// Numbas version: finer_feedback_settings
{"name": "Binary to Decimal", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "b1", "b2", "b3", "b4", "b5", "b6", "b7", "b8"], "name": "Binary to Decimal", "tags": ["rebelmaths"], "preamble": {"css": "", "js": ""}, "advice": "<p>The position of each digit indicates a power&nbsp;of 2. Beginning with the power of zero in the rightmost position and increasing by 1 every time you move one digit to the left. A zero in a given position means that that particular power of 2&nbsp;should <strong>not</strong> be included. A one in a given position means that that particular power of 2&nbsp;<strong>should</strong> be included.</p>\n<p>Once each power of 2 that should be included has been noted, add them all together.</p>\n<p></p>\n<p>For example, to convert the binary number 1010 to decimal, we start with the rightmost digit, 0.</p>\n<p>The rightmost digit represents 2 to the power of 0 (i.e., 1). Since the rightmost digit is a 0, we do <strong>not</strong> include this power of 2. <strong>So 1 is not included.</strong></p>\n<p>Next, we move to the 2nd digit from the right, 1. This digit represents 2 to the power of 1 (i.e., 2). Since this digit is a 1, we <strong>do</strong> include this power of 2. <strong>So 2 is included.</strong></p>\n<p>Next, we move to the 3rd digit from the right, 0. This digit represents 2 to the power of 2 (i.e., 4). Since this digit is a 0, we do not include this power of 2. <strong>So 4 is not included.</strong></p>\n<p>Finally, we move to the 4th digit from the right, 1. This digit represents 2 to the power of 3 (i.e., 8). Since this digit is a 1, we do include this power of 2. <strong>So 8 is included.</strong></p>\n<p>Now, since we have gone through all digits in our binary number, we add up all of the powers of 2 that&nbsp;we&nbsp;have identified to be&nbsp;included:</p>\n<p>2+8=10.</p>", "rulesets": {}, "parts": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{b8}*1+{b7}*2+{b6}*4+{b5}*8+{b4}*16+{b3}*32+{b2}*64+{b1}*128", "minValue": "{b8}*1+{b7}*2+{b6}*4+{b5}*8+{b4}*16+{b3}*32+{b2}*64+{b1}*128", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "2", "type": "numberentry", "showPrecisionHint": false}], "extensions": [], "statement": "<p>Convert the number $\\var{b1}\\var{b2}\\var{b3}\\var{b4}\\var{b5}\\var{b6}\\var{b7}\\var{b8}$ to decimal.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(1..10000#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a", "description": ""}, "b4": {"definition": "random(0..1#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "b4", "description": ""}, "b5": {"definition": "random(0..1#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "b5", "description": ""}, "b6": {"definition": "random(0..1#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "b6", "description": ""}, "b7": {"definition": "random(0..1#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "b7", "description": ""}, "b1": {"definition": "random(0..1#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "b1", "description": ""}, "b2": {"definition": "random(0..1#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "b2", "description": ""}, "b3": {"definition": "random(0..1#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "b3", "description": ""}, "b8": {"definition": "random(0..1#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "b8", "description": ""}}, "metadata": {"description": "<p>rebelmaths</p>\n<p>Converting a number from binary to decimal.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}]}]}], "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}]}