{"id":486,"date":"2019-12-06T08:08:00","date_gmt":"2019-12-06T06:08:00","guid":{"rendered":"http:\/\/skolarbbos.net\/?p=486"},"modified":"2019-12-22T18:17:36","modified_gmt":"2019-12-22T16:17:36","slug":"pretvaranje-binarnih-brojeva-u-ostale","status":"publish","type":"post","link":"https:\/\/skolarbbos.net\/?p=486","title":{"rendered":"Pretvaranje binarnih brojeva u ostale"},"content":{"rendered":"<p>Dekadni sistem brojeva ima osnovu broj 10 i koristi cifre 0, 1, 2, 3, 4, 5, 6, 7, 8 i 9. Svaka cifra dekadnog sistema brojeva ima svoju te\u017einu koja je predstavljena stepenom broja 10 i to se prikazuje kao 10<sup>i<\/sup>, gde je eksponent i ceo broj i njegova vrednost je odre\u0111ena polo\u017eajem cifre u samom broju. Na primer, slede\u0107i brojevi mogu da se prika\u017eu kao:<\/p>\n<p>42 = 4\u00b710<sup>1<\/sup> +2\u00b710<sup>0<\/sup> ,<\/p>\n<p>432 = 4\u00b710<sup>2<\/sup> +3\u00b710<sup>1<\/sup> +2\u00b710<sup>0<\/sup> ,<\/p>\n<p>4321 = 4\u00b710<sup>3<\/sup> +3\u00b710<sup>2<\/sup> +2\u00b710<sup>1<\/sup> +1\u00b710<sup>0<\/sup> ,<\/p>\n<p><strong>Pretvaranje binarnog broja u dekadni <\/strong><\/p>\n<p>Za razliku od dekadnih brojeva koje koriste osnovu 10, binarni brojevi koriste osnovu 2. Procedura za pretvaranje binarnog broja 101101<sub>2<\/sub> u dekadni je slede\u0107a:<\/p>\n<p>101101<sub>2<\/sub> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = 1 \u00b72<sup>5<\/sup> + 0\u00b72<sup>4<\/sup> + 1\u00b72<sup>3<\/sup> + 1\u00b72<sup>2<\/sup> + 0\u00b72<sup>1<\/sup> + 1\u00b72<sup>0<\/sup> =<\/p>\n<p>= 32 + 0 + 8 + 4 + 0 + 1 =<\/p>\n<p>= 45 <sub>10<\/sub><\/p>\n<p>Evo jo\u0161 dva primera. Treba pretvoriti brojeve 1100<sub>2<\/sub> i 100101110<sub>2<\/sub> u dekadne. Postupak za pretvaranje broja 1100<sub>2<\/sub> u dekadni je slede\u0107i:<\/p>\n<p>1100<sub>2<\/sub> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= 1 \u00b72<sup>3<\/sup> +1\u00b72<sup>2<\/sup> +0\u00b72<sup>1<\/sup> +0\u00b72<sup>0<\/sup> =<\/p>\n<p>= 8 + 4 + 0 + 0 =<\/p>\n<p>= 12<sub>10<\/sub><\/p>\n<p>Postupak za pretvaranje broja 100101110<sub>2<\/sub> u dekadni je slede\u0107i:<\/p>\n<p>100101110<sub>2<\/sub> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= 1 \u00b72<sup>8<\/sup>\u00a0+\u00a00 \u00b72<sup>7<\/sup>\u00a0+ 0 \u00b72<sup>6<\/sup> + 1\u00b72<sup>5<\/sup> + 0 \u00b72<sup>4<\/sup> + 1\u00b72<sup>3<\/sup> +1\u00b72<sup>2<\/sup> + 1\u00b72<sup>1<\/sup> + 0\u00b72<sup>0<\/sup> =<\/p>\n<p>= 256 + 0 + 0 + 32 + 0 + 8 + 4 + 2 + 0 =<\/p>\n<p>= 302<sub>10<\/sub><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Pretvaranje binarnog broja u oktalni <\/strong><\/p>\n<p>Broj 8, \u0161to je osnova oktalnog sistema, mo\u017ee da se napi\u0161e kao 2<sup>3<\/sup>, tako da binarni broj treba grupisati u grupe od po 3 cifre, i to sa desne u levu stranu. Ako na kraju nedostaju cifre, treba dodati jednu ili dve nule sa leve strane. Svaku grupu od tri bita treba zameniti jednom oktalnom cifrom. Evo dva primera. Treba pretvoriti brojeve 1101101111<sub>2<\/sub> i 1011<sub>2<\/sub> u oktalne.<\/p>\n<p>Postupak za pretvaranje broja 1101101111<sub>2<\/sub> u oktalni je slede\u0107i:<\/p>\n<p>1101101111<sub>2<\/sub> = 001 101 101 111<\/p>\n<p>001\u00a0\u00a0\u00a0\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0 * 2<sup>2<\/sup> + 0 * 2<sup>1<\/sup> + 1 * 2<sup>0<\/sup>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1<\/p>\n<p>101\u00a0\u00a0\u00a0\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1 * 2<sup>2<\/sup> + 0 * 2<sup>1<\/sup> + 1 * 2<sup>0<\/sup>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 5<\/p>\n<p>101\u00a0\u00a0\u00a0\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1 * 2<sup>2<\/sup> + 0 * 2<sup>1<\/sup> + 1 * 2<sup>0<\/sup>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 5<\/p>\n<p>111\u00a0\u00a0\u00a0\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1 * 2<sup>2<\/sup> + 1 * 2<sup>1<\/sup> + 1 * 2<sup>0<\/sup>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 7<\/p>\n<p>= 1557<sub>8<\/sub><\/p>\n<p>Postupak za pretvaranje broja 1011<sub>2<\/sub> u oktalni je slede\u0107i:<\/p>\n<p>1011<sub>2<\/sub> = 001 011<\/p>\n<p>001\u00a0\u00a0\u00a0\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0 * 2<sup>2<\/sup> + 0 * 2<sup>1<\/sup> + 1 * 2<sup>0<\/sup>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1<\/p>\n<p>011\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0 * 2<sup>2<\/sup> + 1 * 2<sup>1<\/sup> + 1 * 2<sup>0<\/sup>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3<\/p>\n<p>= 13<sub>8<\/sub><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Pretvaranje binarnog broja u heksadekadni <\/strong><\/p>\n<p>Broj 16, \u0161to je osnova heksadekadnog sistema, mo\u017ee da se napi\u0161e kao 2<sup>4<\/sup>, tako da binarni broj treba grupisati u grupe od po 4 cifre, i to sa desne u levu stranu. Ako na kraju nedostaju cifre, treba dodati jednu, dve ili tri nule sa leve strane. Svaku grupu od \u010detiri bita treba zameniti jednom heksadekadnom cifrom. Evo dva primera. Treba pretvoriti brojeve 101011110011<sub>2<\/sub> i 1110110011<sub>2<\/sub> u heksadekadne. Postupak za pretvaranje broja 101011110011<sub>2<\/sub> u heksadekadni je slede\u0107i:<\/p>\n<p>101011110011<sub>2<\/sub> = 1010 1111 0011<\/p>\n<p>1010\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0\u00a0 1 * 2<sup>3<\/sup> + 0 * 2<sup>2<\/sup> + 1 * 2<sup>1<\/sup> + 0 * 2<sup>0<\/sup>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10\u00a0\u00a0 (A)<\/p>\n<p>1111\u00a0\u00a0 \u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a01 * 2<sup>3<\/sup> + 1 * 2<sup>2<\/sup> + 1 * 2<sup>1<\/sup> + 1 * 2<sup>0<\/sup>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 16\u00a0\u00a0 (F)<\/p>\n<p>0011\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0\u00a0 0 * 2<sup>3<\/sup> + 0 * 2<sup>2<\/sup> + 1 * 2<sup>1<\/sup> + 1 * 2<sup>0<\/sup>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 3<\/p>\n<p>= AF3<sub>16<\/sub><\/p>\n<p>Postupak za pretvaranje broja 1110110011<sub>2<\/sub> u heksadekadni je slede\u0107i:<\/p>\n<p>1110110011<sub>2<\/sub> = 0011 1011 0011<\/p>\n<p>0011\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0\u00a0 0 * 2<sup>3<\/sup> + 0 * 2<sup>2<\/sup> + 1 * 2<sup>1<\/sup> + 1 * 2<sup>0<\/sup>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 3<\/p>\n<p>1011\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0\u00a0 1 * 2<sup>3<\/sup> + 0 * 2<sup>2<\/sup> + 1 * 2<sup>1<\/sup> + 1 * 2<sup>0<\/sup>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 11\u00a0\u00a0 (B)<\/p>\n<p>0011\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0\u00a0 0 * 2<sup>3<\/sup> + 0 * 2<sup>2<\/sup> + 1 * 2<sup>1<\/sup> + 1 * 2<sup>0<\/sup>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 3<\/p>\n<p>&nbsp;<\/p>\n<p>= 3B3<sub>16<\/sub><\/p>\n","protected":false},"excerpt":{"rendered":"Dekadni sistem brojeva ima osnovu broj 10 i koristi cifre 0, 1, \n<a class=\"moretag\" href=\"https:\/\/skolarbbos.net\/?p=486\"> <\/a>","protected":false},"author":1,"featured_media":524,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18],"tags":[],"class_list":["post-486","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-binarni-sistemi"],"_links":{"self":[{"href":"https:\/\/skolarbbos.net\/index.php?rest_route=\/wp\/v2\/posts\/486","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/skolarbbos.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/skolarbbos.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/skolarbbos.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/skolarbbos.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=486"}],"version-history":[{"count":3,"href":"https:\/\/skolarbbos.net\/index.php?rest_route=\/wp\/v2\/posts\/486\/revisions"}],"predecessor-version":[{"id":1379,"href":"https:\/\/skolarbbos.net\/index.php?rest_route=\/wp\/v2\/posts\/486\/revisions\/1379"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/skolarbbos.net\/index.php?rest_route=\/wp\/v2\/media\/524"}],"wp:attachment":[{"href":"https:\/\/skolarbbos.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=486"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/skolarbbos.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=486"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/skolarbbos.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=486"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}