{"id":99,"date":"2026-02-18T10:25:25","date_gmt":"2026-02-18T08:25:25","guid":{"rendered":"https:\/\/blog.edu.turku.fi\/allu\/?page_id=99"},"modified":"2026-04-02T11:54:01","modified_gmt":"2026-04-02T08:54:01","slug":"lukujarjestelmat","status":"publish","type":"page","link":"https:\/\/blog.edu.turku.fi\/allu\/sivu-1\/lukujarjestelmat\/","title":{"rendered":"Lukuj\u00e4rjestelm\u00e4t"},"content":{"rendered":"\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-black-color has-text-color has-background has-link-color wp-element-button\" href=\"https:\/\/blog.edu.turku.fi\/allu\/sivu-1\/\" style=\"background-color:#d6d6ff\">Palaa takaisin<\/a><\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Lukuj\u00e4rjestelm\u00e4t<\/h2>\n\n\n\n<p class=\"has-text-align-left\">Teht\u00e4v\u00e4t on jaoteltu v\u00e4rin mukaan helppoihin, perus ja vaikeisiin teht\u00e4viin.<\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-black-color has-text-color has-background has-link-color wp-element-button\" style=\"background-color:#e6f3b7\">Helppo<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-black-color has-text-color has-background has-link-color has-text-align-center wp-element-button\" style=\"background-color:#d6d6ff\">Perus<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-black-color has-text-color has-background has-link-color wp-element-button\" style=\"background-color:#fcd8c8\">Vaikea<\/a><\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 1.<\/strong> Vastaa kirjallisesti seuraaviin kysymyksiin.<\/h3>\n\n\n\n<ol style=\"list-style-type:lower-alpha\" class=\"wp-block-list\">\n<li>Mitk\u00e4 luvut ovat k\u00e4yt\u00f6ss\u00e4 10-j\u00e4rjestelm\u00e4ss\u00e4?<\/li>\n\n\n\n<li>Miksi luku 102 ei ole kelvollinen luku 2-j\u00e4rjestelm\u00e4ss\u00e4?<\/li>\n\n\n\n<li>Mik\u00e4 on <math data-latex=\"1100_2\"><semantics><msub><mn>1100<\/mn><mn>2<\/mn><\/msub><annotation encoding=\"application\/x-tex\">1100_2<\/annotation><\/semantics><\/math>&nbsp;luvun arvo 10-j\u00e4rjestelm\u00e4ss\u00e4?<\/li>\n\n\n\n<li>Jaa 2463 luku kantalukujen potenssien summaksi 10-j\u00e4rjestelm\u00e4ss\u00e4.<\/li>\n\n\n\n<li>Mitk\u00e4 luvut ovat k\u00e4yt\u00f6ss\u00e4 16-j\u00e4rjestelm\u00e4ss\u00e4&nbsp;eli heksadesimaalissa?&nbsp;<\/li>\n\n\n\n<li>Onko&nbsp;luku 2536&nbsp;8-j\u00e4rjestelm\u00e4n eli&nbsp;oktaalij\u00e4rjestelm\u00e4n mukainen?&nbsp;<\/li>\n<\/ol>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-1&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#e6f3b7\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-1-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-1\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-1\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-1-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>a. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9\u00a0<br>b. Luku 102 ei ole kelvollinen 2-j\u00e4rjestelm\u00e4ss\u00e4, koska 2-j\u00e4rjestelm\u00e4ss\u00e4 on k\u00e4yt\u00f6ss\u00e4 vain\u00a0luvut 0 ja 1.\u00a0<br>c. Luku <math data-latex=\"1100_2\"><semantics><msub><mn>1100<\/mn><mn>2<\/mn><\/msub><annotation encoding=\"application\/x-tex\">1100_2<\/annotation><\/semantics><\/math> on\u00a010-j\u00e4rjestelm\u00e4ss\u00e4 luku 12.\u00a0<br>d. <math data-latex=\"   2\u22c510^3+4\u22c510^2+6\u22c510^1+3\u22c510^0\"><semantics><mrow><mn>2<\/mn><mo>\u22c5<\/mo><msup><mn>10<\/mn><mn>3<\/mn><\/msup><mo>+<\/mo><mn>4<\/mn><mo>\u22c5<\/mo><msup><mn>10<\/mn><mn>2<\/mn><\/msup><mo>+<\/mo><mn>6<\/mn><mo>\u22c5<\/mo><msup><mn>10<\/mn><mn>1<\/mn><\/msup><mo>+<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><msup><mn>10<\/mn><mn>0<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">2\u22c510^3+4\u22c510^2+6\u22c510^1+3\u22c510^0<\/annotation><\/semantics><\/math><br>e. 0,\u00a01, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F\u00a0<br>f. Luku 2536 on\u00a08-j\u00e4rjestelm\u00e4n mukainen, koska se sis\u00e4lt\u00e4\u00e4 vain lukuja, jotka kuuluvat 8-j\u00e4rjestelm\u00e4\u00e4n. Sallitut luvut\u00a00-7.\u00a0<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 2.<\/strong> Valitse oikea muutos, kun muutetaan 10-j\u00e4rjestelm\u00e4n luvut bin\u00e4\u00e4riin eli 2-j\u00e4rjestelm\u00e4\u00e4n ja vastaukset ovat 5-bittisi\u00e4 eli 5-numeroisia.<\/h3>\n\n\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-11\" class=\"h5p-iframe\" data-content-id=\"11\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Muunna 10-j\u00e4rjejestelm\u00e4n luku bin\u00e4\u00e4riin\"><\/iframe><\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 3.<\/strong> Kirjoita jakolaskua vastaava jakoyht\u00e4l\u00f6<\/h3>\n\n\n\n<p>a. <math data-latex=\"\\frac{96}{7}\"><semantics><mfrac><mn>96<\/mn><mn>7<\/mn><\/mfrac><annotation encoding=\"application\/x-tex\">\\frac{96}{7}<\/annotation><\/semantics><\/math><br><br>b. <math data-latex=\"\\frac {53}{6}\"><semantics><mfrac><mn>53<\/mn><mn>6<\/mn><\/mfrac><annotation encoding=\"application\/x-tex\">\\frac {53}{6}<\/annotation><\/semantics><\/math><br><br>c. <math data-latex=\"-\\frac {23}{4}\"><semantics><mrow><mo>\u2212<\/mo><mfrac><mn>23<\/mn><mn>4<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">-\\frac {23}{4}<\/annotation><\/semantics><\/math><br><br>d. <math data-latex=\"-\\frac {15}{7}\"><semantics><mrow><mo>\u2212<\/mo><mfrac><mn>15<\/mn><mn>7<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">-\\frac {15}{7}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-2&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#e6f3b7\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-2-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-2\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">VINKKI!<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-2\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-2-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>jakoyht\u00e4l\u00f6 on muotoa:<\/p>\n\n\n\n<p><math data-latex=\"a=b\\cdot q+r\"><semantics><mrow><mi>a<\/mi><mo>=<\/mo><mi>b<\/mi><mo>\u22c5<\/mo><mi>q<\/mi><mo>+<\/mo><mi>r<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">a=b\\cdot q+r<\/annotation><\/semantics><\/math> eli <math data-latex=\"jaettava = jakaja \\cdot  osam\u00e4\u00e4r\u00e4 + jakoj\u00e4\u00e4nn\u00f6s\"><semantics><mrow><mi>j<\/mi><mi>a<\/mi><mi>e<\/mi><mi>t<\/mi><mi>t<\/mi><mi>a<\/mi><mi>v<\/mi><mi>a<\/mi><mo>=<\/mo><mi>j<\/mi><mi>a<\/mi><mi>k<\/mi><mi>a<\/mi><mi>j<\/mi><mi>a<\/mi><mo>\u22c5<\/mo><mi>o<\/mi><mi>s<\/mi><mi>a<\/mi><mi>m<\/mi><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>r<\/mi><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mo>+<\/mo><mi>j<\/mi><mi>a<\/mi><mi>k<\/mi><mi>o<\/mi><mi>j<\/mi><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>n<\/mi><mi>n<\/mi><mover><mi>o<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>s<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">jaettava = jakaja \\cdot osam\u00e4\u00e4r\u00e4 + jakoj\u00e4\u00e4nn\u00f6s<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-3&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#e6f3b7\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-3-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-3\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-3\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-3-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<ul class=\"wp-block-list\">\n<li>a. <math data-latex=\"97=7\\cdot 13+5\"><semantics><mrow><mn>97<\/mn><mo>=<\/mo><mn>7<\/mn><mo>\u22c5<\/mo><mn>13<\/mn><mo>+<\/mo><mn>5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">97=7\\cdot 13+5<\/annotation><\/semantics><\/math><\/li>\n\n\n\n<li>b. <math data-latex=\"53=6\\cdot8+5\"><semantics><mrow><mn>53<\/mn><mo>=<\/mo><mn>6<\/mn><mo>\u22c5<\/mo><mn>8<\/mn><mo>+<\/mo><mn>5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">53=6\\cdot8+5<\/annotation><\/semantics><\/math><\/li>\n\n\n\n<li>c. <math data-latex=\"-23=4\\cdot (-6)+1\"><semantics><mrow><mo>\u2212<\/mo><mn>23<\/mn><mo>=<\/mo><mn>4<\/mn><mo>\u22c5<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mo form=\"prefix\" stretchy=\"false\">\u2212<\/mo><mn>6<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>+<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">-23=4\\cdot (-6)+1<\/annotation><\/semantics><\/math><\/li>\n\n\n\n<li>d. <math data-latex=\"-15= 7\\cdot (-3)+6\"><semantics><mrow><mo>\u2212<\/mo><mn>15<\/mn><mo>=<\/mo><mn>7<\/mn><mo>\u22c5<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mo form=\"prefix\" stretchy=\"false\">\u2212<\/mo><mn>3<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>+<\/mo><mn>6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">-15= 7\\cdot (-3)+6<\/annotation><\/semantics><\/math><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 4. <\/strong>Muunna annetut bin\u00e4\u00e4riluvut 10-j\u00e4rjestelm\u00e4\u00e4n<\/h3>\n\n\n\n<p>a. <math data-latex=\"\t10111_2\"><semantics><msub><mn>10111<\/mn><mn>2<\/mn><\/msub><annotation encoding=\"application\/x-tex\">\t10111_2<\/annotation><\/semantics><\/math> <br>b. <math data-latex=\"\t110110_2\"><semantics><msub><mn>110110<\/mn><mn>2<\/mn><\/msub><annotation encoding=\"application\/x-tex\">\t110110_2<\/annotation><\/semantics><\/math><br>c. <math data-latex=\"\t11001101_2\"><semantics><msub><mn>11001101<\/mn><mn>2<\/mn><\/msub><annotation encoding=\"application\/x-tex\">\t11001101_2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-4&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#e6f3b7\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-4-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-4\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-4\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-4-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>a. <math data-latex=\"\t10111_2\"><semantics><msub><mn>10111<\/mn><mn>2<\/mn><\/msub><annotation encoding=\"application\/x-tex\">\t10111_2<\/annotation><\/semantics><\/math><br> <math data-latex=\"=1\u22c52^4+0\u22c52^3+1\u22c52^2+1\u22c52^1+1\u22c52^0\"><semantics><mrow><mo>=<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>4<\/mn><\/msup><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>3<\/mn><\/msup><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>2<\/mn><\/msup><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>1<\/mn><\/msup><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>0<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">=1\u22c52^4+0\u22c52^3+1\u22c52^2+1\u22c52^1+1\u22c52^0<\/annotation><\/semantics><\/math><br> <math data-latex=\"=1\u22c516+0\u22c58+1\u22c54+1\u22c52+1\u22c51\"><semantics><mrow><mo>=<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>16<\/mn><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><mn>8<\/mn><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>4<\/mn><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=1\u22c516+0\u22c58+1\u22c54+1\u22c52+1\u22c51<\/annotation><\/semantics><\/math><br> <math data-latex=\"=16+4+2+1\"><semantics><mrow><mo>=<\/mo><mn>16<\/mn><mo>+<\/mo><mn>4<\/mn><mo>+<\/mo><mn>2<\/mn><mo>+<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=16+4+2+1<\/annotation><\/semantics><\/math><br> <math data-latex=\"=23\"><semantics><mrow><mo>=<\/mo><mn>23<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=23<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>b. <math data-latex=\"110110_2\"><semantics><msub><mn>110110<\/mn><mn>2<\/mn><\/msub><annotation encoding=\"application\/x-tex\">110110_2<\/annotation><\/semantics><\/math><br> <math data-latex=\"=1\u22c52^6+0\u22c52^5+1\u22c52^4+0\u22c52^3+1\u22c52^2+1\u22c52^1+0\u22c52^0\"><semantics><mrow><mo>=<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>6<\/mn><\/msup><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>5<\/mn><\/msup><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>4<\/mn><\/msup><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>3<\/mn><\/msup><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>2<\/mn><\/msup><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>1<\/mn><\/msup><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>0<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">=1\u22c52^6+0\u22c52^5+1\u22c52^4+0\u22c52^3+1\u22c52^2+1\u22c52^1+0\u22c52^0<\/annotation><\/semantics><\/math><br> <math data-latex=\" =1\u22c564+0\u22c532+1\u22c516+0\u22c58+1\u22c54+1\u22c52+0\u22c51\"><semantics><mrow><mo>=<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>64<\/mn><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><mn>32<\/mn><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>16<\/mn><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><mn>8<\/mn><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>4<\/mn><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\"> =1\u22c564+0\u22c532+1\u22c516+0\u22c58+1\u22c54+1\u22c52+0\u22c51<\/annotation><\/semantics><\/math><br> <math data-latex=\"=64+16+4+2\"><semantics><mrow><mo>=<\/mo><mn>64<\/mn><mo>+<\/mo><mn>16<\/mn><mo>+<\/mo><mn>4<\/mn><mo>+<\/mo><mn>2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=64+16+4+2<\/annotation><\/semantics><\/math><br> <math data-latex=\"=86\"><semantics><mrow><mo>=<\/mo><mn>86<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=86<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>c. <math data-latex=\"11001101_2\"><semantics><msub><mn>11001101<\/mn><mn>2<\/mn><\/msub><annotation encoding=\"application\/x-tex\">11001101_2<\/annotation><\/semantics><\/math><br> <math data-latex=\"=1\u22c52^7+1\u22c52^6+0\u22c52^5+0\u22c52^4+1\u22c52^3+1\u22c52^2+0\u22c52^1+1\u22c52^0\"><semantics><mrow><mo>=<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>7<\/mn><\/msup><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>6<\/mn><\/msup><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>5<\/mn><\/msup><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>4<\/mn><\/msup><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>3<\/mn><\/msup><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>2<\/mn><\/msup><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>1<\/mn><\/msup><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>0<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">=1\u22c52^7+1\u22c52^6+0\u22c52^5+0\u22c52^4+1\u22c52^3+1\u22c52^2+0\u22c52^1+1\u22c52^0<\/annotation><\/semantics><\/math><br> <math data-latex=\" =1\u22c5128+1\u22c564+0\u22c532+0\u22c516+1\u22c58+1\u22c54+0\u22c52+1\u22c51\"><semantics><mrow><mo>=<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>128<\/mn><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>64<\/mn><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><mn>32<\/mn><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><mn>16<\/mn><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>8<\/mn><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>4<\/mn><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\"> =1\u22c5128+1\u22c564+0\u22c532+0\u22c516+1\u22c58+1\u22c54+0\u22c52+1\u22c51<\/annotation><\/semantics><\/math><br> <math data-latex=\"= 128+64+8+4+1\"><semantics><mrow><mo>=<\/mo><mn>128<\/mn><mo>+<\/mo><mn>64<\/mn><mo>+<\/mo><mn>8<\/mn><mo>+<\/mo><mn>4<\/mn><mo>+<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= 128+64+8+4+1<\/annotation><\/semantics><\/math><br> <math data-latex=\"=205\"><semantics><mrow><mo>=<\/mo><mn>205<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=205<\/annotation><\/semantics><\/math><br><\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 5.<\/strong> Muunna annetut 10-j\u00e4rjestelm\u00e4n luvut bin\u00e4\u00e4riin<\/h3>\n\n\n\n<p>a. <math data-latex=\"25\"><semantics><mn>25<\/mn><annotation encoding=\"application\/x-tex\">25<\/annotation><\/semantics><\/math><br>b. <math data-latex=\"189\"><semantics><mn>189<\/mn><annotation encoding=\"application\/x-tex\">189<\/annotation><\/semantics><\/math><br>c. <math data-latex=\"78\"><semantics><mn>78<\/mn><annotation encoding=\"application\/x-tex\">78<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-5&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#e6f3b7\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-5-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-5\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-5\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-5-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>a. <math data-latex=\"25_{10}\"><semantics><msub><mn>25<\/mn><mn>10<\/mn><\/msub><annotation encoding=\"application\/x-tex\">25_{10}<\/annotation><\/semantics><\/math><br><br> <math data-latex=\"\\frac{25}{2}=12{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 1\"><semantics><mrow><mfrac><mn>25<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>12,<\/mn><mtext>&nbsp;<\/mtext><mi>j<\/mi><mi>a<\/mi><mi>k<\/mi><mi>o<\/mi><mi>j<\/mi><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>n<\/mi><mi>n<\/mi><mover><mi>o<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>s<\/mi><mtext>&nbsp;<\/mtext><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{25}{2}=12{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 1<\/annotation><\/semantics><\/math><br><br> <math data-latex=\"\\frac{12}{2}=6{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 0\"><semantics><mrow><mfrac><mn>12<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>6,<\/mn><mtext>&nbsp;<\/mtext><mi>j<\/mi><mi>a<\/mi><mi>k<\/mi><mi>o<\/mi><mi>j<\/mi><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>n<\/mi><mi>n<\/mi><mover><mi>o<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>s<\/mi><mtext>&nbsp;<\/mtext><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{12}{2}=6{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 0<\/annotation><\/semantics><\/math><br><br> <math data-latex=\"\\frac{6}{2}=3{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 0\"><semantics><mrow><mfrac><mn>6<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>3,<\/mn><mtext>&nbsp;<\/mtext><mi>j<\/mi><mi>a<\/mi><mi>k<\/mi><mi>o<\/mi><mi>j<\/mi><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>n<\/mi><mi>n<\/mi><mover><mi>o<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>s<\/mi><mtext>&nbsp;<\/mtext><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{6}{2}=3{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 0<\/annotation><\/semantics><\/math><br><br> <math data-latex=\"\\frac{3}{2}=1{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 1\"><semantics><mrow><mfrac><mn>3<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>1,<\/mn><mtext>&nbsp;<\/mtext><mi>j<\/mi><mi>a<\/mi><mi>k<\/mi><mi>o<\/mi><mi>j<\/mi><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>n<\/mi><mi>n<\/mi><mover><mi>o<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>s<\/mi><mtext>&nbsp;<\/mtext><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{3}{2}=1{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 1<\/annotation><\/semantics><\/math><br><br><math data-latex=\"\\frac{1}{2}=0{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 1\"><semantics><mrow><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>0,<\/mn><mtext>&nbsp;<\/mtext><mi>j<\/mi><mi>a<\/mi><mi>k<\/mi><mi>o<\/mi><mi>j<\/mi><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>n<\/mi><mi>n<\/mi><mover><mi>o<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>s<\/mi><mtext>&nbsp;<\/mtext><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1}{2}=0{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 1<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>vastaus: <math data-latex=\"11001_2\"><semantics><msub><mn>11001<\/mn><mn>2<\/mn><\/msub><annotation encoding=\"application\/x-tex\">11001_2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>b. <math data-latex=\"189_{10}\"><semantics><msub><mn>189<\/mn><mn>10<\/mn><\/msub><annotation encoding=\"application\/x-tex\">189_{10}<\/annotation><\/semantics><\/math><br><br> <math data-latex=\"\\frac{189}{2}=94{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 1\"><semantics><mrow><mfrac><mn>189<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>94,<\/mn><mtext>&nbsp;<\/mtext><mi>j<\/mi><mi>a<\/mi><mi>k<\/mi><mi>o<\/mi><mi>j<\/mi><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>n<\/mi><mi>n<\/mi><mover><mi>o<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>s<\/mi><mtext>&nbsp;<\/mtext><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{189}{2}=94{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 1<\/annotation><\/semantics><\/math><br><br><math data-latex=\"\\frac{94}{2}=47{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 0\"><semantics><mrow><mfrac><mn>94<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>47,<\/mn><mtext>&nbsp;<\/mtext><mi>j<\/mi><mi>a<\/mi><mi>k<\/mi><mi>o<\/mi><mi>j<\/mi><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>n<\/mi><mi>n<\/mi><mover><mi>o<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>s<\/mi><mtext>&nbsp;<\/mtext><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{94}{2}=47{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 0<\/annotation><\/semantics><\/math><br><br> <math data-latex=\"\\frac{47}{2}=23{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 1\"><semantics><mrow><mfrac><mn>47<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>23,<\/mn><mtext>&nbsp;<\/mtext><mi>j<\/mi><mi>a<\/mi><mi>k<\/mi><mi>o<\/mi><mi>j<\/mi><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>n<\/mi><mi>n<\/mi><mover><mi>o<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>s<\/mi><mtext>&nbsp;<\/mtext><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{47}{2}=23{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 1<\/annotation><\/semantics><\/math><br><br><math data-latex=\"\\frac{23}{2}=11{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 1\"><semantics><mrow><mfrac><mn>23<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>11,<\/mn><mtext>&nbsp;<\/mtext><mi>j<\/mi><mi>a<\/mi><mi>k<\/mi><mi>o<\/mi><mi>j<\/mi><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>n<\/mi><mi>n<\/mi><mover><mi>o<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>s<\/mi><mtext>&nbsp;<\/mtext><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{23}{2}=11{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 1<\/annotation><\/semantics><\/math><br><br><math data-latex=\"\\frac{11}{2}=5{,}\\ \\ jakoj\u00e4\u00e4nn\u00f6s\\ 1\"><semantics><mrow><mfrac><mn>11<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>5,<\/mn><mtext>&nbsp;<\/mtext><mtext>&nbsp;<\/mtext><mi>j<\/mi><mi>a<\/mi><mi>k<\/mi><mi>o<\/mi><mi>j<\/mi><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>n<\/mi><mi>n<\/mi><mover><mi>o<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>s<\/mi><mtext>&nbsp;<\/mtext><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{11}{2}=5{,}\\ \\ jakoj\u00e4\u00e4nn\u00f6s\\ 1<\/annotation><\/semantics><\/math><br><br><math data-latex=\"\\frac{5}{2}=2{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 1\"><semantics><mrow><mfrac><mn>5<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>2,<\/mn><mtext>&nbsp;<\/mtext><mi>j<\/mi><mi>a<\/mi><mi>k<\/mi><mi>o<\/mi><mi>j<\/mi><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>n<\/mi><mi>n<\/mi><mover><mi>o<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>s<\/mi><mtext>&nbsp;<\/mtext><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{5}{2}=2{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 1<\/annotation><\/semantics><\/math><br><br> <math data-latex=\"\\frac{2}{2}=1{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 0\"><semantics><mrow><mfrac><mn>2<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>1,<\/mn><mtext>&nbsp;<\/mtext><mi>j<\/mi><mi>a<\/mi><mi>k<\/mi><mi>o<\/mi><mi>j<\/mi><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>n<\/mi><mi>n<\/mi><mover><mi>o<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>s<\/mi><mtext>&nbsp;<\/mtext><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{2}{2}=1{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 0<\/annotation><\/semantics><\/math><br><br> <math data-latex=\"\\frac{1}{2}=0{,}\\ \\ jakoj\u00e4\u00e4nn\u00f6s\\ 1\"><semantics><mrow><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>0,<\/mn><mtext>&nbsp;<\/mtext><mtext>&nbsp;<\/mtext><mi>j<\/mi><mi>a<\/mi><mi>k<\/mi><mi>o<\/mi><mi>j<\/mi><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>n<\/mi><mi>n<\/mi><mover><mi>o<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>s<\/mi><mtext>&nbsp;<\/mtext><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1}{2}=0{,}\\ \\ jakoj\u00e4\u00e4nn\u00f6s\\ 1<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>vastaus: <math data-latex=\"10111101_2\"><semantics><msub><mn>10111101<\/mn><mn>2<\/mn><\/msub><annotation encoding=\"application\/x-tex\">10111101_2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>c. <math data-latex=\"78_{10}\"><semantics><msub><mn>78<\/mn><mn>10<\/mn><\/msub><annotation encoding=\"application\/x-tex\">78_{10}<\/annotation><\/semantics><\/math><br><br> <math data-latex=\"\\frac{78}{2}=39{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 0\"><semantics><mrow><mfrac><mn>78<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>39,<\/mn><mtext>&nbsp;<\/mtext><mi>j<\/mi><mi>a<\/mi><mi>k<\/mi><mi>o<\/mi><mi>j<\/mi><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>n<\/mi><mi>n<\/mi><mover><mi>o<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>s<\/mi><mtext>&nbsp;<\/mtext><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{78}{2}=39{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 0<\/annotation><\/semantics><\/math><br><br> <math data-latex=\"\\frac{39}{2}=19.\\ jakoj\u00e4\u00e4nn\u00f6s\\ 1\"><semantics><mrow><mfrac><mn>39<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>19.<\/mn><mtext>&nbsp;<\/mtext><mi>j<\/mi><mi>a<\/mi><mi>k<\/mi><mi>o<\/mi><mi>j<\/mi><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>n<\/mi><mi>n<\/mi><mover><mi>o<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>s<\/mi><mtext>&nbsp;<\/mtext><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{39}{2}=19.\\ jakoj\u00e4\u00e4nn\u00f6s\\ 1<\/annotation><\/semantics><\/math><br><br> <math data-latex=\"\\frac{19}{2}=9.\\ jakoj\u00e4\u00e4nn\u00f6s\\ 1\"><semantics><mrow><mfrac><mn>19<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>9.<\/mn><mtext>&nbsp;<\/mtext><mi>j<\/mi><mi>a<\/mi><mi>k<\/mi><mi>o<\/mi><mi>j<\/mi><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>n<\/mi><mi>n<\/mi><mover><mi>o<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>s<\/mi><mtext>&nbsp;<\/mtext><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{19}{2}=9.\\ jakoj\u00e4\u00e4nn\u00f6s\\ 1<\/annotation><\/semantics><\/math><br><br> <math data-latex=\"\\frac{9}{2}=4{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 1\"><semantics><mrow><mfrac><mn>9<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>4,<\/mn><mtext>&nbsp;<\/mtext><mi>j<\/mi><mi>a<\/mi><mi>k<\/mi><mi>o<\/mi><mi>j<\/mi><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>n<\/mi><mi>n<\/mi><mover><mi>o<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>s<\/mi><mtext>&nbsp;<\/mtext><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9}{2}=4{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 1<\/annotation><\/semantics><\/math><br><br> <math data-latex=\"\\frac{4}{2}=2{,}\\ jakoj\u00e4nn\u00f6s\\ 0\"><semantics><mrow><mfrac><mn>4<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>2,<\/mn><mtext>&nbsp;<\/mtext><mi>j<\/mi><mi>a<\/mi><mi>k<\/mi><mi>o<\/mi><mi>j<\/mi><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>n<\/mi><mi>n<\/mi><mover><mi>o<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>s<\/mi><mtext>&nbsp;<\/mtext><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{4}{2}=2{,}\\ jakoj\u00e4nn\u00f6s\\ 0<\/annotation><\/semantics><\/math><br><br> <math data-latex=\"\\frac{2}{2}=1{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 0\"><semantics><mrow><mfrac><mn>2<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>1,<\/mn><mtext>&nbsp;<\/mtext><mi>j<\/mi><mi>a<\/mi><mi>k<\/mi><mi>o<\/mi><mi>j<\/mi><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>n<\/mi><mi>n<\/mi><mover><mi>o<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>s<\/mi><mtext>&nbsp;<\/mtext><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{2}{2}=1{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 0<\/annotation><\/semantics><\/math><br><br><math data-latex=\"\\frac{1}{2}=0{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 1\"><semantics><mrow><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>0,<\/mn><mtext>&nbsp;<\/mtext><mi>j<\/mi><mi>a<\/mi><mi>k<\/mi><mi>o<\/mi><mi>j<\/mi><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mover><mi>a<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>n<\/mi><mi>n<\/mi><mover><mi>o<\/mi><mo stretchy=\"false\" class=\"tml-xshift\">\u00a8<\/mo><\/mover><mi>s<\/mi><mtext>&nbsp;<\/mtext><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1}{2}=0{,}\\ jakoj\u00e4\u00e4nn\u00f6s\\ 1<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>vastaus: <math data-latex=\"1001110_2\"><semantics><msub><mn>1001110<\/mn><mn>2<\/mn><\/msub><annotation encoding=\"application\/x-tex\">1001110_2<\/annotation><\/semantics><\/math><\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 6.<\/strong> Muuta annetut luvut heksadesimaaleista 10-j\u00e4rjestelm\u00e4\u00e4n.<\/h3>\n\n\n\n<p>a. <math data-latex=\"FF_{16}\"><semantics><mrow><mi>F<\/mi><msub><mi>F<\/mi><mn>16<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">FF_{16}<\/annotation><\/semantics><\/math><br>b. <math data-latex=\"7E9_{16}\"><semantics><mrow><mn>7<\/mn><mi>E<\/mi><msub><mn>9<\/mn><mn>16<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">7E9_{16}<\/annotation><\/semantics><\/math><br>c. <math data-latex=\"E6F3B7_{16}\"><semantics><mrow><mi>E<\/mi><mn>6<\/mn><mi>F<\/mi><mn>3<\/mn><mi>B<\/mi><msub><mn>7<\/mn><mn>16<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">E6F3B7_{16}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-6&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#d6d6ff\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-6-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-6\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-6\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-6-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>a. <math data-latex=\"FF_{16}\"><semantics><mrow><mi>F<\/mi><msub><mi>F<\/mi><mn>16<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">FF_{16}<\/annotation><\/semantics><\/math><br><math data-latex=\"=15\\cdot16^1+15\\cdot16^0\"><semantics><mrow><mo>=<\/mo><mn>15<\/mn><mo>\u22c5<\/mo><msup><mn>16<\/mn><mn>1<\/mn><\/msup><mo>+<\/mo><mn>15<\/mn><mo>\u22c5<\/mo><msup><mn>16<\/mn><mn>0<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">=15\\cdot16^1+15\\cdot16^0<\/annotation><\/semantics><\/math><br><math data-latex=\"=15\\cdot16+15\\cdot1\"><semantics><mrow><mo>=<\/mo><mn>15<\/mn><mo>\u22c5<\/mo><mn>16<\/mn><mo>+<\/mo><mn>15<\/mn><mo>\u22c5<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=15\\cdot16+15\\cdot1<\/annotation><\/semantics><\/math><br><math data-latex=\"=240+15\"><semantics><mrow><mo>=<\/mo><mn>240<\/mn><mo>+<\/mo><mn>15<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=240+15<\/annotation><\/semantics><\/math><br><math data-latex=\"=255\"><semantics><mrow><mo>=<\/mo><mn>255<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=255<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>b. <math data-latex=\"7E9_{16}\"><semantics><mrow><mn>7<\/mn><mi>E<\/mi><msub><mn>9<\/mn><mn>16<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">7E9_{16}<\/annotation><\/semantics><\/math><br><math data-latex=\"=7\\cdot16^2+14\\cdot16^1+9\\cdot16^0\"><semantics><mrow><mo>=<\/mo><mn>7<\/mn><mo>\u22c5<\/mo><msup><mn>16<\/mn><mn>2<\/mn><\/msup><mo>+<\/mo><mn>14<\/mn><mo>\u22c5<\/mo><msup><mn>16<\/mn><mn>1<\/mn><\/msup><mo>+<\/mo><mn>9<\/mn><mo>\u22c5<\/mo><msup><mn>16<\/mn><mn>0<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">=7\\cdot16^2+14\\cdot16^1+9\\cdot16^0<\/annotation><\/semantics><\/math><br><math data-latex=\"=7\\cdot256+14\\cdot16+9\\cdot1\"><semantics><mrow><mo>=<\/mo><mn>7<\/mn><mo>\u22c5<\/mo><mn>256<\/mn><mo>+<\/mo><mn>14<\/mn><mo>\u22c5<\/mo><mn>16<\/mn><mo>+<\/mo><mn>9<\/mn><mo>\u22c5<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=7\\cdot256+14\\cdot16+9\\cdot1<\/annotation><\/semantics><\/math><br><math data-latex=\"=1792+224+9\"><semantics><mrow><mo>=<\/mo><mn>1792<\/mn><mo>+<\/mo><mn>224<\/mn><mo>+<\/mo><mn>9<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=1792+224+9<\/annotation><\/semantics><\/math><br><math data-latex=\"=2025\"><semantics><mrow><mo>=<\/mo><mn>2025<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=2025<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>c. <math data-latex=\"E6F3B7_{16}\"><semantics><mrow><mi>E<\/mi><mn>6<\/mn><mi>F<\/mi><mn>3<\/mn><mi>B<\/mi><msub><mn>7<\/mn><mn>16<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">E6F3B7_{16}<\/annotation><\/semantics><\/math><br><math data-latex=\"=14\\cdot16^5+6\\cdot16^4+15\\cdot16^3+3\\cdot16^2+11\\cdot16^1+7\\cdot16^0\"><semantics><mrow><mo>=<\/mo><mn>14<\/mn><mo>\u22c5<\/mo><msup><mn>16<\/mn><mn>5<\/mn><\/msup><mo>+<\/mo><mn>6<\/mn><mo>\u22c5<\/mo><msup><mn>16<\/mn><mn>4<\/mn><\/msup><mo>+<\/mo><mn>15<\/mn><mo>\u22c5<\/mo><msup><mn>16<\/mn><mn>3<\/mn><\/msup><mo>+<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><msup><mn>16<\/mn><mn>2<\/mn><\/msup><mo>+<\/mo><mn>11<\/mn><mo>\u22c5<\/mo><msup><mn>16<\/mn><mn>1<\/mn><\/msup><mo>+<\/mo><mn>7<\/mn><mo>\u22c5<\/mo><msup><mn>16<\/mn><mn>0<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">=14\\cdot16^5+6\\cdot16^4+15\\cdot16^3+3\\cdot16^2+11\\cdot16^1+7\\cdot16^0<\/annotation><\/semantics><\/math><br><math data-latex=\"=14\\cdot1048576+6\\cdot65536+15\\cdot4096+3\\cdot256+11\\cdot16+7\\cdot1\"><semantics><mrow><mo>=<\/mo><mn>14<\/mn><mo>\u22c5<\/mo><mn>1048576<\/mn><mo>+<\/mo><mn>6<\/mn><mo>\u22c5<\/mo><mn>65536<\/mn><mo>+<\/mo><mn>15<\/mn><mo>\u22c5<\/mo><mn>4096<\/mn><mo>+<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>256<\/mn><mo>+<\/mo><mn>11<\/mn><mo>\u22c5<\/mo><mn>16<\/mn><mo>+<\/mo><mn>7<\/mn><mo>\u22c5<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=14\\cdot1048576+6\\cdot65536+15\\cdot4096+3\\cdot256+11\\cdot16+7\\cdot1<\/annotation><\/semantics><\/math><br><math data-latex=\"=14680064+393216+61440+768+176+7\"><semantics><mrow><mo>=<\/mo><mn>14680064<\/mn><mo>+<\/mo><mn>393216<\/mn><mo>+<\/mo><mn>61440<\/mn><mo>+<\/mo><mn>768<\/mn><mo>+<\/mo><mn>176<\/mn><mo>+<\/mo><mn>7<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=14680064+393216+61440+768+176+7<\/annotation><\/semantics><\/math><br><math data-latex=\"=15&nbsp;135&nbsp;671\"><semantics><mrow><mo>=<\/mo><mn>15135671<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=15&nbsp;135&nbsp;671<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 7.<\/strong> Muuta 10-j\u00e4rjestelm\u00e4n luvut heksadesimaaliin.<\/h3>\n\n\n\n<p>a. <math data-latex=\"282_{10}\"><semantics><msub><mn>282<\/mn><mn>10<\/mn><\/msub><annotation encoding=\"application\/x-tex\">282_{10}<\/annotation><\/semantics><\/math><br>b. <math data-latex=\"63_{10}\"><semantics><msub><mn>63<\/mn><mn>10<\/mn><\/msub><annotation encoding=\"application\/x-tex\">63_{10}<\/annotation><\/semantics><\/math><br>c. <math data-latex=\"1879_{10}\"><semantics><msub><mn>1879<\/mn><mn>10<\/mn><\/msub><annotation encoding=\"application\/x-tex\">1879_{10}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-7&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#d6d6ff\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-7-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-7\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">VINKKI!<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-7\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-7-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>K\u00e4yt\u00e4 jakoj\u00e4\u00e4nn\u00f6s menetelm\u00e4\u00e4. K\u00e4yt\u00e4 jakajana lukua 16. Heksadesimaali vastaus luetaan jakoj\u00e4\u00e4nn\u00f6ksist\u00e4 alhaalta yl\u00f6sp\u00e4in.<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-8&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#d6d6ff\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-8-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-8\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-8\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-8-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>a. <\/p>\n\n\n\n<p><math data-latex=\"\\frac{282}{16}=17\"><semantics><mrow><mfrac><mn>282<\/mn><mn>16<\/mn><\/mfrac><mo>=<\/mo><mn>17<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{282}{16}=17<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 10<br><br><math data-latex=\"\\frac{17}{16}=1\"><semantics><mrow><mfrac><mn>17<\/mn><mn>16<\/mn><\/mfrac><mo>=<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{17}{16}=1<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 1<br><br><math data-latex=\"\\frac{1}{16}=0\"><semantics><mrow><mfrac><mn>1<\/mn><mn>16<\/mn><\/mfrac><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1}{16}=0<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 1<\/p>\n\n\n\n<p>vastaus: <math data-latex=\"11A_{16}\"><semantics><mrow><mn>11<\/mn><msub><mi>A<\/mi><mn>16<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">11A_{16}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>b.<\/p>\n\n\n\n<p><math data-latex=\"\\frac{63}{16}=3\"><semantics><mrow><mfrac><mn>63<\/mn><mn>16<\/mn><\/mfrac><mo>=<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{63}{16}=3<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 15<br><br><math data-latex=\"\\frac{3}{16}=0\"><semantics><mrow><mfrac><mn>3<\/mn><mn>16<\/mn><\/mfrac><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{3}{16}=0<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 3<\/p>\n\n\n\n<p>vastaus: <math data-latex=\"3E_{16}\"><semantics><mrow><mn>3<\/mn><msub><mi>E<\/mi><mn>16<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">3E_{16}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>c.<\/p>\n\n\n\n<p><math data-latex=\"\\frac{1879}{16}=117\"><semantics><mrow><mfrac><mn>1879<\/mn><mn>16<\/mn><\/mfrac><mo>=<\/mo><mn>117<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1879}{16}=117<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 7<br><br><math data-latex=\"\\frac{117}{16}=7\"><semantics><mrow><mfrac><mn>117<\/mn><mn>16<\/mn><\/mfrac><mo>=<\/mo><mn>7<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{117}{16}=7<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 5<br><br><math data-latex=\"\\frac{7}{16}=0\"><semantics><mrow><mfrac><mn>7<\/mn><mn>16<\/mn><\/mfrac><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{7}{16}=0<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 7<\/p>\n\n\n\n<p>vastaus: <math data-latex=\"757_{16}\"><semantics><msub><mn>757<\/mn><mn>16<\/mn><\/msub><annotation encoding=\"application\/x-tex\">757_{16}<\/annotation><\/semantics><\/math><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 8. <\/strong>Kumpi luvuista on suurempi <math data-latex=\"1101100_2\"><semantics><msub><mn>1101100<\/mn><mn>2<\/mn><\/msub><annotation encoding=\"application\/x-tex\">1101100_2<\/annotation><\/semantics><\/math> vai <math data-latex=\"106_{10}\"><semantics><msub><mn>106<\/mn><mn>10<\/mn><\/msub><annotation encoding=\"application\/x-tex\">106_{10}<\/annotation><\/semantics><\/math><\/h3>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-9&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#d6d6ff\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-9-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-9\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-9\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-9-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p><math data-latex=\"=1\u22c52^6+1\u22c52^5+0\u22c52^4+1\u22c52^3+1\u22c52^2+0\u22c52^1+0\u22c52^0\"><semantics><mrow><mo>=<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>6<\/mn><\/msup><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>5<\/mn><\/msup><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>4<\/mn><\/msup><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>3<\/mn><\/msup><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>2<\/mn><\/msup><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>1<\/mn><\/msup><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>0<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">=1\u22c52^6+1\u22c52^5+0\u22c52^4+1\u22c52^3+1\u22c52^2+0\u22c52^1+0\u22c52^0<\/annotation><\/semantics><\/math><br><math data-latex=\"=1\u22c564+1\u22c532+0\u22c516+1\u22c58+1\u22c54+0\u22c52+0\u22c51\"><semantics><mrow><mo>=<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>64<\/mn><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>32<\/mn><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><mn>16<\/mn><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>8<\/mn><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>4<\/mn><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=1\u22c564+1\u22c532+0\u22c516+1\u22c58+1\u22c54+0\u22c52+0\u22c51<\/annotation><\/semantics><\/math><br><math data-latex=\"=64+32+8+4\"><semantics><mrow><mo>=<\/mo><mn>64<\/mn><mo>+<\/mo><mn>32<\/mn><mo>+<\/mo><mn>8<\/mn><mo>+<\/mo><mn>4<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=64+32+8+4<\/annotation><\/semantics><\/math><br><math data-latex=\"=108\"><semantics><mrow><mo>=<\/mo><mn>108<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=108<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>vastaus: 2-j\u00e4rjestelm\u00e4n luku on suurempi.&nbsp;<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 9.<\/strong> P\u00e4\u00e4ttele &nbsp;x arvo, kun <math data-latex=\"110x1100_2\\ =\\ 2x4_{10}\"><semantics><mrow><mn>110<\/mn><mi>x<\/mi><msub><mn>1100<\/mn><mn>2<\/mn><\/msub><mtext>&nbsp;<\/mtext><mo>=<\/mo><mtext>&nbsp;<\/mtext><mn>2<\/mn><mi>x<\/mi><msub><mn>4<\/mn><mn>10<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">110x1100_2\\ =\\ 2x4_{10}<\/annotation><\/semantics><\/math><\/h3>\n\n\n\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-10&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#fcd8c8\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-10-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-10\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">VINKKI!<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-10\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-10-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>x voi olla vain 1 tai 0, koska bin\u00e4\u00e4riss\u00e4 ei esiinny muita lukuja.<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-11&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#fcd8c8\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-11-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-11\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-11\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-11-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>Kirjoitetaan auki molempien kantalukujen potenssien summat.<\/p>\n\n\n\n<p><math data-latex=\"110x1100_2\\ =\\ 2x4_{10}\"><semantics><mrow><mn>110<\/mn><mi>x<\/mi><msub><mn>1100<\/mn><mn>2<\/mn><\/msub><mtext>&nbsp;<\/mtext><mo>=<\/mo><mtext>&nbsp;<\/mtext><mn>2<\/mn><mi>x<\/mi><msub><mn>4<\/mn><mn>10<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">110x1100_2\\ =\\ 2x4_{10}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\"1\\cdot2^7+1\\cdot2^6+0\\cdot2^5+x\\cdot2^4+1\\cdot2^3+1\\cdot2^2+0\\cdot2^1+0\\cdot2^0\\ =\\ 2\\cdot10^2+x\\cdot10^1+4\\cdot10^0\"><semantics><mrow><mn>1<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>7<\/mn><\/msup><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>6<\/mn><\/msup><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>5<\/mn><\/msup><mo>+<\/mo><mi>x<\/mi><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>4<\/mn><\/msup><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>3<\/mn><\/msup><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>2<\/mn><\/msup><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>1<\/mn><\/msup><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>0<\/mn><\/msup><mtext>&nbsp;<\/mtext><mo>=<\/mo><mtext>&nbsp;<\/mtext><mn>2<\/mn><mo>\u22c5<\/mo><msup><mn>10<\/mn><mn>2<\/mn><\/msup><mo>+<\/mo><mi>x<\/mi><mo>\u22c5<\/mo><msup><mn>10<\/mn><mn>1<\/mn><\/msup><mo>+<\/mo><mn>4<\/mn><mo>\u22c5<\/mo><msup><mn>10<\/mn><mn>0<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">1\\cdot2^7+1\\cdot2^6+0\\cdot2^5+x\\cdot2^4+1\\cdot2^3+1\\cdot2^2+0\\cdot2^1+0\\cdot2^0\\ =\\ 2\\cdot10^2+x\\cdot10^1+4\\cdot10^0<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\"1\\cdot128+1\\cdot64+x\\cdot34+0\\cdot16+1\\cdot8+1\\cdot4+0\\cdot2+0\\cdot1\\ =\\ 2\\cdot100+x\\cdot10+4\\cdot1\"><semantics><mrow><mn>1<\/mn><mo>\u22c5<\/mo><mn>128<\/mn><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>64<\/mn><mo>+<\/mo><mi>x<\/mi><mo>\u22c5<\/mo><mn>34<\/mn><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><mn>16<\/mn><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>8<\/mn><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>4<\/mn><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><mn>1<\/mn><mtext>&nbsp;<\/mtext><mo>=<\/mo><mtext>&nbsp;<\/mtext><mn>2<\/mn><mo>\u22c5<\/mo><mn>100<\/mn><mo>+<\/mo><mi>x<\/mi><mo>\u22c5<\/mo><mn>10<\/mn><mo>+<\/mo><mn>4<\/mn><mo>\u22c5<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">1\\cdot128+1\\cdot64+x\\cdot34+0\\cdot16+1\\cdot8+1\\cdot4+0\\cdot2+0\\cdot1\\ =\\ 2\\cdot100+x\\cdot10+4\\cdot1<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\"128+64+x\\cdot34+8+4\\ =\\ 200+x\\cdot10+4\"><semantics><mrow><mn>128<\/mn><mo>+<\/mo><mn>64<\/mn><mo>+<\/mo><mi>x<\/mi><mo>\u22c5<\/mo><mn>34<\/mn><mo>+<\/mo><mn>8<\/mn><mo>+<\/mo><mn>4<\/mn><mtext>&nbsp;<\/mtext><mo>=<\/mo><mtext>&nbsp;<\/mtext><mn>200<\/mn><mo>+<\/mo><mi>x<\/mi><mo>\u22c5<\/mo><mn>10<\/mn><mo>+<\/mo><mn>4<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">128+64+x\\cdot34+8+4\\ =\\ 200+x\\cdot10+4<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\"10x-34x\\ =\\ 128+64+8+4-200-4\"><semantics><mrow><mn>10<\/mn><mi>x<\/mi><mo>\u2212<\/mo><mn>34<\/mn><mi>x<\/mi><mtext>&nbsp;<\/mtext><mo>=<\/mo><mtext>&nbsp;<\/mtext><mn>128<\/mn><mo>+<\/mo><mn>64<\/mn><mo>+<\/mo><mn>8<\/mn><mo>+<\/mo><mn>4<\/mn><mo>\u2212<\/mo><mn>200<\/mn><mo>\u2212<\/mo><mn>4<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">10x-34x\\ =\\ 128+64+8+4-200-4<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\"-24x\\ =\\ 0\\ \\parallel :\\left(-24\\right)\"><semantics><mrow><mo>\u2212<\/mo><mn>24<\/mn><mi>x<\/mi><mtext>&nbsp;<\/mtext><mo>=<\/mo><mtext>&nbsp;<\/mtext><mn>0<\/mn><mtext>&nbsp;<\/mtext><mo rspace=\"0em\">\u2225<\/mo><mo lspace=\"0em\" rspace=\"0.2222em\">:<\/mo><mrow><mo fence=\"true\" form=\"prefix\">(<\/mo><mo>\u2212<\/mo><mn>24<\/mn><mo fence=\"true\" form=\"postfix\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">-24x\\ =\\ 0\\ \\parallel :\\left(-24\\right)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\"x=0\"><semantics><mrow><mi>x<\/mi><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x=0<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>vastaus on tosi, koska numero 0 l\u00f6ytyy molemmista j\u00e4rjestelmist\u00e4.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 10.1.<\/strong> Laske annetut laskut muuttamatta lukujen lukuj\u00e4rjestelm\u00e4\u00e4.<\/h3>\n\n\n\n<p>a. <math data-latex=\"11001_2+1101_2\"><semantics><mrow><msub><mn>11001<\/mn><mn>2<\/mn><\/msub><mo>+<\/mo><msub><mn>1101<\/mn><mn>2<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">11001_2+1101_2<\/annotation><\/semantics><\/math><br>b. <math data-latex=\"F6F2A_{16}-CC54_{16}\"><semantics><mrow><mi>F<\/mi><mn>6<\/mn><mi>F<\/mi><mn>2<\/mn><msub><mi>A<\/mi><mn>16<\/mn><\/msub><mo>\u2212<\/mo><mi>C<\/mi><mi>C<\/mi><msub><mn>54<\/mn><mn>16<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">F6F2A_{16}-CC54_{16}<\/annotation><\/semantics><\/math><br>c. <math data-latex=\"10111_2\\cdot 10_2\"><semantics><mrow><msub><mn>10111<\/mn><mn>2<\/mn><\/msub><mo>\u22c5<\/mo><msub><mn>10<\/mn><mn>2<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">10111_2\\cdot 10_2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-12&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#fcd8c8\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-12-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-12\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">VINKKI!<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-12\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-12-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>1+1=0 ,(muistiin j\u00e4\u00e4 1)<br>0+0=0<br>0+1=1<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-13&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#fcd8c8\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-13-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-13\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-13\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-13-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>a. <math data-latex=\"\\begin{array}{r r r r}    &amp; &amp; 1 &amp; 1 &amp; 0 &amp; 0 &amp; 1 \\\\  + &amp; &amp;  &amp;1 &amp;1 &amp;0 &amp;1 \\\\    \\hline    &amp;1 &amp; 0 &amp; 0 &amp; 1 &amp; 1 &amp;0 \\end{array}\"><semantics><mtable columnalign=\"right right right right\"><mtr><mtd class=\"tml-right\" style=\"padding-left:0pt;padding-right:5.9776pt\"><mrow><\/mrow><\/mtd><mtd class=\"tml-right\" style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mrow><\/mrow><\/mtd><mtd class=\"tml-right\" style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mn>1<\/mn><\/mtd><mtd class=\"tml-right\" style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mn>1<\/mn><\/mtd><mtd style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mn>0<\/mn><\/mtd><mtd style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mn>0<\/mn><\/mtd><mtd style=\"padding-left:5.9776pt;padding-right:0pt\"><mn>1<\/mn><\/mtd><\/mtr><mtr><mtd class=\"tml-right\" style=\"border-bottom:0.06em solid;padding-left:0pt;padding-right:5.9776pt\"><mo>+<\/mo><\/mtd><mtd class=\"tml-right\" style=\"border-bottom:0.06em solid;padding-left:5.9776pt;padding-right:5.9776pt\"><mrow><\/mrow><\/mtd><mtd class=\"tml-right\" style=\"border-bottom:0.06em solid;padding-left:5.9776pt;padding-right:5.9776pt\"><mrow><\/mrow><\/mtd><mtd class=\"tml-right\" style=\"border-bottom:0.06em solid;padding-left:5.9776pt;padding-right:5.9776pt\"><mn>1<\/mn><\/mtd><mtd style=\"border-bottom:0.06em solid;padding-left:5.9776pt;padding-right:5.9776pt\"><mn>1<\/mn><\/mtd><mtd style=\"border-bottom:0.06em solid;padding-left:5.9776pt;padding-right:5.9776pt\"><mn>0<\/mn><\/mtd><mtd style=\"border-bottom:0.06em solid;padding-left:5.9776pt;padding-right:0pt\"><mn>1<\/mn><\/mtd><\/mtr><mtr><mtd class=\"tml-right\" style=\"padding-left:0pt;padding-right:5.9776pt\"><mrow><\/mrow><\/mtd><mtd class=\"tml-right\" style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mn>1<\/mn><\/mtd><mtd class=\"tml-right\" style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mn>0<\/mn><\/mtd><mtd class=\"tml-right\" style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mn>0<\/mn><\/mtd><mtd style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mn>1<\/mn><\/mtd><mtd style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mn>1<\/mn><\/mtd><mtd style=\"padding-left:5.9776pt;padding-right:0pt\"><mn>0<\/mn><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\begin{array}{r r r r}    &amp; &amp; 1 &amp; 1 &amp; 0 &amp; 0 &amp; 1 \\\\  + &amp; &amp;  &amp;1 &amp;1 &amp;0 &amp;1 \\\\    \\hline    &amp;1 &amp; 0 &amp; 0 &amp; 1 &amp; 1 &amp;0 \\end{array}<\/annotation><\/semantics><\/math><br>vastaus: <math data-latex=\"100110_2\"><semantics><msub><mn>100110<\/mn><mn>2<\/mn><\/msub><annotation encoding=\"application\/x-tex\">100110_2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>b. <math data-latex=\"\\begin{array}{r r r r}    &amp; F &amp; 6 &amp; F &amp; 2 &amp; A \\\\  -  &amp;  &amp;C &amp;C &amp;5 &amp;4 \\\\    \\hline    &amp;E &amp; A &amp; 2 &amp; D &amp; 6 \\end{array}\"><semantics><mtable columnalign=\"right right right right\"><mtr><mtd class=\"tml-right\" style=\"padding-left:0pt;padding-right:5.9776pt\"><mrow><\/mrow><\/mtd><mtd class=\"tml-right\" style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mi>F<\/mi><\/mtd><mtd class=\"tml-right\" style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mn>6<\/mn><\/mtd><mtd class=\"tml-right\" style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mi>F<\/mi><\/mtd><mtd style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mn>2<\/mn><\/mtd><mtd style=\"padding-left:5.9776pt;padding-right:0pt\"><mi>A<\/mi><\/mtd><\/mtr><mtr><mtd class=\"tml-right\" style=\"border-bottom:0.06em solid;padding-left:0pt;padding-right:5.9776pt\"><mo>\u2212<\/mo><\/mtd><mtd class=\"tml-right\" style=\"border-bottom:0.06em solid;padding-left:5.9776pt;padding-right:5.9776pt\"><mrow><\/mrow><\/mtd><mtd class=\"tml-right\" style=\"border-bottom:0.06em solid;padding-left:5.9776pt;padding-right:5.9776pt\"><mi>C<\/mi><\/mtd><mtd class=\"tml-right\" style=\"border-bottom:0.06em solid;padding-left:5.9776pt;padding-right:5.9776pt\"><mi>C<\/mi><\/mtd><mtd style=\"border-bottom:0.06em solid;padding-left:5.9776pt;padding-right:5.9776pt\"><mn>5<\/mn><\/mtd><mtd style=\"border-bottom:0.06em solid;padding-left:5.9776pt;padding-right:0pt\"><mn>4<\/mn><\/mtd><\/mtr><mtr><mtd class=\"tml-right\" style=\"padding-left:0pt;padding-right:5.9776pt\"><mrow><\/mrow><\/mtd><mtd class=\"tml-right\" style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mi>E<\/mi><\/mtd><mtd class=\"tml-right\" style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mi>A<\/mi><\/mtd><mtd class=\"tml-right\" style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mn>2<\/mn><\/mtd><mtd style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mi>D<\/mi><\/mtd><mtd style=\"padding-left:5.9776pt;padding-right:0pt\"><mn>6<\/mn><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\begin{array}{r r r r}    &amp; F &amp; 6 &amp; F &amp; 2 &amp; A \\\\  &#8211;  &amp;  &amp;C &amp;C &amp;5 &amp;4 \\\\    \\hline    &amp;E &amp; A &amp; 2 &amp; D &amp; 6 \\end{array}<\/annotation><\/semantics><\/math><br>vastaus: <math data-latex=\"EA2D6_{16}\"><semantics><mrow><mi>E<\/mi><mi>A<\/mi><mn>2<\/mn><mi>D<\/mi><msub><mn>6<\/mn><mn>16<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">EA2D6_{16}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>c. <math data-latex=\"\\begin{array}{r r r r}   &amp; &amp; 1 &amp; 0 &amp; 1 &amp; 1 &amp; 1 \\\\  \\cdot  &amp; &amp;  &amp; &amp; &amp;1&amp;0 \\\\    \\hline   &amp; &amp;0 &amp;0 &amp; 0 &amp;0  &amp;0 \\\\ +  &amp;1&amp;0&amp;1&amp;1&amp;1&amp; \\\\ \\hline &amp;1 &amp;0 &amp;1 &amp;1 &amp;1 &amp;0 \\end{array}\"><semantics><mtable columnalign=\"right right right right\"><mtr><mtd class=\"tml-right\" style=\"padding-left:0pt;padding-right:5.9776pt\"><mrow><\/mrow><\/mtd><mtd class=\"tml-right\" style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mrow><\/mrow><\/mtd><mtd class=\"tml-right\" style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mn>1<\/mn><\/mtd><mtd class=\"tml-right\" style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mn>0<\/mn><\/mtd><mtd style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mn>1<\/mn><\/mtd><mtd style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mn>1<\/mn><\/mtd><mtd style=\"padding-left:5.9776pt;padding-right:0pt\"><mn>1<\/mn><\/mtd><\/mtr><mtr><mtd class=\"tml-right\" style=\"border-bottom:0.06em solid;padding-left:0pt;padding-right:5.9776pt\"><mo>\u22c5<\/mo><\/mtd><mtd class=\"tml-right\" style=\"border-bottom:0.06em solid;padding-left:5.9776pt;padding-right:5.9776pt\"><mrow><\/mrow><\/mtd><mtd class=\"tml-right\" style=\"border-bottom:0.06em solid;padding-left:5.9776pt;padding-right:5.9776pt\"><mrow><\/mrow><\/mtd><mtd class=\"tml-right\" style=\"border-bottom:0.06em solid;padding-left:5.9776pt;padding-right:5.9776pt\"><mrow><\/mrow><\/mtd><mtd style=\"border-bottom:0.06em solid;padding-left:5.9776pt;padding-right:5.9776pt\"><mrow><\/mrow><\/mtd><mtd style=\"border-bottom:0.06em solid;padding-left:5.9776pt;padding-right:5.9776pt\"><mn>1<\/mn><\/mtd><mtd style=\"border-bottom:0.06em solid;padding-left:5.9776pt;padding-right:0pt\"><mn>0<\/mn><\/mtd><\/mtr><mtr><mtd class=\"tml-right\" style=\"padding-left:0pt;padding-right:5.9776pt\"><mrow><\/mrow><\/mtd><mtd class=\"tml-right\" style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mrow><\/mrow><\/mtd><mtd class=\"tml-right\" style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mn>0<\/mn><\/mtd><mtd class=\"tml-right\" style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mn>0<\/mn><\/mtd><mtd style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mn>0<\/mn><\/mtd><mtd style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mn>0<\/mn><\/mtd><mtd style=\"padding-left:5.9776pt;padding-right:0pt\"><mn>0<\/mn><\/mtd><\/mtr><mtr><mtd class=\"tml-right\" style=\"border-bottom:0.06em solid;padding-left:0pt;padding-right:5.9776pt\"><mo>+<\/mo><\/mtd><mtd class=\"tml-right\" style=\"border-bottom:0.06em solid;padding-left:5.9776pt;padding-right:5.9776pt\"><mn>1<\/mn><\/mtd><mtd class=\"tml-right\" style=\"border-bottom:0.06em solid;padding-left:5.9776pt;padding-right:5.9776pt\"><mn>0<\/mn><\/mtd><mtd class=\"tml-right\" style=\"border-bottom:0.06em solid;padding-left:5.9776pt;padding-right:5.9776pt\"><mn>1<\/mn><\/mtd><mtd style=\"border-bottom:0.06em solid;padding-left:5.9776pt;padding-right:5.9776pt\"><mn>1<\/mn><\/mtd><mtd style=\"border-bottom:0.06em solid;padding-left:5.9776pt;padding-right:5.9776pt\"><mn>1<\/mn><\/mtd><mtd style=\"border-bottom:0.06em solid;padding-left:5.9776pt;padding-right:0pt\"><mrow><\/mrow><\/mtd><\/mtr><mtr><mtd class=\"tml-right\" style=\"padding-left:0pt;padding-right:5.9776pt\"><mrow><\/mrow><\/mtd><mtd class=\"tml-right\" style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mn>1<\/mn><\/mtd><mtd class=\"tml-right\" style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mn>0<\/mn><\/mtd><mtd class=\"tml-right\" style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mn>1<\/mn><\/mtd><mtd style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mn>1<\/mn><\/mtd><mtd style=\"padding-left:5.9776pt;padding-right:5.9776pt\"><mn>1<\/mn><\/mtd><mtd style=\"padding-left:5.9776pt;padding-right:0pt\"><mn>0<\/mn><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\begin{array}{r r r r}   &amp; &amp; 1 &amp; 0 &amp; 1 &amp; 1 &amp; 1 \\\\  \\cdot  &amp; &amp;  &amp; &amp; &amp;1&amp;0 \\\\    \\hline   &amp; &amp;0 &amp;0 &amp; 0 &amp;0  &amp;0 \\\\ +  &amp;1&amp;0&amp;1&amp;1&amp;1&amp; \\\\ \\hline &amp;1 &amp;0 &amp;1 &amp;1 &amp;1 &amp;0 \\end{array}<\/annotation><\/semantics><\/math><br>vastaus: <math data-latex=\"101110_2\"><semantics><msub><mn>101110<\/mn><mn>2<\/mn><\/msub><annotation encoding=\"application\/x-tex\">101110_2<\/annotation><\/semantics><\/math><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:21.1px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 10.2.<\/strong> Muunna teht\u00e4v\u00e4n <strong>10.1. <\/strong>vastaukset pyydettyihin j\u00e4rjestelmiin.<\/h3>\n\n\n\n<p>a. muunna <strong>10.1.<\/strong> a-kohdan vastaus 8-j\u00e4rjestelm\u00e4\u00e4n.<br>b. muunna <strong>10.1.<\/strong> b-kohdan vastaus 2-j\u00e4rjestelm\u00e4\u00e4n eli bin\u00e4\u00e4riin.<br>c. muunna <strong>10.1. <\/strong>c-kohdan vastaus 10-j\u00e4rjestelm\u00e4\u00e4n.<\/p>\n\n\n\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-14&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#fcd8c8\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-14-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-14\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">VINKKI!<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-14\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-14-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>Bin\u00e4\u00e4rin 3-bitin ryhm\u00e4 vastaa yht\u00e4 8-j\u00e4rjestelm\u00e4n numeroa. <\/p>\n\n\n\n<p>Bin\u00e4\u00e4rin 4-bitin ryhm\u00e4 vastaa yht\u00e4 16-j\u00e4rjestelm\u00e4n numeroa.<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-15&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#fcd8c8\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-15-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-15\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-15\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-15-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>a. <math data-latex=\"100110_2\"><semantics><msub><mn>100110<\/mn><mn>2<\/mn><\/msub><annotation encoding=\"application\/x-tex\">100110_2<\/annotation><\/semantics><\/math><br> <math data-latex=\"100=1\\cdot4+0\\cdot2+0\\cdot1=4\"><semantics><mrow><mn>100<\/mn><mo>=<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>4<\/mn><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><mn>1<\/mn><mo>=<\/mo><mn>4<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">100=1\\cdot4+0\\cdot2+0\\cdot1=4<\/annotation><\/semantics><\/math><br> <math data-latex=\"110=1\\cdot4+1\\cdot2+0\\cdot1=4+2=6\"><semantics><mrow><mn>110<\/mn><mo>=<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>4<\/mn><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><mn>1<\/mn><mo>=<\/mo><mn>4<\/mn><mo>+<\/mo><mn>2<\/mn><mo>=<\/mo><mn>6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">110=1\\cdot4+1\\cdot2+0\\cdot1=4+2=6<\/annotation><\/semantics><\/math><br>vastaus: <math data-latex=\"46_8\"><semantics><msub><mn>46<\/mn><mn>8<\/mn><\/msub><annotation encoding=\"application\/x-tex\">46_8<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>b. <math data-latex=\"EA2D6_{16}\"><semantics><mrow><mi>E<\/mi><mi>A<\/mi><mn>2<\/mn><mi>D<\/mi><msub><mn>6<\/mn><mn>16<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">EA2D6_{16}<\/annotation><\/semantics><\/math><br><br> <math data-latex=\"\\frac{14}{2}=7\"><semantics><mrow><mfrac><mn>14<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>7<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{14}{2}=7<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 0<br><br> <math data-latex=\"\\frac{7}{2}=3\"><semantics><mrow><mfrac><mn>7<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{7}{2}=3<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 1<br><br> <math data-latex=\"\\frac{3}{2}=1\"><semantics><mrow><mfrac><mn>3<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{3}{2}=1<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 1<br><br> <math data-latex=\"\\frac{1}{2}=7\"><semantics><mrow><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>7<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1}{2}=7<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 1<br> <math data-latex=\"E_{16}=1110_2\"><semantics><mrow><msub><mi>E<\/mi><mn>16<\/mn><\/msub><mo>=<\/mo><msub><mn>1110<\/mn><mn>2<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">E_{16}=1110_2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p> <math data-latex=\"\\frac{10}{2}=5\"><semantics><mrow><mfrac><mn>10<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{10}{2}=5<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 0<br><br> <math data-latex=\"\\frac{5}{2}=2\"><semantics><mrow><mfrac><mn>5<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{5}{2}=2<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 1<br><br> <math data-latex=\"\\frac{2}{2}=1\"><semantics><mrow><mfrac><mn>2<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{2}{2}=1<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 0<br><br> <math data-latex=\"\\frac{1}{2}=0\"><semantics><mrow><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1}{2}=0<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 1<br> <math data-latex=\"A_{16}=1010_2\"><semantics><mrow><msub><mi>A<\/mi><mn>16<\/mn><\/msub><mo>=<\/mo><msub><mn>1010<\/mn><mn>2<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">A_{16}=1010_2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p> <math data-latex=\"\\frac{2}{2}=1\"><semantics><mrow><mfrac><mn>2<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{2}{2}=1<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 0<br> <br> <math data-latex=\"\\frac{1}{2}=0\"><semantics><mrow><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1}{2}=0<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 1<br> <math data-latex=\"2_{16}=0010_2\"><semantics><mrow><msub><mn>2<\/mn><mn>16<\/mn><\/msub><mo>=<\/mo><msub><mn>0010<\/mn><mn>2<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">2_{16}=0010_2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p> <math data-latex=\"\\frac{13}{2}=6\"><semantics><mrow><mfrac><mn>13<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{13}{2}=6<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 1<br><br> <math data-latex=\"\\frac{6}{2}=3\"><semantics><mrow><mfrac><mn>6<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{6}{2}=3<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 0<br><br> <math data-latex=\"\\frac{3}{2}=1\"><semantics><mrow><mfrac><mn>3<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{3}{2}=1<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 1<br><br> <math data-latex=\"\\frac{1}{2}=0\"><semantics><mrow><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1}{2}=0<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 1<br><math data-latex=\"D_{16}=1101_2\"><semantics><mrow><msub><mi>D<\/mi><mn>16<\/mn><\/msub><mo>=<\/mo><msub><mn>1101<\/mn><mn>2<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">D_{16}=1101_2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p> <math data-latex=\"\\frac{6}{2}=3\"><semantics><mrow><mfrac><mn>6<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{6}{2}=3<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 0<br><br> <math data-latex=\"\\frac{3}{2}=1\"><semantics><mrow><mfrac><mn>3<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{3}{2}=1<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 1<br><br> <math data-latex=\"\\frac{1}{2}=0\"><semantics><mrow><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1}{2}=0<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 1<br> <math data-latex=\"6_{16}=0110_2\"><semantics><mrow><msub><mn>6<\/mn><mn>16<\/mn><\/msub><mo>=<\/mo><msub><mn>0110<\/mn><mn>2<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">6_{16}=0110_2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>vastaus: <math data-latex=\"1110 1010 0010 1101 0110_2\"><semantics><msub><mn>11101010001011010110<\/mn><mn>2<\/mn><\/msub><annotation encoding=\"application\/x-tex\">1110 1010 0010 1101 0110_2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>c. <math data-latex=\"101110_2\"><semantics><msub><mn>101110<\/mn><mn>2<\/mn><\/msub><annotation encoding=\"application\/x-tex\">101110_2<\/annotation><\/semantics><\/math><br> <math data-latex=\"=1\\cdot2^5+0\\cdot2^4+1\\cdot2^3+1\\cdot2^2+1\\cdot2^1+0\\cdot2^0\"><semantics><mrow><mo>=<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>5<\/mn><\/msup><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>4<\/mn><\/msup><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>3<\/mn><\/msup><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>2<\/mn><\/msup><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>1<\/mn><\/msup><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><msup><mn>2<\/mn><mn>0<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">=1\\cdot2^5+0\\cdot2^4+1\\cdot2^3+1\\cdot2^2+1\\cdot2^1+0\\cdot2^0<\/annotation><\/semantics><\/math><br> <math data-latex=\"=1\\cdot32+0\\cdot16+1\\cdot8+1\\cdot4+1\\cdot2+0\\cdot1\"><semantics><mrow><mo>=<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>32<\/mn><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><mn>16<\/mn><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>8<\/mn><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>4<\/mn><mo>+<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>+<\/mo><mn>0<\/mn><mo>\u22c5<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=1\\cdot32+0\\cdot16+1\\cdot8+1\\cdot4+1\\cdot2+0\\cdot1<\/annotation><\/semantics><\/math><br> <math data-latex=\"=32+8+4+2\"><semantics><mrow><mo>=<\/mo><mn>32<\/mn><mo>+<\/mo><mn>8<\/mn><mo>+<\/mo><mn>4<\/mn><mo>+<\/mo><mn>2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=32+8+4+2<\/annotation><\/semantics><\/math><br> <math data-latex=\"=46\"><semantics><mrow><mo>=<\/mo><mn>46<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=46<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>vastaus: 46<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Lukuj\u00e4rjestelm\u00e4t Teht\u00e4v\u00e4t on jaoteltu v\u00e4rin mukaan helppoihin, perus ja vaikeisiin teht\u00e4viin. Teht\u00e4v\u00e4 1. Vastaa kirjallisesti seuraaviin kysymyksiin. Teht\u00e4v\u00e4 2. Valitse oikea muutos, kun muutetaan 10-j\u00e4rjestelm\u00e4n luvut bin\u00e4\u00e4riin eli 2-j\u00e4rjestelm\u00e4\u00e4n ja vastaukset ovat 5-bittisi\u00e4 eli 5-numeroisia. Teht\u00e4v\u00e4 3. Kirjoita jakolaskua vastaava<\/p>\n","protected":false},"author":3745,"featured_media":0,"parent":4,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-99","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/pages\/99","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/users\/3745"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/comments?post=99"}],"version-history":[{"count":37,"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/pages\/99\/revisions"}],"predecessor-version":[{"id":2840,"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/pages\/99\/revisions\/2840"}],"up":[{"embeddable":true,"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/pages\/4"}],"wp:attachment":[{"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/media?parent=99"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}