00:04:30.041 --> 00:04:33.383 Yeka ndicacise lento. Ke, lento ilapha yona ithetha ukuthi 00:04:33.383 --> 00:04:39.159 1,2 kunye no0,1. 00:04:39.189 --> 00:04:42.595 Ndifuna ukuqinisekisa ukuba uyawuqonda lomzekelo apha. 00:04:42.595 --> 00:04:45.149 Kwi isinqu ka u10... mandibhale inani elikhulu apha kwi siqu ka u10... 00:04:45.149 --> 00:04:49.266 ...kwaye ke ukuba ndibhala elinani u256 kwi 'base' ka u10... 00:04:49.266 --> 00:04:53.833 ngoko ke, leyana phana yi'base' ka u10, lento ithetha ukuthini? 00:04:53.833 --> 00:04:58.777 Lento ithetha ukuthi u200, ngoku ke, u2 umphinde ngo u100... 00:04:58.777 --> 00:05:03.337 okanye, mhlawumbi mandibhale phantsi eligama ukuze ndinga phazamisi amaphawu.. 00:05:03.337 --> 00:05:09.391 u200 udibanise u5 uphinde ngo... okanye mhlawmbi mandithi u200 00:05:09.391 --> 00:05:19.917 umdibanise no u5 ophindwe ngo u10... u200, umdibanise no u5 ophindwe ngo u10, udibanise u6 ophindwe ngo u1. 00:05:19.917 --> 00:05:22.133 Lento yilena ndiyibonisayo apha, kwaye ihlobo esiyazi ngayo thina lento kukuba 00:05:22.133 --> 00:05:25.578 siyayazi ukuba sibhekela kabini ngasekhohlo, lena yindawo yesi u100 00:05:25.578 --> 00:05:31.469 lena yona yindawo yesi u10, lena yona ibeyindawo yesi u1. 00:05:31.469 --> 00:05:36.290 Kwaye ukuba uyazazi i"exponents" zakho, lento ilingana no u10 umphinda phinde ngo u10. 00:05:36.290 --> 00:05:39.964 Lento apha iyodwa nje ilingana no u10 umphinde kwangaye kanye 00:05:39.964 --> 00:05:42.473 kwaye lento iyalingana no10 aziphindaphinde kokwakhw, ndiyathemba 00:05:42.473 --> 00:05:43.958 ungayibiza, u0 umphinde. 00:05:43.958 --> 00:05:46.650 Okanye, ukuba uyazazi i"exponents" zakho, lento ngu 00:05:46.650 --> 00:05:49.900 u10 kwi "power" ka u2, lena yona ngu u10 kwi "power" ka u1, 00:05:49.900 --> 00:05:52.209 kwaye lena yona ngu u10 kwi "power" ka u0. 00:05:52.209 --> 00:05:53.355 ukuba ubudibanise enye i"digit" apha, lonto 00:05:53.355 --> 00:05:55.055 ibizakuba yindawo yesi u1000, ebizakuba ngu 00:05:55.055 --> 00:05:56.848 u10 umphinde ngo u10 uphinde kwakhona umphinde ngo u10. 00:05:56.848 --> 00:05:58.871 Siza kuphinda senze ngqo kwalento inye kwi "base" ka u2 00:05:58.871 --> 00:06:00.755 kodwa, endaweni yokusebenzisa u10, sizaku 00:06:00.755 --> 00:06:03.407 kusebenzisa u2.Ngoku Ke lena yindawo ka u2. 00:06:03.407 --> 00:06:06.580 Lena apha yindawo ka u2. lena yona yindawo ka u1. 00:06:06.580 --> 00:06:09.507 ukuba sidibanisa ezinye i"digits'... manditsho ndiyicacise... 00:06:09.507 --> 00:06:13.733 Ke kwi base ka u2... mandibhale 00:06:13.733 --> 00:06:17.356 Khumbula, kiwsiqu sika2 ndinga sebenzisa u0 okanye u1. 00:06:17.356 --> 00:06:22.315 Ngoko ke, kwisiqu sika2, mhlawumbi ndienani u1010 00:06:22.315 --> 00:06:25.608 ngoko ke xa ucinga ngayo ngalendlela, ukuba lento ibinesiqu u10 00:06:25.608 --> 00:06:29.167 ungayiza lento ukuba ikwi ndawoye10, kwindawo 100, kwaye kwindawo 1000. 00:06:29.167 --> 00:06:32.262 Kodwa, lento ngoku inesiqu u2. ngoko ke mandicacise. 00:06:32.262 --> 00:06:35.435 Sisebenzisa imivo eyi2. Ngoko ke kwisiqu u2 00:06:35.435 --> 00:06:37.928 lento apha isekwindawo yokuqala 00:06:37.928 --> 00:06:40.731 ngoku lento izakuba kwindawo yesibini 00:06:40.731 --> 00:06:42.815 khumbula, kwisiqu u10 ibikwindawo ye10, ngoku 00:06:42.815 --> 00:06:44.346 lento ikwindawo yesibini. 00:06:44.346 --> 00:06:47.577 Ngoku izakuba ngu, kwaye ungenza uqikelelo apha 00:06:47.577 --> 00:06:49.615 100 ibingu 10 umphinda-phinde ngo10. 00:06:49.615 --> 00:06:53.252 Xa sisiya kabini ngasekunene kwisiqu u2 00:06:53.252 --> 00:06:55.760 lento ufenele ukuba ibe ngu 2 umphinda-phinde ngo 2 kwindawo yesibini. 00:06:55.760 --> 00:07:03.695 Okanye lento ibekwindawo yesine. Lento ilapha izakuba kwindawo yesibhozo. 00:07:03.695 --> 00:07:06.662 Ngoko ke, ukuba ufuna ukucinga ngayo ngendlela 00:07:06.662 --> 00:07:12.564 yesiqu esingu 2, lento ngu 1, ngu 18, dibanisa 00:07:12.564 --> 00:07:22.613 dibanisa u1 2, dibanisa 0. Dibanisa 0. 00:07:22.613 --> 00:07:25.336 Ngoko ke, ukuba ubufuna ukubala lento nganye gqo elinani 00:07:25.336 --> 00:07:30.134 kwisiqu u10, ngu 1, 8 dibanisa 1, 2. 00:07:30.149 --> 00:07:34.562 ngoko ke kwisiqu esingu 10 lento izakuba ... mandiyibhale phezulu apha... 00:07:34.562 --> 00:07:39.173 kwisiqu sia10 izokuba ngu8 umdibanise no2, into ethetha ukuba ngu10 00:07:39.173 --> 00:07:43.941 Ngoko ke, lento enisiqu esingu 10. Lento uyibonisa ngoluhlobo 00:07:43.941 --> 00:07:47.517 siyazi nggendlela ezininzi- nje ngezinto eziyi10. 00:07:47.517 --> 00:07:50.152 Lento uzakuyibonisa ngoluhlobo inesiqu esingu 2. 00:07:50.152 --> 00:07:53.763 Lento siyazi ngoluhlobo ukuba ngesiyibonisile inesiqu esingu 10. 00:07:53.763 --> 00:07:56.334 Ngoku masiqhubekele phambili apha, ukuqinisekisa ukuba siyaziqonda kakuhle izinto. 00:07:56.334 --> 00:08:01.256 Ngoko ke lento ingaveza, kulungile, kwisiqu esingu 2 sino 1... 00:08:01.256 --> 00:08:04.708 ukuba ufuna izinto zibe mbini- ngu 1, 2 kunye 0, 1 00:08:04.708 --> 00:08:08.795 ngoku xa zintathu izinto zethu izakuba 1,2 dibanisa 1. 00:08:08.795 --> 00:08:11.469 Ngoko ke mandiyenze phezulu apha, ngoko ke lento izakuba 1,2 00:08:11.469 --> 00:08:13.031 dibanisa 1. 00:08:13.031 --> 00:08:18.085 ngoko ke lento zizinto ezontathu ezinesiqu u2. 00:08:18.085 --> 00:08:23.967 Ngoku xa sihamba lendlela lento, ngoko ke phezululu apha zizakuba no 1,4... 00:08:23.967 --> 00:08:25.855 0,2 kunye 0,1. 00:08:25.871 --> 00:08:27.924 Ngoko ke ngoku siya kwindawo yesine. 00:08:27.924 --> 00:08:29.948 Ngoba ngokukhawuleza sidibanise yonke into. 00:08:29.948 --> 00:08:32.402 Ukuba ziqwalasela ezininzi, kuzakufuneka siye kwindawo ezininzi 00:08:32.402 --> 00:08:34.333 nje ngokuba besenzile kwisiqu esingu 10, kodwa ngoku singasebenzisa 00:08:34.333 --> 00:08:35.971 imivo u 0 kunye no 1. 00:08:35.971 --> 00:08:41.008 Ngoko ke ngoku sizakuba no1 abayi 4, 0 abayi 2, no0 oyi1. 00:08:41.008 --> 00:08:44.069 ngoku xa sidibanisa u1 kwakhona, sizakudibanisa u1 kunye nomye u1 00:08:44.069 --> 00:08:49.915 ngoko ke, ngoku sino 1 abiyi 4, no0 abayi 2, kunye no1 oyi 1. 00:08:49.915 --> 00:08:53.215 kwaye xa ndicacisa, lento zizinto ezininzi. 00:08:53.215 --> 00:08:57.767 Lento zizinto ezininzi kwisiqu esingu 2, lento ikwindawo yesine 00:08:57.767 --> 00:09:00.006 oo-1 abayi 4 kunye no 1 oyi 1. Ukuba ufuna ukuguqula 00:09:00.006 --> 00:09:02.263 lento ibe kwindawo wesishumi, unga khangela 00:09:02.263 --> 00:09:08.146 " lona angu 1 no 4, no 0 abayi 2, kunye no 1 oyi 1." 00:09:08.146 --> 00:09:11.444 Ngoko ke ukuba uno 4 kunye no1, singaba bhala 00:09:11.444 --> 00:09:14.082 ngophawu luka 5 isiqu ibe ngu 10, kodwa 00:09:14.082 --> 00:09:16.992 asinaphawu lokulive kwisiqu sethu esingu 2. 00:09:16.992 --> 00:09:19.602 Masiye kulento. Ngoko ke, ngoku sizakwandisa onye u1 ngaphezulu. 00:09:19.602 --> 00:09:21.590 Ngoko ke, singayibonisa njani lonto kwisiqu esingu 2? 00:09:21.590 --> 00:09:23.367 Lento ngokuqinisekileyo, sizakufumana oo-1 abayi 4... 00:09:23.367 --> 00:09:27.163 kwaye kwango ko sizakufumana oo-1 abyi 2..kwaye kwango ko 00:09:27.163 --> 00:09:29.257 sizakuba no-0 omnye. 00:09:29.257 --> 00:09:32.248 Kwaye ukuba siyayigcina ...izakonwabisa ukuyaphambili 00:09:32.248 --> 00:09:34.133 kwisiqu u2, uzakuqala kuxhomo lwayo. 00:09:34.133 --> 00:09:36.587 Ngoko ke, apha sizakudibanisa u1 no1 kulento ngoko ke si- 00:09:36.587 --> 00:09:38.610 funa 1, 1, 1. 00:09:38.610 --> 00:09:40.125 Kwaye ngoku xa sifika ku8, akukho 00:09:40.125 --> 00:09:42.025 ndlela yokwangeza nayiphi na naka- 00:09:42.025 --> 00:09:44.518 ngakanani na, ngoko ke kufuneka sifumane indawo entsha...kufuneka siye 00:09:44.518 --> 00:09:46.761 kwindawo yesibhozo. ngoko ke sino 8 omnye... 00:09:46.761 --> 00:09:50.723 no0 abayi 4, no 0 abayi 2, kunye no0 omnye. 00:09:50.723 --> 00:09:52.983 Lento apha, ingakhangeleka ngathi nje ngo 1000 kuwe 00:09:52.983 --> 00:09:55.475 kodwa ibizakuba ngu 1000 ukuba besinesiqu esingu 10. 00:09:55.475 --> 00:10:02.023 Kwisiqu esingu 2, lento zizinto ezininzi. Lento zizi eziyi 8 kwisiqu u 2. 00:10:02.023 --> 00:10:04.237 Xa sisiya... xa usandisa ku1, siza 00:10:04.237 --> 00:10:07.064 kuba nezinto ezininzi, sizakuba no 8 omnye, kwaye kwangoko sizakuba no 1 omnye. 00:10:07.064 --> 00:10:10.181 Ngoko ke izakuba ngu 1001. 00:10:10.181 --> 00:10:15.026 Kwaye kwangoko, ndizakuohela apha, kulento siyithatha ukuba zizinto ezyi10... 00:10:15.026 --> 00:10:20.485 kwisiqu 10, ubungathi uno 8 omnye, kwaye uzakudinga u2 omnye. 00:10:20.485 --> 00:10:23.648 ngoko ke oo- 0 abayi 4, kunye no no 1 abangekhoyo. 00:10:23.648 --> 00:10:28.029 Ngoko ke, lento apha ngu 10 onesiqu u2. 00:10:28.029 --> 00:10:30.537 Lento ngu 10 kwisiqu u 10. 00:10:30.583 --> 99:59:59.999 ngethemba lokuba ayinibhidekisi kakhulu.