// Numbas version: finer_feedback_settings
{"name": "Addition in anderen Stellenwertsystemen", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Addition in anderen Stellenwertsystemen", "tags": [], "metadata": {"description": "<p>Aufgabe zum schriftlichen Addieren in b-adischen Systemen</p>", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "statement": "<p>Wir wollen die Summe der Zahlen $\\left(\\var{z14},\\var{z13},\\var{z12},\\var{z11}\\right)_\\var{base}$ und&nbsp;$\\left(\\var{z24},\\var{z23},\\var{z22},\\var{z21}\\right)_\\var{base}$ ermitteln.</p>", "advice": "<p>a)</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\Big($</td>\n<td style=\"text-align: right;\">{z14}</td>\n<td style=\"text-align: right;\">,</td>\n<td style=\"text-align: right;\">{z13}</td>\n<td style=\"text-align: right;\">,</td>\n<td style=\"text-align: right;\">{z12}</td>\n<td style=\"text-align: right;\">,</td>\n<td style=\"text-align: right;\">{z11}$\\Big)_\\var{base}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$+\\Big($</td>\n<td style=\"text-align: right;\">{z24 }</td>\n<td style=\"text-align: right;\">,</td>\n<td style=\"text-align: right;\">{z23}</td>\n<td style=\"text-align: right;\">,</td>\n<td style=\"text-align: right;\">{z22}</td>\n<td style=\"text-align: right;\">,</td>\n<td style=\"text-align: right;\">{z21}$\\Big)_\\var{base}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: right;\">{u3}</td>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: right;\">{u2}</td>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: right;\">{u1}</td>\n<td style=\"text-align: right;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\Big($</td>\n<td style=\"text-align: right;\">{e4}</td>\n<td style=\"text-align: right;\">,</td>\n<td style=\"text-align: right;\">{e3}</td>\n<td style=\"text-align: right;\">,</td>\n<td style=\"text-align: right;\">{e2}</td>\n<td style=\"text-align: right;\">,</td>\n<td style=\"text-align: right;\">{e1}$\\Big)_\\var{base}$</td>\n</tr>\n</tbody>\n</table>\n<p>b)</p>\n<p>$\\left(\\var{z14},\\var{z13},\\var{z12},\\var{z11}\\right)_\\var{base}=\\var{z14}\\cdot\\var{base}^3+\\var{z13}\\cdot\\var{base}^2+\\var{z12}\\cdot\\var{base}^1+\\var{z11}\\cdot\\var{base}^0=\\var{a}$</p>\n<p>$\\left(\\var{z24},\\var{z23},\\var{z22},\\var{z21}\\right)_\\var{base}=\\var{z24}\\cdot\\var{base}^3+\\var{z23}\\cdot\\var{base}^2+\\var{z22}\\cdot\\var{base}^1+\\var{z21}\\cdot\\var{base}^0=\\var{b}$</p>\n<p>$\\var{a}+\\var{b}=\\var{sum}=\\var{e4}\\cdot\\var{base}^3+\\var{e3}\\cdot\\var{base}^2+\\var{e2}\\cdot\\var{base}^1+\\var{e1}\\cdot\\var{base}^0$</p>", "rulesets": {}, "extensions": [], "variables": {"base": {"name": "base", "group": "Ungrouped variables", "definition": "random(11..18)", "description": "", "templateType": "anything"}, "choice": {"name": "choice", "group": "Ungrouped variables", "definition": "deal(base)", "description": "", "templateType": "anything"}, "z11": {"name": "z11", "group": "Ungrouped variables", "definition": "choice[0]", "description": "", "templateType": "anything"}, "z12": {"name": "z12", "group": "Ungrouped variables", "definition": "choice[1]", "description": "", "templateType": "anything"}, "z13": {"name": "z13", "group": "Ungrouped variables", "definition": "choice[2]", "description": "", "templateType": "anything"}, "z14": {"name": "z14", "group": "Ungrouped variables", "definition": "1", "description": "", "templateType": "anything"}, "z21": {"name": "z21", "group": "Ungrouped variables", "definition": "base-z11", "description": "", "templateType": "anything"}, "z22": {"name": "z22", "group": "Ungrouped variables", "definition": "base-1-z12", "description": "", "templateType": "anything"}, "z23": {"name": "z23", "group": "Ungrouped variables", "definition": "z13", "description": "", "templateType": "anything"}, "z24": {"name": "z24", "group": "Ungrouped variables", "definition": "base-3", "description": "", "templateType": "anything"}, "e1": {"name": "e1", "group": "Ungrouped variables", "definition": "mod(z11+z21,base)", "description": "", "templateType": "anything"}, "u1": {"name": "u1", "group": "Ungrouped variables", "definition": "floor((z11+z21)/base)", "description": "", "templateType": "anything"}, "e2": {"name": "e2", "group": "Ungrouped variables", "definition": "mod(z12+z22+u1,base)", "description": "", "templateType": "anything"}, "u2": {"name": "u2", "group": "Ungrouped variables", "definition": "floor((z12+z22+u1)/base)", "description": "", "templateType": "anything"}, "e3": {"name": "e3", "group": "Ungrouped variables", "definition": "mod(z13+z23+u2,base)", "description": "", "templateType": "anything"}, "u3": {"name": "u3", "group": "Ungrouped variables", "definition": "floor((z13+z23+u2)/base)", "description": "", "templateType": "anything"}, "e4": {"name": "e4", "group": "Ungrouped variables", "definition": "z14+z24+u3", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "z14*base^3+z13*base^2+z12*base+z11", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "z24*base^3+z23*base^2+z22*base+z21", "description": "", "templateType": "anything"}, "sum": {"name": "sum", "group": "Ungrouped variables", "definition": "a+b", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["base", "choice", "z11", "z12", "z13", "z14", "z21", "z22", "z23", "z24", "e1", "u1", "e2", "u2", "e3", "u3", "e4", "a", "b", "sum"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": "table {\n  border-collapse: collapse;\n}\ntable {\n  border-collapse: collapse;\n}\ntr:last-child { \n  border-top: solid;\n  border-width: 1px 0;\n}\n"}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Ermitteln Sie die Summe schriftliche ohne vorherige Umwandlung in das Dezimalsystem!</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\Big($</td>\n<td style=\"text-align: right;\">{z14}</td>\n<td style=\"text-align: center;\">,</td>\n<td style=\"text-align: right;\">{z13}</td>\n<td style=\"text-align: center;\">,</td>\n<td>{z12}</td>\n<td style=\"text-align: center;\">,</td>\n<td style=\"text-align: right;\">{z11}$\\Big)_\\var{base}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$+\\Big($</td>\n<td style=\"text-align: right;\">{z24}</td>\n<td style=\"text-align: center;\">,</td>\n<td style=\"text-align: right;\">{z23}</td>\n<td style=\"text-align: center;\">,</td>\n<td style=\"text-align: right;\">{z22}</td>\n<td style=\"text-align: center;\">,</td>\n<td style=\"text-align: right;\">{z21}$\\Big)_\\var{base}$</td>\n</tr>\n<tr>\n<td></td>\n<td></td>\n<td style=\"text-align: right;\">[[4]]</td>\n<td></td>\n<td style=\"text-align: right;\">[[5]]</td>\n<td></td>\n<td style=\"text-align: right;\">[[6]]</td>\n<td></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\Big($</td>\n<td style=\"padding-left: 30px;\">[[0]]</td>\n<td style=\"text-align: center;\">,</td>\n<td style=\"text-align: right;\">[[1]]</td>\n<td style=\"text-align: center;\">,</td>\n<td>[[2]]</td>\n<td style=\"text-align: center;\">,</td>\n<td style=\"text-align: right;\">[[3]]$\\Big)_\\var{base}$</td>\n</tr>\n</tbody>\n</table>\n<p><em>Hinweis: Tragen Sie f&uuml;hr fehlende &Uuml;bertr&auml;ge bitte eine $0$ ein!</em></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "e4", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "e4", "maxValue": "e4", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": true, "customName": "e3", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "e3", "maxValue": "e3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": true, "customName": "e2", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "e2", "maxValue": "e2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": true, "customName": "e1", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "e1", "maxValue": "e1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": true, "customName": "u3", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "u3", "maxValue": "u3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": true, "customName": "u2", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "u2", "maxValue": "u2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": true, "customName": "u1", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "u1", "maxValue": "u1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain-eu"], "correctAnswerStyle": "plain-eu"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Wandeln Sie die beiden Zahlen und deren Summe&nbsp;in das Dezimalsystem um!</p>\n<p>$\\left(\\var{z14},\\var{z13},\\var{z12},\\var{z11}\\right)_\\var{base}=$[[0]]</p>\n<p>$\\left(\\var{z24},\\var{z23},\\var{z22},\\var{z21}\\right)_\\var{base}=$[[1]]</p>\n<p>$\\left(\\var{z14},\\var{z13},\\var{z12},\\var{z11}\\right)_\\var{base}+\\left(\\var{z24},\\var{z23},\\var{z22},\\var{z21}\\right)_\\var{base}=$[[2]]&nbsp;</p>\n<p>&nbsp;</p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "a", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "a", "maxValue": "a", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["eu", "plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": true, "customName": "b", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "b", "maxValue": "b", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["eu", "plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": true, "customName": "sum", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "sum", "maxValue": "sum", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["eu", "plain-eu"], "correctAnswerStyle": "plain-eu"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}], "resources": []}]}], "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}]}