{"id":630,"date":"2020-11-13T17:06:00","date_gmt":"2020-11-13T13:06:00","guid":{"rendered":"https:\/\/iremi.univ-reunion.fr\/?p=630"},"modified":"2025-07-25T12:48:46","modified_gmt":"2025-07-25T08:48:46","slug":"machines-a-registres","status":"publish","type":"post","link":"https:\/\/iremi.univ-reunion.fr\/?p=630","title":{"rendered":"Machines \u00e0 registres"},"content":{"rendered":"\n<p>Le langage <a href=\"https:\/\/iremi.univ-reunion.fr\/?p=687\" data-type=\"post\" data-id=\"687\">Fractran<\/a> est en fait obtenu en appliquant la num\u00e9rotation de G\u00f6del \u00e0 un autre mod\u00e8le, o\u00f9 des nombres entiers sont m\u00e9moris\u00e9s dans des registres :<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/registres1.pdf\" type=\"application\/pdf\" style=\"width:100%;height:450px\" aria-label=\"Contenu embarqu\u00e9 registres1.\"><\/object><a id=\"wp-block-file--media-b4aac8ef-234c-4351-8bd2-1441e4beee52\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/registres1.pdf\">registres1<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/registres1.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-b4aac8ef-234c-4351-8bd2-1441e4beee52\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<p>Lors de la f\u00eate de la semaine des maths 2019 (th\u00e8me : jouons ensemble aux math\u00e9matiques), une animation sur ce mod\u00e8le a \u00e9t\u00e9 propos\u00e9e, o\u00f9 les registres \u00e9taient mat\u00e9rialis\u00e9s par des bo\u00eetes, et les entiers par le nombre de  graines pr\u00e9sentes dans les bo\u00eetes. <\/p>\n\n\n\n<p>Voici des fiches d&rsquo;exercices cr\u00e9\u00e9es \u00e0 cette occasion, le recto donnant l&rsquo;\u00e9nonc\u00e9 et le verso donnant le corrig\u00e9 :<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/fichesregistres.pdf\" type=\"application\/pdf\" style=\"width:100%;height:930px\" aria-label=\"Contenu embarqu\u00e9 fichesregistres.\"><\/object><a id=\"wp-block-file--media-a7eed56d-a7d2-4d6e-8eac-71e0eb01840b\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/fichesregistres.pdf\">fichesregistres<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/fichesregistres.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-a7eed56d-a7d2-4d6e-8eac-71e0eb01840b\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<p>Pour la f\u00eate de la science 2019, les plateaux de <a href=\"https:\/\/iremi.univ-reunion.fr\/?p=689\" data-type=\"post\" data-id=\"689\">Sowing<\/a> ont \u00e9t\u00e9 instrumentalis\u00e9s (chaque case repr\u00e9sentant une case m\u00e9moire, le registre \u00e9tant l&rsquo;alignement des cases). Dans un premier temps, on a consid\u00e9r\u00e9 un cas particulier, o\u00f9 chaque case ne peut contenir au maximum qu&rsquo;une graine :<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">La machine de Post<\/h2>\n\n\n\n<p>Dans la description donn\u00e9e par Emil Post de sa machine (qui pr\u00e9figure celle de Turing), un ouvrier coche (ou efface un coche, ou regarde si la bo\u00eete est coch\u00e9e) sur des bo\u00eetes. L&rsquo;id\u00e9e de l&rsquo;activit\u00e9 sur les machines de Post est de remplacer un coche <em>sur<\/em> la bo\u00eete, par un marqueur <em>dans<\/em> la case. Il s&rsquo;agit d&rsquo;un objet suffisamment petit pour entrer dans la case, et suffisamment gros pour qu&rsquo;on ne puisse pas en placer un autre dans la m\u00eame case. Les programmes \u00e0 tester sur cette machine ont \u00e9t\u00e9 donn\u00e9s sous forme de graphes de flot de contr\u00f4le :<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/controlflow.pdf\" type=\"application\/pdf\" style=\"width:100%;height:340px\" aria-label=\"Contenu embarqu\u00e9 controlflow.\"><\/object><a id=\"wp-block-file--media-4b5171dd-7dae-4188-9325-807e0a410915\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/controlflow.pdf\">controlflow<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/controlflow.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-4b5171dd-7dae-4188-9325-807e0a410915\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<p>Les deux derniers exemples montrent le fonctionnement d&rsquo;un jeu de solitaire monodimensionnel. Voici un exemple de saut vers la droite :<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"349\" height=\"129\" src=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/animsolitaire1.gif\" alt=\"\" class=\"wp-image-751\" \/><\/figure>\n\n\n\n<p>et un exemple de saut vers la gauche :<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"342\" height=\"131\" src=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/animsolitaire2.gif\" alt=\"\" class=\"wp-image-752\" \/><\/figure>\n\n\n\n<p>Des machines de Post interactives sont pr\u00e9sentes dans le bloc <em>de Post \u00e0 Wang<\/em> de <a href=\"http:\/\/revue.sesamath.net\/spip.php?article681\">cet article<\/a>.<\/p>\n\n\n\n<p>Mais les enfants n&rsquo;\u00e9tant pas tr\u00e8s \u00e0 l&rsquo;aise avec le binaire (ils ont d\u00e9j\u00e0 du mal avec la num\u00e9ration d\u00e9cimale), il a \u00e9t\u00e9 d\u00e9cid\u00e9 de revenir aux machines \u00e0 registre, en utilisant des graines plus petites.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Manipulation de machines \u00e0 registres<\/h2>\n\n\n\n<p>Pour la f\u00eate de la science de 2021 (pour cause de Covid), le mat\u00e9riel de Sowing a \u00e9t\u00e9 utilis\u00e9 (plateau type moiti\u00e9 de bac \u00e0 gla\u00e7ons, graines de soja noir) avec des graphes de flots de contr\u00f4le.<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/manuel_bf-1.pdf\" type=\"application\/pdf\" style=\"width:100%;height:940px\" aria-label=\"Contenu embarqu\u00e9 manuel_bf.\"><\/object><a id=\"wp-block-file--media-45b140df-2895-4647-8f51-72057ffa6d73\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/manuel_bf-1.pdf\">manuel_bf<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/manuel_bf-1.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-45b140df-2895-4647-8f51-72057ffa6d73\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<p>L\u00e0 encore, les programmes ont \u00e9t\u00e9 donn\u00e9s sous forme de graphes de flot de contr\u00f4le (dans l&rsquo;ordre, addition, soustraction, multiplication, division euclidienne, pgcd) :<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/flotcontroleregistres.pdf\" type=\"application\/pdf\" style=\"width:100%;height:690px\" aria-label=\"Contenu embarqu\u00e9 flotcontroleregistres.\"><\/object><a id=\"wp-block-file--media-9c7c2bd7-bdc1-4973-a257-164e9ae41266\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/flotcontroleregistres.pdf\">flotcontroleregistres<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/flotcontroleregistres.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-9c7c2bd7-bdc1-4973-a257-164e9ae41266\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Les registres en cycle 2<\/h2>\n\n\n\n<p>Comme la num\u00e9ration d\u00e9cimale n&rsquo;est pas n\u00e9cessaire pour faire des calculs avec une machine \u00e0 registres, on peut l&rsquo;exp\u00e9rimenter d\u00e8s le CP. Ce qui a \u00e9t\u00e9 fait en 2022,  \u00e0 l&rsquo;\u00e9cole Aristide Briand du Tampon. Une fiche d&rsquo;exercices a \u00e9t\u00e9 pr\u00e9par\u00e9e pour ces activit\u00e9s :<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/booklet-2.pdf\" type=\"application\/pdf\" style=\"width:100%;height:350px\" aria-label=\"Contenu embarqu\u00e9 booklet.\"><\/object><a id=\"wp-block-file--media-6f38a2d5-a24e-413e-b4f1-412d03757984\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/booklet-2.pdf\">booklet<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/booklet-2.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-6f38a2d5-a24e-413e-b4f1-412d03757984\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<p>ainsi qu&rsquo;un diaporama destin\u00e9 \u00e0 \u00eatre projet\u00e9 en classe avant les exercices :<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/Presentation_registres.pdf\" type=\"application\/pdf\" style=\"width:100%;height:430px\" aria-label=\"Contenu embarqu\u00e9 Presentation_registres.\"><\/object><a id=\"wp-block-file--media-e61b09a5-3dae-42a1-bf11-eb5cca91965b\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/Presentation_registres.pdf\">Presentation_registres<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/Presentation_registres.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-e61b09a5-3dae-42a1-bf11-eb5cca91965b\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<p>(le pion qui se d\u00e9place sur le graphe de flot de contr\u00f4le a \u00e9t\u00e9 baptis\u00e9 Monsieur Post, donc les \u00e9l\u00e8ves ont appel\u00e9 machine de Post ce qui est en r\u00e9alit\u00e9 une machine \u00e0 registres)<\/p>\n\n\n\n<p>Un index en plastique a \u00e9t\u00e9 fourni afin de lib\u00e9rer les mains des \u00e9l\u00e8ves (il fallait d\u00e9placer Monsieur Post sur le graphe, l&rsquo;index devant le registre et semer ou r\u00e9colter des graines) :<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"480\" height=\"349\" src=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/p4.gif\" alt=\"\" class=\"wp-image-767\" \/><\/figure>\n\n\n\n<p>Pour ajouter une graine au registre, on la transf\u00e8re depuis la r\u00e9serve de graines jusqu&rsquo;au registre (le doigt indique o\u00f9 on s\u00e8me la graine). Pour d\u00e9cr\u00e9menter un registre non vide, il fallait enlever la graine point\u00e9e par l&rsquo;index, et la placer dans la r\u00e9serve de graines. Le r\u00e9servoir est juste une grosse bo\u00eete :<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"720\" height=\"481\" src=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/p10a.jpg\" alt=\"\" class=\"wp-image-768\" srcset=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/p10a.jpg 720w, https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/p10a-300x200.jpg 300w\" sizes=\"auto, (max-width: 720px) 100vw, 720px\" \/><\/figure>\n\n\n\n<p>Voici les compte-rendus des exp\u00e9rimentation men\u00e9es en CP et CE 1 (il y en a eu aussi en CM 1) :<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/visites.pdf\" type=\"application\/pdf\" style=\"width:100%;height:260px\" aria-label=\"Contenu embarqu\u00e9 visites.\"><\/object><a id=\"wp-block-file--media-e217968d-b1df-4d66-9321-93f6cf991b52\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/visites.pdf\">visites<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2020\/11\/visites.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-e217968d-b1df-4d66-9321-93f6cf991b52\">T\u00e9l\u00e9charger<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Le langage Fractran est en fait obtenu en appliquant la num\u00e9rotation de G\u00f6del \u00e0 un autre mod\u00e8le, o\u00f9 des nombres entiers sont m\u00e9moris\u00e9s dans des registres : Lors de la f\u00eate de la semaine des maths 2019 (th\u00e8me : jouons ensemble aux math\u00e9matiques), une animation sur ce mod\u00e8le a \u00e9t\u00e9 propos\u00e9e, o\u00f9 les registres \u00e9taient [&hellip;]<\/p>\n","protected":false},"author":6,"featured_media":770,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[10],"tags":[29],"coauthors":[54],"class_list":["post-630","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-machines-information-codage","tag-cycle-2"],"_links":{"self":[{"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/posts\/630","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=630"}],"version-history":[{"count":12,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/posts\/630\/revisions"}],"predecessor-version":[{"id":1269,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/posts\/630\/revisions\/1269"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/media\/770"}],"wp:attachment":[{"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=630"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=630"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=630"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcoauthors&post=630"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}