{"id":59,"date":"2022-03-03T11:58:00","date_gmt":"2022-03-03T10:58:00","guid":{"rendered":""},"modified":"2023-08-04T22:43:45","modified_gmt":"2023-08-04T20:43:45","slug":"dvojkova-sustava","status":"publish","type":"post","link":"https:\/\/www.jankafialka.sk\/?p=59","title":{"rendered":"Ke\u010f 1+1=10"},"content":{"rendered":"\n

Mo\u017eno ste pod\u013ea nadpisu uh\u00e1dli. A mo\u017eno nie. Tento pr\u00edspevok bude o dvojkovej \u010d\u00edselnej s\u00fastave. Dvojkov\u00e1 s\u00fastava? \u00c1no, to je t\u00e1, kde sa pou\u017e\u00edvaj\u00fa iba nuly a jednotky. To je t\u00e1, ktor\u00e1 sa ukr\u00fdva v po\u010d\u00edta\u010doch. Z jednoduch\u00e9ho d\u00f4vodu: po\u010d\u00edta\u010d vie rozli\u0161ova\u0165 medzi dvoma stavmi: ide pr\u00fad – 1, nejde pr\u00fad – 0. Predstavme si to ako rad \u017eiaroviek. Ka\u017ed\u00e1 m\u00e1 svoj vyp\u00edna\u010d. Povedzme, \u017ee \u017eiaroviek je desa\u0165. Ak\u00e9 \u010d\u00edsla m\u00f4\u017eeme zn\u00e1zorni\u0165 zasvieten\u00edm niektor\u00fdch \u017eiaroviek?<\/p>\n\n\n\n

\"\"
\u017diarovky<\/figcaption><\/figure>\n\n\n\n

Najjednoduch\u0161ie by bolo za\u017en\u00fa\u0165 to\u013eko \u017eiaroviek, ko\u013eko chceme vyjadri\u0165. Ale to by n\u00e1m desa\u0165 \u017eiaroviek sta\u010dilo iba na desa\u0165 \u010d\u00edsel. Dos\u0165 m\u00e1lo. Existuje ale pomerne jednoduch\u00fd sp\u00f4sob, ako vyjadri\u0165 viac ako tis\u00edc \u010d\u00edsel len s pomocou desiatich \u017eiaroviek.<\/p>\n\n\n\n

Desiatkov\u00e1 \u010d\u00edseln\u00e1 s\u00fastava<\/h2>\n\n\n\n

Aby sme tento sp\u00f4sob pochopili, mus\u00edme si pripomen\u00fa\u0165, ako vlastne funguje na\u0161a desiatkov\u00e1 \u010d\u00edseln\u00e1 s\u00fastava. Mne osobne sa ve\u013emi p\u00e1\u010di princ\u00edp, ako sa pribli\u017euje u\u017e v pred\u0161kolskom veku v Montessori pedagogike.<\/p>\n\n\n\n

\u010c\u00edslo je reprezentovan\u00e9 po\u010dtom \u0161peci\u00e1lnych kor\u00e1lkov. Jednotliv\u00e9 kor\u00e1lky sa m\u00f4\u017eu zdru\u017eova\u0165 do radov po desiatkach. Vznikn\u00fa tak\u00e9 pali\u010dky. Tieto pali\u010dky sa zasa daj\u00fa spoji\u0165 po desiatich a tak vytvoria \u0161tvorec – ten u\u017e obsahuje sto jednotliv\u00fdch kor\u00e1lkov. \u0160tvorce sa zasa daj\u00fa uklada\u0165 na seba po desiatich a tak vytvoria kocku. \u010ealej to u\u017e pre pred\u0161kol\u00e1kov nepokra\u010duje, ale vedeli by sme si predstavi\u0165, \u017ee kocky zasa vytvoria rad, tie zasa \u0161tvorec a t.\u010f.<\/p>\n\n\n\n

Ke\u010f teda chceme vyjadri\u0165 nejak\u00e9 v\u00e4\u010d\u0161ie \u010d\u00edslo – m\u00e1me napr\u00edklad ve\u013ek\u00fa hromadu kor\u00e1lkov, tak budeme postupova\u0165 tak, \u017ee najprv ich posklad\u00e1me do radov po desiatich. Niektor\u00e9 zostan\u00fa nezaraden\u00e9 – to\u013eko jednotiek bude ma\u0165 v\u00fdsledn\u00e9 \u010d\u00edslo. Potom rady zoskup\u00edme po desiatich do \u0161tvorcov – stoviek. Nejak\u00e9 rady zostan\u00fa – to\u013eko desiatok bude ma\u0165 v\u00fdsledn\u00e9 \u010d\u00edslo. Pokra\u010dujeme, a\u017e k\u00fdm e\u0161te m\u00e1me, \u010do zoskupova\u0165 po desiatkach.<\/p>\n\n\n\n

Dvojkov\u00e1 \u010d\u00edseln\u00e1 s\u00fastava<\/h2>\n\n\n\n

Presne na takomto princ\u00edpe funguje prevod ak\u00e9hoko\u013evek \u010d\u00edsla do akejko\u013evek \u010d\u00edselnej s\u00fastavy. Teda aj do dvojkovej. Jedin\u00fd rozdiel je v tom, po ko\u013ek\u00fdch zoskupujeme. V pr\u00edklade vy\u0161\u0161ie sme d\u00e1vali spolu v\u017edy desa\u0165 kor\u00e1lkov\/radov\/\u0161tvorcov… Dvojkov\u00e1 s\u00fastava vy\u017eaduje, \u017ee to budeme robi\u0165 po dvojiciach.<\/p>\n\n\n\n

Pr\u00edklad: ako vyjadr\u00edme \u010d\u00edslo trin\u00e1s\u0165 v dvojkovej \u010d\u00edselnej s\u00fastave?<\/p>\n\n\n\n

\u0160k\u00f4lkarsky postup: vezmeme trin\u00e1s\u0165 kor\u00e1lkov a d\u00e1me ich do dvoj\u00edc. Jedna zostane sama – na konci bude jednotka. Vzniklo n\u00e1m \u0161es\u0165 dvoj\u00edc – radov. Tieto zasa ulo\u017e\u00edme do dvoj\u00edc – \u0161tvorcov. Vznikli tri \u0161tvorce. \u017diadny rad nezostal s\u00e1m. \u0160tvorce zasa d\u00e1me do dvoj\u00edc – vznikla jedna kocka a zostal jeden \u0161tvorec. Ulo\u017e\u00edme pekne ved\u013ea seba z\u013eava – kocka, \u0161tvorec, ni\u010d a kor\u00e1lka. Teda je to \u010d\u00edslo 1101.<\/p>\n\n\n\n

Ne\u0161k\u00f4lkarsky sa to rob\u00ed vlastne \u00faplne rovnako \ud83d\ude01. Del\u00edme opakovane dan\u00e9 \u010d\u00edslo dvojkou, zvy\u0161ky zapisujeme a z nich n\u00e1m vznikne v\u00fdsledok. \u010c\u00edtame ho odspodu nahor.<\/p>\n\n\n\n

13:2=6 zv.1<\/p>\n\n\n\n

6:2=3 zv.0<\/p>\n\n\n\n

3:2=1 zv.1<\/p>\n\n\n\n

1:2=0 zv.1<\/p>\n\n\n\n

V\u0161imnime si, ak\u00fd po\u010det vyjadruj\u00fa jednotliv\u00e9 \u010d\u00edslice. Sprava m\u00e1me jednotky – jednotliv\u00e9 kor\u00e1lky. V\u013eavo od nich je po\u010det dvojek – radov, \u010falej po\u010det \u0161tvoriek a osmi\u010diek. Ka\u017ed\u00fd \u010fal\u0161\u00ed r\u00e1d je dvojn\u00e1sobkom predch\u00e1dzaj\u00faceho. Zisti\u0165, ak\u00fd po\u010det je vyjadren\u00fd \u010d\u00edslom zap\u00edsan\u00fdm v dvojkovej s\u00fastave, je preto \u00fapln\u00e1 hra\u010dka. Sta\u010d\u00ed vedie\u0165, ak\u00fd po\u010det vyjadruje jednotka na konkr\u00e9tnom mieste. \u010c\u00edslo 10 je preto skuto\u010dne dva. \u010c\u00edslo 10101 je zasa 16+4+1=21.<\/p>\n\n\n\n

Tak\u017ee v prvej ilustr\u00e1ci\u00ed desa\u0165 \u017eiaroviek m\u00f4\u017ee ozna\u010dova\u0165 \u010d\u00edsla od nula – ke\u010f s\u00fa v\u0161etky vypnut\u00e9 a\u017e po 512+256+128+64+32+16+8+4+2+1=1023, ke\u010f s\u00fa v\u0161etky zasvieten\u00e9.<\/p>\n","protected":false},"excerpt":{"rendered":"

Mo\u017eno ste pod\u013ea nadpisu uh\u00e1dli. A mo\u017eno nie. Tento pr\u00edspevok bude o dvojkovej \u010d\u00edselnej s\u00fastave. Dvojkov\u00e1 s\u00fastava? \u00c1no, to je t\u00e1, kde sa pou\u017e\u00edvaj\u00fa iba nuly a jednotky. To je t\u00e1, ktor\u00e1 sa ukr\u00fdva v po\u010d\u00edta\u010doch. Z jednoduch\u00e9ho d\u00f4vodu: po\u010d\u00edta\u010d vie rozli\u0161ova\u0165 medzi dvoma stavmi: ide pr\u00fad – 1, nejde pr\u00fad – 0. Predstavme si […]<\/p>\n","protected":false},"author":2,"featured_media":1939,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-59","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-nezaradene"],"yoast_head":"\nKe\u010f 1+1=10 alebo dvojkov\u00e1 s\u00fastava<\/title>\n<meta name=\"description\" content=\"Ako funguje dvojkov\u00e1 \u010d\u00edseln\u00e1 s\u00fastava. 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