{"id":375,"date":"2024-05-19T18:24:58","date_gmt":"2024-05-19T16:24:58","guid":{"rendered":"https:\/\/ctwiki.cartrust.ch\/?p=375"},"modified":"2024-05-23T17:26:28","modified_gmt":"2024-05-23T15:26:28","slug":"erklaerung-des-rechenwegs","status":"publish","type":"post","link":"https:\/\/ctwiki.cartrust.ch\/index.php\/2024\/05\/19\/erklaerung-des-rechenwegs\/","title":{"rendered":"4\/5 Erkl\u00e4rung des Rechenwegs"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"375\" class=\"elementor elementor-375\">\n\t\t\t\t<div class=\"elementor-element elementor-element-c84c84c e-flex e-con-boxed e-con e-parent\" data-id=\"c84c84c\" data-element_type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-6019d15 elementor-view-default elementor-position-top elementor-mobile-position-top elementor-widget elementor-widget-icon-box\" data-id=\"6019d15\" data-element_type=\"widget\" data-widget_type=\"icon-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<link rel=\"stylesheet\" href=\"https:\/\/ctwiki.cartrust.ch\/wp-content\/plugins\/elementor\/assets\/css\/widget-icon-box.min.css\">\t\t<div class=\"elementor-icon-box-wrapper\">\n\n\t\t\t\t\t\t<div class=\"elementor-icon-box-icon\">\n\t\t\t\t<span  class=\"elementor-icon elementor-animation-\">\n\t\t\t\t<svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-clipboard-list\" viewBox=\"0 0 384 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M336 64h-80c0-35.3-28.7-64-64-64s-64 28.7-64 64H48C21.5 64 0 85.5 0 112v352c0 26.5 21.5 48 48 48h288c26.5 0 48-21.5 48-48V112c0-26.5-21.5-48-48-48zM96 424c-13.3 0-24-10.7-24-24s10.7-24 24-24 24 10.7 24 24-10.7 24-24 24zm0-96c-13.3 0-24-10.7-24-24s10.7-24 24-24 24 10.7 24 24-10.7 24-24 24zm0-96c-13.3 0-24-10.7-24-24s10.7-24 24-24 24 10.7 24 24-10.7 24-24 24zm96-192c13.3 0 24 10.7 24 24s-10.7 24-24 24-24-10.7-24-24 10.7-24 24-24zm128 368c0 4.4-3.6 8-8 8H168c-4.4 0-8-3.6-8-8v-16c0-4.4 3.6-8 8-8h144c4.4 0 8 3.6 8 8v16zm0-96c0 4.4-3.6 8-8 8H168c-4.4 0-8-3.6-8-8v-16c0-4.4 3.6-8 8-8h144c4.4 0 8 3.6 8 8v16zm0-96c0 4.4-3.6 8-8 8H168c-4.4 0-8-3.6-8-8v-16c0-4.4 3.6-8 8-8h144c4.4 0 8 3.6 8 8v16z\"><\/path><\/svg>\t\t\t\t<\/span>\n\t\t\t<\/div>\n\t\t\t\n\t\t\t\t\t\t<div class=\"elementor-icon-box-content\">\n\n\t\t\t\t\t\t\t\t\t<h3 class=\"elementor-icon-box-title\">\n\t\t\t\t\t\t<span  >\n\t\t\t\t\t\t\tFunktions\u00fcbersicht\t\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/h3>\n\t\t\t\t\n\t\t\t\t\n\t\t\t<\/div>\n\t\t\t\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-393dce8 elementor-widget elementor-widget-text-editor\" data-id=\"393dce8\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.21.0 - 08-05-2024 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<p>Als weitere Hilfestellung zeigt der Calculator bei jeder Berechnung den <b>Rechenweg<\/b> an.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8e49972 elementor-widget elementor-widget-heading\" data-id=\"8e49972\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.21.0 - 08-05-2024 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h2 class=\"elementor-heading-title elementor-size-default\">Addition<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ef2b96e elementor-widget elementor-widget-text-editor\" data-id=\"ef2b96e\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Die <b>Addition<\/b> ist die einfachste der verf\u00fcgbaren Rechenoperationen. Die beiden Operanden werden im <b>Bin\u00e4rformat<\/b> \u00fcbernommen und <b>addiert<\/b>. Das Feld &#8220;<b>Calculation<\/b> <b>steps<\/b>&#8221; bleibt leer, da nur der \u00dcbertrag (<b>Carry<\/b>) neben den beiden Operanden f\u00fcr die Berechnung ben\u00f6tigt wird.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6f224cf elementor-widget elementor-widget-image\" data-id=\"6f224cf\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.21.0 - 08-05-2024 *\/\n.elementor-widget-image{text-align:center}.elementor-widget-image a{display:inline-block}.elementor-widget-image a img[src$=\".svg\"]{width:48px}.elementor-widget-image img{vertical-align:middle;display:inline-block}<\/style>\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"766\" height=\"183\" src=\"https:\/\/ctwiki.cartrust.ch\/wp-content\/uploads\/2024\/05\/calculator_addition.png\" class=\"attachment-large size-large wp-image-378\" alt=\"\" srcset=\"https:\/\/ctwiki.cartrust.ch\/wp-content\/uploads\/2024\/05\/calculator_addition.png 766w, https:\/\/ctwiki.cartrust.ch\/wp-content\/uploads\/2024\/05\/calculator_addition-300x72.png 300w\" sizes=\"(max-width: 766px) 100vw, 766px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Platzhalterbild einer Addition<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ad8960e elementor-widget elementor-widget-heading\" data-id=\"ad8960e\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Subtraktion<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1ac8463 elementor-widget elementor-widget-text-editor\" data-id=\"1ac8463\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Bei der <b>Subtraktion<\/b> wird zun\u00e4chst der zweite Operand <b>invertiert<\/b>. Dann werden beide Operanden <b>addiert<\/b> und zum Schluss wird <b>1<\/b> <b>addiert<\/b> (<a href=\"https:\/\/www.elektronik-kompendium.de\/sites\/dig\/1807251.htm\">Zweierkomplement<\/a>). Der Rechenweg zeigt somit zuerst den ersten Operanden, dann den invertierten zweiten Operanden und die zu addierende&nbsp;<b>1<\/b>.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-12a7420 elementor-widget elementor-widget-image\" data-id=\"12a7420\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"768\" height=\"205\" src=\"https:\/\/ctwiki.cartrust.ch\/wp-content\/uploads\/2024\/05\/calculator_substraction.png\" class=\"attachment-large size-large wp-image-379\" alt=\"\" srcset=\"https:\/\/ctwiki.cartrust.ch\/wp-content\/uploads\/2024\/05\/calculator_substraction.png 768w, https:\/\/ctwiki.cartrust.ch\/wp-content\/uploads\/2024\/05\/calculator_substraction-300x80.png 300w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Platzhalter f\u00fcr Subtraktion<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9e269f5 elementor-widget elementor-widget-heading\" data-id=\"9e269f5\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Multiplikation<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-172ede2 elementor-widget elementor-widget-text-editor\" data-id=\"172ede2\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Die Multiplikation ist etwas komplexer. Zun\u00e4chst wird der <a href=\"https:\/\/en.wikipedia.org\/\/wiki\/Binary_multiplier\">Multiplikationsalgorithmus<\/a> angewendet, bei dem jedes <b>Bit<\/b> des <b>zweiten<\/b> Operanden mit jedem <b>Bit<\/b> des <b>ersten<\/b> Operanden <b>multipliziert<\/b> wird. Die Ergebnisse dieser Teilschritte werden anschliessend <b>addiert<\/b>. Der Rechenweg zeigt daher die einzelnen <b>Summanden<\/b>, die entsprechend ihrer Position verschoben sind. Der <b>Carry-Wert <\/b>bleibt immer bei 0, da dieser hier nicht sinvoll darstellbar ist.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2bf9ffd elementor-widget elementor-widget-image\" data-id=\"2bf9ffd\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"768\" height=\"296\" src=\"https:\/\/ctwiki.cartrust.ch\/wp-content\/uploads\/2024\/05\/calculator_multiplication.png\" class=\"attachment-large size-large wp-image-380\" alt=\"\" srcset=\"https:\/\/ctwiki.cartrust.ch\/wp-content\/uploads\/2024\/05\/calculator_multiplication.png 768w, https:\/\/ctwiki.cartrust.ch\/wp-content\/uploads\/2024\/05\/calculator_multiplication-300x116.png 300w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Platzhalter f\u00fcr Multiplikation<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9a4bff0 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"9a4bff0\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.21.0 - 08-05-2024 *\/\n.elementor-widget-divider{--divider-border-style:none;--divider-border-width:1px;--divider-color:#0c0d0e;--divider-icon-size:20px;--divider-element-spacing:10px;--divider-pattern-height:24px;--divider-pattern-size:20px;--divider-pattern-url:none;--divider-pattern-repeat:repeat-x}.elementor-widget-divider .elementor-divider{display:flex}.elementor-widget-divider .elementor-divider__text{font-size:15px;line-height:1;max-width:95%}.elementor-widget-divider .elementor-divider__element{margin:0 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.elementor-divider__text{direction:rtl}.e-con-inner>.elementor-widget-divider,.e-con>.elementor-widget-divider{width:var(--container-widget-width,100%);--flex-grow:var(--container-widget-flex-grow)}<\/style>\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-507b545 elementor-widget elementor-widget-heading\" data-id=\"507b545\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">N\u00e4chster Schritt: Unterst\u00fctzung durch den Visualizer<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-62e141d7 e-con-full e-flex e-con e-parent\" data-id=\"62e141d7\" data-element_type=\"container\">\n\t\t<div class=\"elementor-element elementor-element-6595b5f8 e-con-full e-flex e-con e-child\" data-id=\"6595b5f8\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2ef6834b elementor-align-left elementor-widget elementor-widget-button\" data-id=\"2ef6834b\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/ctwiki.cartrust.ch\/index.php\/2024\/05\/14\/aufgabe-alu-size-verstehen\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">< Zur\u00fcck<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-24b5fb6a e-con-full e-flex e-con e-child\" data-id=\"24b5fb6a\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-6c4ebdc1 elementor-widget elementor-widget-progress\" data-id=\"6c4ebdc1\" data-element_type=\"widget\" data-widget_type=\"progress.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.21.0 - 08-05-2024 *\/\n.elementor-widget-progress{text-align:start}.elementor-progress-wrapper{position:relative;background-color:#eee;color:#fff;height:100%;border-radius:2px}.elementor-progress-bar{display:flex;background-color:#69727d;width:0;font-size:11px;height:30px;line-height:30px;border-radius:2px;transition:width 1s ease-in-out}.elementor-progress-text{flex-grow:1;white-space:nowrap;text-overflow:ellipsis;overflow:hidden;padding-inline-start:15px}.elementor-progress-percentage{padding-inline-end:15px}.elementor-widget-progress .elementor-progress-wrapper.progress-info .elementor-progress-bar{background-color:#5bc0de}.elementor-widget-progress .elementor-progress-wrapper.progress-success .elementor-progress-bar{background-color:#5cb85c}.elementor-widget-progress .elementor-progress-wrapper.progress-warning .elementor-progress-bar{background-color:#f0ad4e}.elementor-widget-progress .elementor-progress-wrapper.progress-danger .elementor-progress-bar{background-color:#d9534f}.elementor-progress .elementor-title{display:block}@media (max-width:767px){.elementor-progress-text{padding-inline-start:10px}}.e-con-inner .elementor-progress-wrapper,.e-con .elementor-progress-wrapper{height:auto}<\/style>\n\t\t<div class=\"elementor-progress-wrapper\" role=\"progressbar\" aria-valuemin=\"0\" aria-valuemax=\"100\" aria-valuenow=\"80\">\n\t\t\t<div class=\"elementor-progress-bar\" data-max=\"80\">\n\t\t\t\t<span class=\"elementor-progress-text\"><\/span>\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-progress-percentage\">80%<\/span>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-47464a70 e-con-full e-flex e-con e-child\" data-id=\"47464a70\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-77311d6d elementor-widget elementor-widget-button\" data-id=\"77311d6d\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/ctwiki.cartrust.ch\/index.php\/2024\/05\/19\/unterstuetzung-durch-den-visualizer\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Weiter &gt;<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-cb66542 e-flex e-con-boxed e-con e-parent\" data-id=\"cb66542\" 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Addition Die Addition ist die einfachste der verf\u00fcgbaren Rechenoperationen. Die beiden Operanden werden im Bin\u00e4rformat \u00fcbernommen und addiert. Das Feld &#8220;Calculation steps&#8221; bleibt leer, da nur der \u00dcbertrag (Carry) neben den beiden Operanden f\u00fcr die Berechnung ben\u00f6tigt wird. Platzhalterbild einer Addition Subtraktion [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"_links":{"self":[{"href":"https:\/\/ctwiki.cartrust.ch\/index.php\/wp-json\/wp\/v2\/posts\/375"}],"collection":[{"href":"https:\/\/ctwiki.cartrust.ch\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ctwiki.cartrust.ch\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ctwiki.cartrust.ch\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ctwiki.cartrust.ch\/index.php\/wp-json\/wp\/v2\/comments?post=375"}],"version-history":[{"count":30,"href":"https:\/\/ctwiki.cartrust.ch\/index.php\/wp-json\/wp\/v2\/posts\/375\/revisions"}],"predecessor-version":[{"id":855,"href":"https:\/\/ctwiki.cartrust.ch\/index.php\/wp-json\/wp\/v2\/posts\/375\/revisions\/855"}],"wp:attachment":[{"href":"https:\/\/ctwiki.cartrust.ch\/index.php\/wp-json\/wp\/v2\/media?parent=375"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ctwiki.cartrust.ch\/index.php\/wp-json\/wp\/v2\/categories?post=375"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ctwiki.cartrust.ch\/index.php\/wp-json\/wp\/v2\/tags?post=375"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}