// Numbas version: finer_feedback_settings
{"timing": {"allowPause": false, "timedwarning": {"action": "warn", "message": "<p>Only 5 minutes left!</p>"}, "timeout": {"action": "none", "message": "<p>Timeo</p>"}}, "showstudentname": true, "name": "Fei's copy of EEE2013 Digital Electronics Assignment 2018", "showQuestionGroupNames": false, "feedback": {"showtotalmark": true, "feedbackmessages": [], "showanswerstate": false, "advicethreshold": 0, "allowrevealanswer": false, "intro": "", "showactualmark": false, "enterreviewmodeimmediately": true, "showexpectedanswerswhen": "inreview", "showpartfeedbackmessageswhen": "oncompletion", "showactualmarkwhen": "oncompletion", "showtotalmarkwhen": "always", "showanswerstatewhen": "oncompletion", "showadvicewhen": "never"}, "question_groups": [{"pickQuestions": 1, "name": "Group", "pickingStrategy": "all-ordered", "questions": [{"name": "Graeme's copy of CLA adder", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Graeme Chester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/189/"}], "variables": {"c1": {"description": "", "definition": "carry(0,p,g)[1]", "name": "c1", "templateType": "anything", "group": "Ungrouped variables"}, "nb": {"description": "", "definition": "bin2dec(b)", "name": "nb", "templateType": "anything", "group": "Ungrouped variables"}, "s": {"description": "", "definition": "map(mod(x+y,2),[x,y],zip(p,[cin]+c[0..abs(c)-1]))", "name": "s", "templateType": "anything", "group": "Ungrouped variables"}, "pp": {"description": "", "definition": "carry(1,p,repeat(0,abs(p)))[abs(p)-1]", "name": "pp", "templateType": "anything", "group": "Ungrouped variables"}, "ns": {"description": "", "definition": "bin2dec(s+[c[abs(c)-1]])", "name": "ns", "templateType": "anything", "group": "Ungrouped variables"}, "a": {"description": "", "definition": "[1]+repeat(random(0..1),3)", "name": "a", "templateType": "anything", "group": "Ungrouped variables"}, "c": {"description": "", "definition": "carry(0,p,g)\n", "name": "c", "templateType": "anything", "group": "Ungrouped variables"}, "c2ci": {"description": "", "definition": "carry(1,p,g)[2]", "name": "c2ci", "templateType": "anything", "group": "Ungrouped variables"}, "debug": {"description": "", "definition": "false", "name": "debug", "templateType": "anything", "group": "Ungrouped variables"}, "gp": {"description": "", "definition": "carry(0,p,g)[abs(p)-1]", "name": "gp", "templateType": "anything", "group": "Ungrouped variables"}, "p": {"description": "", "definition": "map(mod(x+y,2),[x,y],zip(a,b))\n", "name": "p", "templateType": "anything", "group": "Ungrouped variables"}, "na": {"description": "", "definition": "bin2dec(a)", "name": "na", "templateType": "anything", "group": "Ungrouped variables"}, "b": {"description": "", "definition": "repeat(random(0..1),4)", "name": "b", "templateType": "anything", "group": "Ungrouped variables"}, "g": {"description": "", "definition": "map(x*y,[x,y],zip(a,b))\n", "name": "g", "templateType": "anything", "group": "Ungrouped variables"}, "ss": {"description": "", "definition": "bin2str(s)", "name": "ss", "templateType": "anything", "group": "Ungrouped variables"}, "cin": {"description": "", "definition": "0", "name": "cin", "templateType": "number", "group": "Ungrouped variables"}}, "advice": "", "parts": [{"scripts": {}, "integerAnswer": true, "marks": 1, "maxValue": "c1", "correctAnswerFraction": false, "minValue": "c1", "showPrecisionHint": false, "integerPartialCredit": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "prompt": "<p>Calculate&nbsp;the value of $C_1$ if $C_{IN}=0$</p>", "allowFractions": false, "type": "numberentry", "showCorrectAnswer": true}, {"scripts": {}, "integerAnswer": true, "marks": 1, "maxValue": "c2ci", "correctAnswerFraction": false, "minValue": "c2ci", "showPrecisionHint": false, "integerPartialCredit": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "prompt": "<p>Calculate&nbsp;the value of $C_2$ if $C_{IN}=1$</p>", "allowFractions": false, "type": "numberentry", "showCorrectAnswer": true}, {"scripts": {}, "marks": 1, "maxValue": "bin2dec(s+[c[3]])", "correctAnswerFraction": false, "minValue": "bin2dec(s+[c[3]])", "showPrecisionHint": false, "showCorrectAnswer": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "prompt": "<p>The carry input $C_{IN}$ is {cin}. Find the sum of A and B as an unsigned decimal number&nbsp;</p>", "allowFractions": false, "type": "numberentry"}, {"scripts": {}, "showCorrectAnswer": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "marks": 0, "gaps": [{"scripts": {}, "integerAnswer": true, "marks": 1, "maxValue": "pp", "correctAnswerFraction": false, "minValue": "pp", "showPrecisionHint": false, "integerPartialCredit": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true}, {"scripts": {}, "integerAnswer": true, "marks": 1, "maxValue": "gp", "correctAnswerFraction": false, "minValue": "gp", "showPrecisionHint": false, "integerPartialCredit": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true}], "type": "gapfill", "prompt": "<p>This adder is now to be used in a block carry look-ahead scheme. Find&nbsp;the values of the signals</p>\n<p>block propagate $P'_{3\\dots0}$[[0]] and</p>\n<p>block generate $G'_{3\\dots0}$[[1]]&nbsp;</p>"}], "variable_groups": [], "showQuestionGroupNames": false, "type": "question", "functions": {"bin2dec": {"language": "jme", "definition": "if(abs(bin)=0,\n  0,\n  bin[0]+2*bin2dec(bin[1..abs(bin)])\n)", "parameters": [["bin", "list"]], "type": "number"}, "bin2str": {"language": "jme", "definition": "join(map(if(x=0,'0','1'),x,reverse(bin)),'')", "parameters": [["bin", "list"]], "type": "string"}, "carry": {"language": "jme", "definition": "if(abs(p)=0 or abs(g)=0,\n  [],\n  [if(p[0]*cin+g[0]>0.5,1,0)]+carry(if(p[0]*cin+g[0]>0.5,1,0),p[1..abs(p)],g[1..abs(g)])\n)", "parameters": [["cin", "number"], ["p", "list"], ["g", "list"]], "type": "number"}}, "statement": "<p>A binary carry look-ahead adder produces&nbsp;propagate and generate signals internally when adding two 4-bit numbers A and B together. The values for a particular addition are shown in the following table:-</p>\n<p>{table([['&lt;i&gt;P&lt;sub&gt;k']+reverse(p),['&lt;i&gt;G&lt;sub&gt;k']+reverse(g)],['&lt;i&gt;k',3,2,1,0])}</p>\n<p>These are used inside the adder to calculate the carry outputs for each bit&nbsp;$C_{k}$.</p>\n<p><span data-jme-visible=\"debug\">a {bin2str(a)} {bin2dec(a)}&nbsp;</span></p>\n<p><span data-jme-visible=\"debug\">b {bin2str(b)}&nbsp;{bin2dec(b)}</span></p>\n<p><span data-jme-visible=\"debug\">p {bin2str(p)}&nbsp;</span></p>\n<p><span data-jme-visible=\"debug\">g {bin2str(g)}&nbsp;</span></p>\n<p><span data-jme-visible=\"debug\">c {bin2str(c)}&nbsp;</span></p>\n<p><span data-jme-visible=\"debug\">s&nbsp;{bin2str(s)}&nbsp;cout {bin2str([c[3]])} {bin2dec(s+[c[3]])}</span></p>\n<p></p>", "tags": [], "metadata": {"description": "", "notes": "", "licence": "All rights reserved"}, "ungrouped_variables": ["a", "b", "p", "g", "c1", "c2ci", "pp", "gp", "c", "s", "cin", "ns", "na", "nb", "ss", "debug"], "question_groups": [{"questions": [], "pickingStrategy": "all-ordered", "pickQuestions": 0, "name": ""}], "preamble": {"css": "", "js": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}}, {"name": "Filling a Karnaugh Map", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Graeme Chester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/189/"}, {"name": "Fei Xia", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2603/"}], "advice": "", "statement": "<p>A Boolean function of 4 variables is given as&nbsp;</p>\n<p>$f=${join(cubetotext(c1,labels),'.')+'+'+join(cubetotext(c2,labels),'.')+'+'+join(cubetotext(c3,labels),'.')}</p>\n<p>{usermap()}</p>", "rulesets": {}, "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "parts": [{"markPerCell": false, "unitTests": [], "numColumns": "4", "prompt": "<p>Complete the Karnaugh map for $f$ by inserting 0 or 1 in each element of the following matrix.</p>", "numRows": "4", "scripts": {}, "type": "matrix", "correctAnswer": "kmap", "variableReplacementStrategy": "originalfirst", "tolerance": 0, "showFeedbackIcon": true, "marks": "3", "showCorrectAnswer": true, "variableReplacements": [], "allowResize": false, "correctAnswerFractions": false, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "allowFractions": false}], "variable_groups": [], "functions": {"usermap": {"language": "javascript", "definition": "// draw a 4x4 Karnaugh map for a function given as a truth table\nfunction drawKmap(ctx,bits,literals)\n{\n\nctx.font = \"20px Arial\";ctx.textAlign=\"center\"; ctx.textBaseline=\"middle\";\n  ctx.lineWidth=2;\n\n//ctx.fillText(n,10,50);\nctx.beginPath();\nctx.moveTo(20,20);\nctx.lineTo(60,60);\nctx.stroke();\n\nctx.fillText(literals[0]+\" \"+literals[1],15,50);\nctx.fillText(literals[2]+\" \"+literals[3],50,10);\ngraycodebin=[\"00\",\"01\",\"11\",\"10\"];\nfor (ncol=0;ncol<=3;ncol++) {\n\tctx.fillText(graycodebin[ncol],80+ncol*40,40);\n\t}\n\nfor (nrow=0;nrow<=3;nrow++) {\n\tctx.fillText(graycodebin[nrow],40,80+nrow*40);\n\tfor (ncol=0;ncol<=3;ncol++) {\n\t\tctx.rect(60+ncol*40,60+nrow*40,40,40);\n\t\tctx.stroke();\n\t\tbitval=bits[nrow][ncol].toString();\n\t\tctx.fillText(bitval,80+ncol*40,80+nrow*40);\n\t\t}\n\t}\n\n}\n\nvar canv=document.createElement(\"canvas\");\ncanv.setAttribute(\"height\",\"250px\");\ncanv.setAttribute(\"width\",\"500px\");\nvar ctx = canv.getContext(\"2d\");\n\nquestion.signals.on('HTMLAttached',function(e) {\n  \n  // Create a Knockout.js observable\n  ko.computed(function(){\n  // Get the student's input string from part 0.\n  var studentString = question.parts[0].display.studentAnswer();\n    ctx.clearRect(0, 0, canv.width, canv.height);\n    drawKmap(ctx,studentString,['a','b','c','d'])\n  });\n});\n              \nreturn canv;", "parameters": [], "type": "html"}, "cubetotext": {"language": "jme", "definition": "// convert a cube to a formatted text string using recursion \n// fixed for bounding box problem 24-04-18\nif(abs(cube)=0,\n  [],\n  switch(cube[0]=0,\n      [\"$\\\\bbox[2pt]{\\\\bar{\"+labels[0]+\"}}$\"],\n    cube[0]=1,\n      [\"$\"+labels[0]+\"$\"],[]) + cubetotext(cube[1..abs(cube)],labels[1..abs(labels)]\n  )\n)\n", "parameters": [["cube", "list"], ["labels", "list"]], "type": "string"}, "f": {"language": "jme", "definition": "// convert a cube to canonical set form using recursion\nif(abs(p)=1, //terminate on the last or only element of p\n    if(p[abs(p)-1]=2, //a \"don't care\" so include both 1 and 0\n    set(0,1),\n    if(p[abs(p)-1]=1,\n      set(1),\n      set(0)\n    )\n  ),\n//else\n    if(p[abs(p)-1]=2,\n      set(map(x*2,x,f(p[0..abs(p)-1]))) or set(map(x*2+1,x,f(p[0..abs(p)-1]))),\n    if(p[abs(p)-1]=1,\n      set(map(x*2+1,x,f(p[0..abs(p)-1]))),\n      set(map(x*2,x,f(p[0..abs(p)-1])))\n      )\n  )\n)", "parameters": [["p", "list"]], "type": "set"}, "mat2cube": {"language": "jme", "definition": "if(abs(list(m))=0,\n  [],\n  [m[0]*2]+mat2cube(m[1..abs(list(m))])\n  )", "parameters": [["m", "matrix"]], "type": "list"}}, "ungrouped_variables": ["a", "b", "c", "d", "e", "m", "n", "kmap1", "canonicalsum", "c1", "c2", "c3", "labels", "kmap"], "preamble": {"js": "", "css": ""}, "variablesTest": {"condition": "abs(list(f(c1)-f(c2)))>0 and\nabs(list(f(c2)-f(c3)))>0 and\nabs(list(f(c3)-f(c1)))>0\n", "maxRuns": 100}, "variables": {"n": {"description": "<p>mat2cube(m)</p>", "templateType": "anything", "definition": "0\n", "group": "Ungrouped variables", "name": "n"}, "d": {"description": "", "templateType": "anything", "definition": "false", "group": "Ungrouped variables", "name": "d"}, "canonicalsum": {"description": "", "templateType": "anything", "definition": "union(union(f(c1),f(c2)),f(c3))", "group": "Ungrouped variables", "name": "canonicalsum"}, "kmap": {"description": "<p>Convert a 4-variable Boolean function from canonical (minterm) set to Karnaugh map matrix</p>", "templateType": "anything", "definition": "map(if(x in canonicalsum,1,0),x,matrix(repeat([0,1,3,2],4))+4*transpose(matrix(repeat([0,1,3,2],4))))", "group": "Ungrouped variables", "name": "kmap"}, "b": {"description": "", "templateType": "anything", "definition": "false", "group": "Ungrouped variables", "name": "b"}, "labels": {"description": "", "templateType": "list of strings", "definition": "[ safe(\"a\"), safe(\"b\"), safe(\"c\"), safe(\"d\") ]", "group": "Ungrouped variables", "name": "labels"}, "a": {"description": "", "templateType": "anything", "definition": "false", "group": "Ungrouped variables", "name": "a"}, "m": {"description": "", "templateType": "anything", "definition": "matrix([1,2],[3,4],[5,6])", "group": "Ungrouped variables", "name": "m"}, "c1": {"description": "", "templateType": "anything", "definition": "shuffle([random(0..1),random(0..1),2,2])", "group": "Ungrouped variables", "name": "c1"}, "c3": {"description": "", "templateType": "anything", "definition": "shuffle([random(0..1),random(0..1),random(0..2),2])", "group": "Ungrouped variables", "name": "c3"}, "kmap1": {"description": "<p>Convert a 4-variable Boolean function from canonical (minterm) set to Karnaugh map matrix</p>\n<p>map(if((4*r+c) in canonicalsum,1,0),[r,c],product([0,1,3,2],[0,1,3,2]))</p>", "templateType": "anything", "definition": "map(if((4*r+c) in canonicalsum,1,0),[r,c],product([0,1,3,2],[0,1,3,2]))", "group": "Ungrouped variables", "name": "kmap1"}, "c2": {"description": "", "templateType": "anything", "definition": "shuffle([random(0..1),random(0..1),random(0..2),2])", "group": "Ungrouped variables", "name": "c2"}, "c": {"description": "", "templateType": "anything", "definition": "false", "group": "Ungrouped variables", "name": "c"}, "e": {"description": "", "templateType": "anything", "definition": "123", "group": "Ungrouped variables", "name": "e"}}, "type": "question"}, {"name": "Karnaugh map 2 2017", "extensions": ["booleanlogic"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Graeme Chester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/189/"}], "variables": {"dkmap": {"templateType": "anything", "group": "Unused variables", "description": "<p>Convert a 4-variable Boolean function from canonical (minterm) set to Karnaugh map matrix</p>", "definition": "map(if(x in canonicalsum,1,0),x,matrix(repeat([0,1,3,2],4))+4*transpose(matrix(repeat([0,1,3,2],4))))", "name": "dkmap"}, "dkmap1": {"templateType": "anything", "group": "Unused variables", "description": "<p>Convert a 4-variable Boolean function from canonical (minterm) set to Karnaugh map matrix</p>\n<p>map(if((4*r+c) in canonicalsum,1,0),[r,c],product([0,1,3,2],[0,1,3,2]))</p>", "definition": "map(if((4*r+c) in canonicalsum,1,0),[r,c],product([0,1,3,2],[0,1,3,2]))", "name": "dkmap1"}, "test": {"templateType": "anything", "group": "Unused variables", "description": "", "definition": "cubedist(c1,c3)", "name": "test"}, "canonicalsum": {"templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "union(union(union(f(c1),f(c2)),f(c3)),f(c4))", "name": "canonicalsum"}, "displayc": {"templateType": "anything", "group": "Unused variables", "description": "", "definition": "matrix(c1,c2,c3)", "name": "displayc"}, "labels": {"templateType": "list of strings", "group": "Ungrouped variables", "description": "", "definition": "[ \"a\", \"b\", \"c\", \"d\" ]", "name": "labels"}, "c1": {"templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "shuffle([random(0..1),random(0..1),random(0..2),2])", "name": "c1"}, "truthtablesum": {"templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "map(if(x in canonicalsum,1,0),x,0..15)", "name": "truthtablesum"}, "c3": {"templateType": "anything", "group": "Ungrouped variables", "description": "<p>shuffle([random(0..1),random(0..1),random(0..2),2])</p>", "definition": "shuffle([random(0..1),random(0..1),random(0..2),2])", "name": "c3"}, "c2": {"templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "shuffle([random(0..1),random(0..1),random(0..2),2])", "name": "c2"}, "c4": {"templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "shuffle([random(0..1),random(0..1),random(0..1),random(0..1)])", "name": "c4"}}, "variablesTest": {"condition": "abs(list(f(c1)-union(union(f(c2),f(c3)),f(c4))))>0 and  //no redundant or duplicate terms\nabs(list(f(c2)-union(union(f(c1),f(c3)),f(c4))))>0 and \nabs(list(f(c3)-union(union(f(c2),f(c1)),f(c4))))>0 and \nabs(list(f(c4)-union(union(f(c2),f(c3)),f(c1))))>0 and \ncubedist(c3,c2)>1 and cubedist(c3,c1)>1 and cubedist(c2,c1)>1\nand cubedist(c4,c1)>1 and cubedist(c2,c4)>1 and cubedist(c4,c3)>1", "maxRuns": 100}, "variable_groups": [{"variables": ["dkmap", "dkmap1", "test", "displayc"], "name": "Unused variables"}, {"variables": [], "name": "test"}], "tags": [], "metadata": {"licence": "All rights reserved", "description": "<p>Development copy to test adding extra terms</p>"}, "advice": "<p>The function is equivalent to {join([join(cubetotext(c1,labels),'.'),join(cubetotext(c2,labels),'.'),join(cubetotext(c3,labels),'.'),join(cubetotext(c4,labels),'.')],'+')}</p>", "ungrouped_variables": ["canonicalsum", "c1", "c2", "c3", "c4", "labels", "truthtablesum"], "preamble": {"css": "", "js": ""}, "rulesets": {}, "functions": {"mat2cube": {"language": "jme", "definition": "if(abs(list(m))=0,\n  [],\n  [m[0]*2]+mat2cube(m[1..abs(list(m))])\n  )", "type": "list", "parameters": [["m", "matrix"]]}, "test": {"language": "jme", "definition": "args[0] or args[1]", "type": "number", "parameters": [["args", "list"]]}, "cubetotext": {"language": "jme", "definition": "// convert a cube to a formatted text string using recursion \n// fixed for bounding box problem 24-04-18\nif(abs(cube)=0,\n  [],\n  switch(cube[0]=0,\n      [\"$\\\\bbox[2pt]{\\\\bar{\"+labels[0]+\"}}$\"],\n    cube[0]=1,\n      [\"$\"+labels[0]+\"$\"],[]) + cubetotext(cube[1..abs(cube)],labels[1..abs(labels)]\n  )\n)\n", "type": "string", "parameters": [["cube", "list"], ["labels", "list"]]}, "cubedist": {"language": "jme", "definition": "// find distance between two cubes using recursion\nif(abs(cube1)=0||abs(cube2)=0,\n  0,\n  if(cube1[0]=cube2[0],\n      cubedist(cube1[1..abs(cube1)], cube2[1..abs(cube2)]),\n      cubedist(cube1[1..abs(cube1)], cube2[1..abs(cube2)])+1\n  )\n)\n", "type": "number", "parameters": [["cube1", "list"], ["cube2", "list"]]}, "makeanswer": {"language": "jme", "definition": "((c1[0]=1) and a or (c1[0]=0) and not a or (c1[0]=2)) and \n((c1[1]=1) and b or (c1[1]=0) and not b or (c1[1]=2)) and  \n((c1[2]=1) and c or (c1[2]=0) and not c or (c1[2]=2)) and  \n((c1[3]=1) and d or (c1[3]=0) and not d or (c1[3]=2)) or \n\n((c2[0]=1) and a or (c2[0]=0) and not a or (c2[0]=2)) and \n((c2[1]=1) and b or (c2[1]=0) and not b or (c2[1]=2)) and  \n((c2[2]=1) and c or (c2[2]=0) and not c or (c2[2]=2)) and  \n((c2[3]=1) and d or (c2[3]=0) and not d or (c2[3]=2)) or \n\n((c3[0]=1) and a or (c3[0]=0) and not a or (c3[0]=2)) and \n((c3[1]=1) and b or (c3[1]=0) and not b or (c3[1]=2)) and  \n((c3[2]=1) and c or (c3[2]=0) and not c or (c3[2]=2)) and  \n((c3[3]=1) and d or (c3[3]=0) and not d or (c3[3]=2))", "type": "boolean", "parameters": [["c1", "list"], ["c2", "list"], ["c3", "list"], ["a", "boolean"], ["b", "boolean"], ["c", "boolean"], ["d", "boolean"]]}, "f": {"language": "jme", "definition": "// convert a cube to canonical set form using recursion\nif(abs(p)=1, //terminate on the last or only element of p\n    if(p[abs(p)-1]=2, //a \"don't care\" so include both 1 and 0\n    set(0,1),\n    if(p[abs(p)-1]=1,\n      set(1),\n      set(0)\n    )\n  ),\n//else\n    if(p[abs(p)-1]=2,\n      set(map(x*2,x,f(p[0..abs(p)-1]))) or set(map(x*2+1,x,f(p[0..abs(p)-1]))),\n    if(p[abs(p)-1]=1,\n      set(map(x*2+1,x,f(p[0..abs(p)-1]))),\n      set(map(x*2,x,f(p[0..abs(p)-1])))\n      )\n  )\n)", "type": "set", "parameters": [["p", "list"]]}, "evalpterm": {"language": "jme", "definition": "((c1[0]=1) and a or (c1[0]=0) and not a or (c1[0]=2)) and \n((c1[1]=1) and b or (c1[1]=0) and not b or (c1[1]=2)) and  \n((c1[2]=1) and c or (c1[2]=0) and not c or (c1[2]=2)) and  \n((c1[3]=1) and d or (c1[3]=0) and not d or (c1[3]=2))", "type": "boolean", "parameters": [["c1", "list"], ["a", "boolean"], ["b", "boolean"], ["c", "boolean"], ["d", "boolean"]]}, "drawKmapcanvas": {"language": "javascript", "definition": "// draw a 4x4 Karnaugh map for a function given as a truth table\nfunction drawKmap(ctx,bits,literals)\n{\n\nctx.font = \"20px Arial\";ctx.textAlign=\"center\"; ctx.textBaseline=\"middle\";\n  ctx.lineWidth=2;\n\n//ctx.fillText(n,10,50);\nctx.beginPath();\nctx.moveTo(20,20);\nctx.lineTo(60,60);\nctx.stroke();\n\nctx.fillText(literals[0]+\" \"+literals[1],15,50);\nctx.fillText(literals[2]+\" \"+literals[3],50,10);\ngraycode=[0,1,3,2];\ngraycodebin=[\"00\",\"01\",\"11\",\"10\"];\nfor (ncol=0;ncol<=3;ncol++) {\n\tctx.fillText(graycodebin[ncol],80+ncol*40,40);\n\t}\n\nfor (nrow=0;nrow<=3;nrow++) {\n\tctx.fillText(graycodebin[nrow],40,80+nrow*40);\n\tfor (ncol=0;ncol<=3;ncol++) {\n\t\tctx.rect(60+ncol*40,60+nrow*40,40,40);\n\t\tctx.stroke();\n\t\tbitval=bits[graycode[nrow]*4+graycode[ncol]].toString();\n\t\tctx.fillText(bitval,80+ncol*40,80+nrow*40);\n\t\t}\n\t}\n\n}\n\n         function drawcanvas(ctx)\n         {\nvar num = 15;\nvar n = num.toString();\nctx.font = \"20px Arial\";ctx.textAlign=\"center\"; ctx.textBaseline=\"middle\";\n\nctx.fillText(n,10,50);\n\n\nfor (nrow=0;nrow<=3;nrow++) {\n\tctx.fillText(\"00\",40,80+nrow*40);\n\tfor (ncol=0;ncol<=3;ncol++) {\n\t\tctx.rect(60+ncol*40,60+nrow*40,40,40);\n\t\tctx.stroke();\n\t\tbitval=bits[nrow*4+ncol].toString();\n\t\tctx.fillText(bitval,80+ncol*40,80+nrow*40);\n\t\t}\n\t}\n\nctx.rect(0,0,400,300);\nctx.stroke();\n           \n           \n\t}\n\n\nvar canv=document.createElement(\"canvas\");\ncanv.setAttribute(\"height\",\"250px\");\ncanv.setAttribute(\"width\",\"500px\");\nvar ctx = canv.getContext(\"2d\");\n\n//literals=[\"a\",\"b\",\"c\",\"d\"];\ndrawKmap(ctx,bits,literals);\n//drawcanvas(ctx)\nreturn canv;", "type": "html", "parameters": [["bits", "list"], ["literals", "list"]]}, "usermap": {"language": "javascript", "definition": "// draw a 4x4 Karnaugh map for a function given as a truth table\nfunction drawKmap(ctx,bits,literals)\n{\n\nctx.font = \"20px Arial\";ctx.textAlign=\"center\"; ctx.textBaseline=\"middle\";\n  ctx.lineWidth=2;\n\n//ctx.fillText(n,10,50);\nctx.beginPath();\nctx.moveTo(20,20);\nctx.lineTo(60,60);\nctx.stroke();\n\nctx.fillText(literals[0]+\" \"+literals[1],15,50);\nctx.fillText(literals[2]+\" \"+literals[3],50,10);\ngraycodebin=[\"00\",\"01\",\"11\",\"10\"];\nfor (ncol=0;ncol<=3;ncol++) {\n\tctx.fillText(graycodebin[ncol],80+ncol*40,40);\n\t}\n\nfor (nrow=0;nrow<=3;nrow++) {\n\tctx.fillText(graycodebin[nrow],40,80+nrow*40);\n\tfor (ncol=0;ncol<=3;ncol++) {\n\t\tctx.rect(60+ncol*40,60+nrow*40,40,40);\n\t\tctx.stroke();\n\t\tbitval=bits[nrow][ncol].toString();\n\t\tctx.fillText(bitval,80+ncol*40,80+nrow*40);\n\t\t}\n\t}\n\n}\n\nvar canv=document.createElement(\"canvas\");\ncanv.setAttribute(\"height\",\"250px\");\ncanv.setAttribute(\"width\",\"500px\");\nvar ctx = canv.getContext(\"2d\");\n\nquestion.signals.on('HTMLAttached',function(e) {\n  \n  // Create a Knockout.js observable\n  ko.computed(function(){\n  // Get the student's input string from part 0.\n  var studentString = question.parts[0].display.studentAnswer();\n    ctx.clearRect(0, 0, canv.width, canv.height);\n    drawKmap(ctx,studentString,['a','b','c','d'])\n  });\n});\n              \nreturn canv;", "type": "html", "parameters": []}}, "statement": "<p>A Boolean function is described by the following Karnaugh map:-</p>\n<p>{drawKmapcanvas(truthtablesum,labels)}</p>\n<p></p>", "parts": [{"prompt": "<p>Enter a Boolean expression for the function&nbsp;shown on the above Karnaugh map, <strong>without</strong> the use of brackets.</p>\n<p>Enter Boolean operators using the&nbsp;words \"and\", \"or\" and \"not\" (without the quotation marks, and remembering to use spaces to separate them). They will be displayed&nbsp;in mathematical notation.</p>\n<p>For example, to enter \"$a.\\bar{b}+c$\" then type \"a and not b or c\", this will display as \"$a \\land \\lnot b \\lor c$\"</p>", "showCorrectAnswer": false, "answer": "evalpterm({c1},a,b,c,d) or evalpterm({c2},a,b,c,d) or evalpterm({c3},a,b,c,d) or evalpterm({c4},a,b,c,d)", "type": "jme", "notallowed": {"strings": ["(", ")"], "showStrings": true, "message": "<p>Brackets may not be used</p>", "partialCredit": 0}, "variableReplacements": [], "vsetrangepoints": 5, "checkingtype": "absdiff", "showFeedbackIcon": false, "scripts": {"validate": {"script": "// Use the jme validation code but with variable types changed to Boolean\ndebugger;\nvar validation = this.validation;\n\t\tif(this.studentAnswer.length===0)\n\t\t{\n\t\t\tthis.giveWarning(R('part.marking.not submitted'));\n\t\t\treturn false;\n\t\t}\n\t\ttry{\n\t\t\tvar scope = new jme.Scope(this.question.scope);\n\t\t\tvar tree = jme.compile(this.studentAnswer,scope);\n\t\t\tvar varnames = jme.findvars(tree);\n\t\t\tfor(i=0;i<varnames.length;i++) {\n\t\t\t\tscope.variables[varnames[i]]=new jme.types.TBool(false); // changed from TNum\n\t\t\t}\n\t\t\tjme.evaluate(tree,scope);\n\t\t}\n\t\tcatch(e)\n\t\t{\n\t\t\tthis.giveWarning(R('part.jme.answer invalid',e.message));\n\t\t\treturn false;\n\t\t}\n\t\tif( validation.failExpectedVariableNames ) {\n\t\t\tvar suggestedNames = validation.unexpectedVariableName.split(jme.re.re_short_name);\n\t\t\tif(suggestedNames.length>3) {\n\t\t\t\tvar suggestion = [];\n\t\t\t\tfor(var i=1;i<suggestedNames.length;i+=2) {\n\t\t\t\t\tsuggestion.push(suggestedNames[i]);\n\t\t\t\t}\n\t\t\t\tsuggestion = suggestion.join('*');\n\t\t\t\tthis.giveWarning(R('part.jme.unexpected variable name suggestion',validation.unexpectedVariableName,suggestion));\n\t\t\t}\n\t\t\telse\n\t\t\t\tthis.giveWarning(R('part.jme.unexpected variable name', validation.unexpectedVariableName));\n\t\t}\n\t\tif( validation.failMinLength)\n\t\t{\n\t\t\tthis.giveWarning(this.settings.minLengthMessage);\n\t\t}\n\t\tif( validation.failMaxLength )\n\t\t{\n\t\t\tthis.giveWarning(this.settings.maxLengthMessage);\n\t\t}\n\t\tif( validation.failMustHave )\n\t\t{\n\t\t\tthis.giveWarning(this.settings.mustHaveMessage);\n\t\t\tif(this.settings.mustHaveShowStrings)\n\t\t\t{\n\t\t\t\tvar strings = this.settings.mustHave.map(function(x){return R('part.jme.must-have bits',x)});\n\t\t\t\tvar message = this.settings.mustHave.length==1 ? R('part.jme.must-have one',strings) : R('part.jme.must-have several',strings)\n\t\t\t\tthis.giveWarning(message);\n\t\t\t}\n\t\t}\n\t\tif( validation.failNotAllowed )\n\t\t{\n\t\t\tthis.giveWarning(this.settings.notAllowedMessage);\n\t\t\tif(this.settings.notAllowedShowStrings)\n\t\t\t{\n\t\t\t\tvar strings = this.settings.notAllowed.map(function(x){return R('part.jme.not-allowed bits',x)});\n\t\t\t\tvar message = this.settings.notAllowed.length==1 ? R('part.jme.not-allowed one',strings) : R('part.jme.not-allowed several',strings)\n\t\t\t\tthis.giveWarning(message);\n\t\t\t}\n\t\t}\n\t\treturn true;\n", "order": "instead"}, "mark": {"script": "function boolResultsEqual(r1,r2,checkingFunction,checkingAccuracy)\n{\t// first checks both expressions are of same type, then uses given checking type to compare results\n\tvar v1 = r1.value, v2 = r2.value;\n\tif(r1.type != r2.type)\n\t{\n\t\treturn false;\n\t}\n\tswitch(r1.type)\n\t{\n\tcase 'boolean':\n\t\treturn checkingFunction( v1, v2, checkingAccuracy );\n\t\tbreak;\n\tcase 'vector':\n\t\tif(v1.length != v2.length)\n\t\t\treturn false;\n\t\tfor(var i=0;i<v1.length;i++)\n\t\t{\n\t\t\tif(!boolResultsEqual(new TBool(v1[i]),new TBool(v2[i]),checkingFunction,checkingAccuracy))\n\t\t\t\treturn false;\n\t\t}\n\t\treturn true;\n\t\tbreak;\n\tcase 'matrix':\n\t\tif(v1.rows != v2.rows || v1.columns != v2.columns)\n\t\t\treturn false;\n\t\tfor(var i=0;i<v1.rows;i++)\n\t\t{\n\t\t\tfor(var j=0;j<v1.columns;j++)\n\t\t\t{\n\t\t\t\tif(!boolResultsEqual(new TBool(v1[i][j]||0),new TBool(v2[i][j]||0),checkingFunction,checkingAccuracy))\n\t\t\t\t\treturn false;\n\t\t\t}\n\t\t}\n\t\treturn true;\n\t\tbreak;\n\tcase 'list':\n\t\tif(v1.length != v2.length)\n\t\t\treturn false;\n\t\tfor(var i=0;i<v1.length;i++)\n\t\t{\n\t\t\tif(!boolResultsEqual(v1[i],v2[i],checkingFunction,checkingAccuracy))\n\t\t\t\treturn false;\n\t\t}\n\t\treturn true;\n\tdefault:\n\t\treturn util.eq(r1,r2);\n\t}\n};\n\nfunction varnamesAgree(array1, array2) {\n\tvar name;\n\tfor(var i=0; i<array1.length; i++) {\n\t\tif( (name=array1[i])[0]!='$' && !array2.contains(name) )\n\t\t\treturn false;\n\t}\n\t\n\treturn true;\n};\n\nfunction boolRandoms(varnames,min,max,times)\n{\n\ttimes *= varnames.length;\n\tvar rs = [];\n\tfor( var i=0; i<times; i++ )\n\t{\n\t\tvar r = {};\n\t\tfor( var j=0; j<varnames.length; j++ )\n\t\t{\n\t\t\tr[varnames[j]] = new Numbas.jme.types.TBool(Math.random()<0.5);\n\t\t}\n\t\trs.push(r);\n\t}\n\treturn rs;\n};\n\nfunction boolCounts(varnames)\n{\n    //enumerate all possible values\n//    debugger;\n\tvar times = Math.pow(2,varnames.length);\n\tvar cs = [];\n\tfor( var i=0; i<times; i++ )\n\t{\n        var cstring=i.toString(2);\n\t\tvar c = {};\n\t\tfor( var j=0; j<varnames.length; j++ )\n\t\t{\n\t\t\tc[varnames[j]] = new Numbas.jme.types.TBool(cstring[cstring.length-1-j]=='1');\n//          console.log(c[varnames[j]]);\n\t\t}\n\t\tcs.push(c);\n\t}\n\treturn cs;\n};\n\nfunction boolCompare(expr1,expr2,settings,scope) {\n//  debugger;\n\t\texpr1 += '';\n\t\texpr2 += '';\n\t\tvar compile = jme.compile, evaluate = jme.evaluate;\n//\t\tvar checkingFunction = checkingFunctions[settings.checkingType.toLowerCase()];\t//work out which checking type is being used\n  var checkingFunction = function(r1,r2,tolerance){return r1===r2} ;\t//Boolean comparison\n\t\ttry {\n\t\t\tvar tree1 = compile(expr1,scope);\n\t\t\tvar tree2 = compile(expr2,scope);\n\t\t\tif(tree1 == null || tree2 == null) \n\t\t\t{\t//one or both expressions are invalid, can't compare\n\t\t\t\treturn false; \n\t\t\t}\n\t\t\t//find variable names used in both expressions - can't compare if different\n\t\t\tvar vars1 = jme.findvars(tree1);\n\t\t\tvar vars2 = jme.findvars(tree2);\n\t\t\tfor(var v in scope.variables)\n\t\t\t{\n\t\t\t\tdelete vars1[v];\n\t\t\t\tdelete vars2[v];\n\t\t\t}\n//removed the following if statement since variable name lists need not match\t\t\t\n/*\t\t\tif( !varnamesAgree(vars1,vars2) ) \n\t\t\t{\t//whoops, differing variables\n\t\t\t\treturn false;\n\t\t\t}\n*/\nif(vars1.length) \n\t\t\t{\t// if variables are used,  evaluate both expressions over a random selection of values and compare results\n\t\t\t\tvar errors = 0;\n// original random routine for numbers is replaced with a Boolean version or full enumeration of all values\n//\t\t\t\tvar rs = randoms(vars1, settings.vsetRangeStart, settings.vsetRangeEnd, settings.vsetRangePoints);\n\n              //\t\t\t\tvar rs = boolRandoms(vars1, settings.vsetRangeStart, settings.vsetRangeEnd, settings.vsetRangePoints);\n\t\t\t\tvar rs = boolCounts(vars1.merge(vars2)); //enumerate over all vars to cope with redundant terms\n\t\t\t\tfor(var i = 0; i<rs.length; i++) {\n\t\t\t\t\tvar nscope = new jme.Scope([scope,{variables:rs[i]}]);\n\t\t\t\t\tutil.copyinto(scope.variables,rs[i]);\n\t\t\t\t\tvar r1 = evaluate(tree1,nscope);\n\t\t\t\t\tvar r2 = evaluate(tree2,nscope);\n\t\t\t\t\tif( !boolResultsEqual(r1,r2,checkingFunction,settings.checkingAccuracy) ) { errors++; }\n\t\t\t\t}\n\t\t\t\tif(errors < settings.failureRate) {\n\t\t\t\t\treturn true;\n\t\t\t\t}else{\n\t\t\t\t\treturn false;\n\t\t\t\t}\n\t\t\t} else {\n\t\t\t\t//if no variables used, can just evaluate both expressions once and compare\n\t\t\t\tr1 = evaluate(tree1,scope);\n\t\t\t\tr2 = evaluate(tree2,scope);\n\t\t\t\treturn boolResultsEqual(r1,r2,checkingFunction,settings.checkingAccuracy);\n\t\t\t}\n\t\t}\n\t\tcatch(e) {\n\t\t\treturn false;\n\t\t}\n\t};\n\ndebugger;\nvar validation = this.validation;\n\t\tif(this.answerList==undefined)\n\t\t{\n\t\t\tthis.setCredit(0,R('part.marking.nothing entered'));\n\t\t\treturn false;\n\t\t}\n\t\ttry\n\t\t{\n\t\t\tvar simplifiedAnswer = Numbas.jme.display.simplifyExpression(this.studentAnswer,'',this.question.scope);\n\t\t}\n\t\tcatch(e)\n\t\t{\n\t\t\tthis.setCredit(0,R('part.jme.answer invalid',e.message));\n\t\t\treturn;\n\t\t}\n\t\tif(this.settings.checkVariableNames) {\n\t\t\tvar tree = jme.compile(this.studentAnswer,this.question.scope);\n\t\t\tvar usedvars = jme.findvars(tree);\n\t\t\tvalidation.failExpectedVariableNames = false;\n\t\t\tfor(var i=0;i<usedvars.length;i++) {\n\t\t\t\tif(!this.settings.expectedVariableNames.contains(usedvars[i].toLowerCase())) {\n\t\t\t\t\tvalidation.failExpectedVariableNames = true;\n\t\t\t\t\tvalidation.unexpectedVariableName = usedvars[i];\n\t\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\t\tvalidation.failMinLength = (this.settings.minLength>0 && simplifiedAnswer.length<this.settings.minLength);\n\t\tvalidation.failMaxLength = (this.settings.maxLength>0 && simplifiedAnswer.length>this.settings.maxLength);\n\t\tvalidation.failNotAllowed = false;\n\t\tvalidation.failMustHave = false;\n\t\t//did student actually write anything?\n\t\tthis.answered = this.studentAnswer.length > 0;\n\t\t\n\t\t//do comparison of student's answer with correct answer\n//\t\tif(!jme.compare(this.studentAnswer, this.settings.correctAnswer, this.settings, this.markingScope))\n\t\tif(!boolCompare(this.studentAnswer, this.settings.correctAnswer, this.settings, this.markingScope))\n\t\t{\n\t\t\tthis.setCredit(0,R('part.marking.incorrect'));\n\t\t\treturn;\n\t\t}\n\t\tvar noSpaceAnswer = this.studentAnswer.replace(/\\s/g,'').toLowerCase();\n\t\t//see if student answer contains any forbidden strings\n\t\tfor( i=0; i<this.settings.notAllowed.length; i++ ) {\n\t\t\tif(noSpaceAnswer.contains(this.settings.notAllowed[i].toLowerCase())) { validation.failNotAllowed = true; }\n\t\t}\n\t\tif(!validation.failNotAllowed) {\n\t\t\t//see if student answer contains all the required strings\n\t\t\tfor( i=0; i<this.settings.mustHave.length; i++ ) {\n\t\t\t\tif(!noSpaceAnswer.contains(this.settings.mustHave[i].toLowerCase())) { validation.failMustHave = true; }\n\t\t\t}\n\t\t}\n\t\t//calculate how many marks will be given for a correct answer\n\t\t//(can be modified if answer wrong length or fails string restrictions)\n\t\tthis.setCredit(1,R('part.jme.marking.correct'));\n\t\tif(validation.failMinLength)\n\t\t{\n\t\t\tthis.multCredit(this.settings.minLengthPC,this.settings.minLengthMessage);\n\t\t}\n\t\tif(validation.failMaxLength)\n\t\t{\n\t\t\tthis.multCredit(this.settings.maxLengthPC,this.settings.maxLengthMessage);\n\t\t}\n\t\tif(validation.failMustHave)\n\t\t{\n\t\t\tif(this.settings.mustHaveShowStrings)\n\t\t\t{\n\t\t\t\tvar strings = this.settings.mustHave.map(function(x){return R('part.jme.must-have bits',x)});\n\t\t\t\tvar message = this.settings.mustHave.length==1 ? R('part.jme.must-have one',strings) : R('part.jme.must-have several',strings)\n\t\t\t\tthis.addCredit(0,message);\n\t\t\t}\n\t\t\tthis.multCredit(this.settings.mustHavePC,this.settings.mustHaveMessage);\n\t\t}\n\t\tif(validation.failNotAllowed)\n\t\t{\n\t\t\tif(this.settings.notAllowedShowStrings)\n\t\t\t{\n\t\t\t\tvar strings = this.settings.notAllowed.map(function(x){return R('part.jme.not-allowed bits',x)});\n\t\t\t\tvar message = this.settings.notAllowed.length==1 ? R('part.jme.not-allowed one',strings) : R('part.jme.not-allowed several',strings)\n\t\t\t\tthis.addCredit(0,message);\n\t\t\t}\n\t\t\tthis.multCredit(this.settings.notAllowedPC,this.settings.notAllowedMessage);\n\t\t}\n", "order": "instead"}}, "variableReplacementStrategy": "originalfirst", "showpreview": true, "checkingaccuracy": 0.001, "vsetrange": [0, "0"], "checkvariablenames": false, "expectedvariablenames": [], "answersimplification": "allboolean", "marks": "4"}], "type": "question"}, {"name": "Karnaugh map 3: common terms 2017", "extensions": ["booleanlogic"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Graeme Chester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/189/"}, {"name": "Fei Xia", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2603/"}], "variable_groups": [{"variables": ["dkmap", "dkmap1", "c4"], "name": "Unused variables"}], "parts": [{"vsetRange": [0, "0"], "marks": "4", "vsetRangePoints": 5, "type": "jme", "answerSimplification": "allboolean", "checkingType": "absdiff", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "checkingAccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": false, "answer": "evalpterm({c3},a,b,c,d) or evalpterm({c4},a,b,c,d)", "showFeedbackIcon": true, "scripts": {"mark": {"script": "function boolResultsEqual(r1,r2,checkingFunction,checkingAccuracy)\n{\t// first checks both expressions are of same type, then uses given checking type to compare results\n\tvar v1 = r1.value, v2 = r2.value;\n\tif(r1.type != r2.type)\n\t{\n\t\treturn false;\n\t}\n\tswitch(r1.type)\n\t{\n\tcase 'boolean':\n\t\treturn checkingFunction( v1, v2, checkingAccuracy );\n\t\tbreak;\n\tcase 'vector':\n\t\tif(v1.length != v2.length)\n\t\t\treturn false;\n\t\tfor(var i=0;i<v1.length;i++)\n\t\t{\n\t\t\tif(!boolResultsEqual(new TBool(v1[i]),new TBool(v2[i]),checkingFunction,checkingAccuracy))\n\t\t\t\treturn false;\n\t\t}\n\t\treturn true;\n\t\tbreak;\n\tcase 'matrix':\n\t\tif(v1.rows != v2.rows || v1.columns != v2.columns)\n\t\t\treturn false;\n\t\tfor(var i=0;i<v1.rows;i++)\n\t\t{\n\t\t\tfor(var j=0;j<v1.columns;j++)\n\t\t\t{\n\t\t\t\tif(!boolResultsEqual(new TBool(v1[i][j]||0),new TBool(v2[i][j]||0),checkingFunction,checkingAccuracy))\n\t\t\t\t\treturn false;\n\t\t\t}\n\t\t}\n\t\treturn true;\n\t\tbreak;\n\tcase 'list':\n\t\tif(v1.length != v2.length)\n\t\t\treturn false;\n\t\tfor(var i=0;i<v1.length;i++)\n\t\t{\n\t\t\tif(!boolResultsEqual(v1[i],v2[i],checkingFunction,checkingAccuracy))\n\t\t\t\treturn false;\n\t\t}\n\t\treturn true;\n\tdefault:\n\t\treturn util.eq(r1,r2);\n\t}\n};\n\nfunction varnamesAgree(array1, array2) {\n\tvar name;\n\tfor(var i=0; i<array1.length; i++) {\n\t\tif( (name=array1[i])[0]!='$' && !array2.contains(name) )\n\t\t\treturn false;\n\t}\n\t\n\treturn true;\n};\n\nfunction boolRandoms(varnames,min,max,times)\n{\n\ttimes *= varnames.length;\n\tvar rs = [];\n\tfor( var i=0; i<times; i++ )\n\t{\n\t\tvar r = {};\n\t\tfor( var j=0; j<varnames.length; j++ )\n\t\t{\n\t\t\tr[varnames[j]] = new Numbas.jme.types.TBool(Math.random()<0.5);\n\t\t}\n\t\trs.push(r);\n\t}\n\treturn rs;\n};\n\nfunction boolCounts(varnames)\n{\n    //enumerate all possible values\n//    debugger;\n\tvar times = Math.pow(2,varnames.length);\n\tvar cs = [];\n\tfor( var i=0; i<times; i++ )\n\t{\n        var cstring=i.toString(2);\n\t\tvar c = {};\n\t\tfor( var j=0; j<varnames.length; j++ )\n\t\t{\n\t\t\tc[varnames[j]] = new Numbas.jme.types.TBool(cstring[cstring.length-1-j]=='1');\n//          console.log(c[varnames[j]]);\n\t\t}\n\t\tcs.push(c);\n\t}\n\treturn cs;\n};\n\nfunction boolCompare(expr1,expr2,settings,scope) {\n//  debugger;\n\t\texpr1 += '';\n\t\texpr2 += '';\n\t\tvar compile = jme.compile, evaluate = jme.evaluate;\n//\t\tvar checkingFunction = checkingFunctions[settings.checkingType.toLowerCase()];\t//work out which checking type is being used\n  var checkingFunction = function(r1,r2,tolerance){return r1===r2} ;\t//Boolean comparison\n\t\ttry {\n\t\t\tvar tree1 = compile(expr1,scope);\n\t\t\tvar tree2 = compile(expr2,scope);\n\t\t\tif(tree1 == null || tree2 == null) \n\t\t\t{\t//one or both expressions are invalid, can't compare\n\t\t\t\treturn false; \n\t\t\t}\n\t\t\t//find variable names used in both expressions - can't compare if different\n\t\t\tvar vars1 = jme.findvars(tree1);\n\t\t\tvar vars2 = jme.findvars(tree2);\n\t\t\tfor(var v in scope.variables)\n\t\t\t{\n\t\t\t\tdelete vars1[v];\n\t\t\t\tdelete vars2[v];\n\t\t\t}\n//removed the following if statement since variable name lists need not match\t\t\t\n/*\t\t\tif( !varnamesAgree(vars1,vars2) ) \n\t\t\t{\t//whoops, differing variables\n\t\t\t\treturn false;\n\t\t\t}\n*/\nif(vars1.length) \n\t\t\t{\t// if variables are used,  evaluate both expressions over a random selection of values and compare results\n\t\t\t\tvar errors = 0;\n// original random routine for numbers is replaced with a Boolean version or full enumeration of all values\n//\t\t\t\tvar rs = randoms(vars1, settings.vsetRangeStart, settings.vsetRangeEnd, settings.vsetRangePoints);\n\n              //\t\t\t\tvar rs = boolRandoms(vars1, settings.vsetRangeStart, settings.vsetRangeEnd, settings.vsetRangePoints);\n\t\t\t\tvar rs = boolCounts(vars1.merge(vars2)); //enumerate over all vars to cope with redundant terms\n\t\t\t\tfor(var i = 0; i<rs.length; i++) {\n\t\t\t\t\tvar nscope = new jme.Scope([scope,{variables:rs[i]}]);\n\t\t\t\t\tutil.copyinto(scope.variables,rs[i]);\n\t\t\t\t\tvar r1 = evaluate(tree1,nscope);\n\t\t\t\t\tvar r2 = evaluate(tree2,nscope);\n\t\t\t\t\tif( !boolResultsEqual(r1,r2,checkingFunction,settings.checkingAccuracy) ) { errors++; }\n\t\t\t\t}\n\t\t\t\tif(errors < settings.failureRate) {\n\t\t\t\t\treturn true;\n\t\t\t\t}else{\n\t\t\t\t\treturn false;\n\t\t\t\t}\n\t\t\t} else {\n\t\t\t\t//if no variables used, can just evaluate both expressions once and compare\n\t\t\t\tr1 = evaluate(tree1,scope);\n\t\t\t\tr2 = evaluate(tree2,scope);\n\t\t\t\treturn boolResultsEqual(r1,r2,checkingFunction,settings.checkingAccuracy);\n\t\t\t}\n\t\t}\n\t\tcatch(e) {\n\t\t\treturn false;\n\t\t}\n\t};\n\ndebugger;\nvar validation = this.validation;\n\t\tif(this.answerList==undefined)\n\t\t{\n\t\t\tthis.setCredit(0,R('part.marking.nothing entered'));\n\t\t\treturn false;\n\t\t}\n\t\ttry\n\t\t{\n\t\t\tvar simplifiedAnswer = Numbas.jme.display.simplifyExpression(this.studentAnswer,'',this.question.scope);\n\t\t}\n\t\tcatch(e)\n\t\t{\n\t\t\tthis.setCredit(0,R('part.jme.answer invalid',e.message));\n\t\t\treturn;\n\t\t}\n\t\tif(this.settings.checkVariableNames) {\n\t\t\tvar tree = jme.compile(this.studentAnswer,this.question.scope);\n\t\t\tvar usedvars = jme.findvars(tree);\n\t\t\tvalidation.failExpectedVariableNames = false;\n\t\t\tfor(var i=0;i<usedvars.length;i++) {\n\t\t\t\tif(!this.settings.expectedVariableNames.contains(usedvars[i].toLowerCase())) {\n\t\t\t\t\tvalidation.failExpectedVariableNames = true;\n\t\t\t\t\tvalidation.unexpectedVariableName = usedvars[i];\n\t\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\t\tvalidation.failMinLength = (this.settings.minLength>0 && simplifiedAnswer.length<this.settings.minLength);\n\t\tvalidation.failMaxLength = (this.settings.maxLength>0 && simplifiedAnswer.length>this.settings.maxLength);\n\t\tvalidation.failNotAllowed = false;\n\t\tvalidation.failMustHave = false;\n\t\t//did student actually write anything?\n\t\tthis.answered = this.studentAnswer.length > 0;\n\t\t\n\t\t//do comparison of student's answer with correct answer\n//\t\tif(!jme.compare(this.studentAnswer, this.settings.correctAnswer, this.settings, this.markingScope))\n\t\tif(!boolCompare(this.studentAnswer, this.settings.correctAnswer, this.settings, this.markingScope))\n\t\t{\n\t\t\tthis.setCredit(0,R('part.marking.incorrect'));\n\t\t\treturn;\n\t\t}\n\t\tvar noSpaceAnswer = this.studentAnswer.replace(/\\s/g,'').toLowerCase();\n\t\t//see if student answer contains any forbidden strings\n\t\tfor( i=0; i<this.settings.notAllowed.length; i++ ) {\n\t\t\tif(noSpaceAnswer.contains(this.settings.notAllowed[i].toLowerCase())) { validation.failNotAllowed = true; }\n\t\t}\n\t\tif(!validation.failNotAllowed) {\n\t\t\t//see if student answer contains all the required strings\n\t\t\tfor( i=0; i<this.settings.mustHave.length; i++ ) {\n\t\t\t\tif(!noSpaceAnswer.contains(this.settings.mustHave[i].toLowerCase())) { validation.failMustHave = true; }\n\t\t\t}\n\t\t}\n\t\t//calculate how many marks will be given for a correct answer\n\t\t//(can be modified if answer wrong length or fails string restrictions)\n\t\tthis.setCredit(1,R('part.jme.marking.correct'));\n\t\tif(validation.failMinLength)\n\t\t{\n\t\t\tthis.multCredit(this.settings.minLengthPC,this.settings.minLengthMessage);\n\t\t}\n\t\tif(validation.failMaxLength)\n\t\t{\n\t\t\tthis.multCredit(this.settings.maxLengthPC,this.settings.maxLengthMessage);\n\t\t}\n\t\tif(validation.failMustHave)\n\t\t{\n\t\t\tif(this.settings.mustHaveShowStrings)\n\t\t\t{\n\t\t\t\tvar strings = this.settings.mustHave.map(function(x){return R('part.jme.must-have bits',x)});\n\t\t\t\tvar message = this.settings.mustHave.length==1 ? R('part.jme.must-have one',strings) : R('part.jme.must-have several',strings)\n\t\t\t\tthis.addCredit(0,message);\n\t\t\t}\n\t\t\tthis.multCredit(this.settings.mustHavePC,this.settings.mustHaveMessage);\n\t\t}\n\t\tif(validation.failNotAllowed)\n\t\t{\n\t\t\tif(this.settings.notAllowedShowStrings)\n\t\t\t{\n\t\t\t\tvar strings = this.settings.notAllowed.map(function(x){return R('part.jme.not-allowed bits',x)});\n\t\t\t\tvar message = this.settings.notAllowed.length==1 ? R('part.jme.not-allowed one',strings) : R('part.jme.not-allowed several',strings)\n\t\t\t\tthis.addCredit(0,message);\n\t\t\t}\n\t\t\tthis.multCredit(this.settings.notAllowedPC,this.settings.notAllowedMessage);\n\t\t}\n", "order": "instead"}, "validate": {"script": "// Use the jme validation code but with variable types changed to Boolean\ndebugger;\nvar validation = this.validation;\n\t\tif(this.studentAnswer.length===0)\n\t\t{\n\t\t\tthis.giveWarning(R('part.marking.not submitted'));\n\t\t\treturn false;\n\t\t}\n\t\ttry{\n\t\t\tvar scope = new jme.Scope(this.question.scope);\n\t\t\tvar tree = jme.compile(this.studentAnswer,scope);\n\t\t\tvar varnames = jme.findvars(tree);\n\t\t\tfor(i=0;i<varnames.length;i++) {\n\t\t\t\tscope.variables[varnames[i]]=new jme.types.TBool(false); // changed from TNum\n\t\t\t}\n\t\t\tjme.evaluate(tree,scope);\n\t\t}\n\t\tcatch(e)\n\t\t{\n\t\t\tthis.giveWarning(R('part.jme.answer invalid',e.message));\n\t\t\treturn false;\n\t\t}\n\t\tif( validation.failExpectedVariableNames ) {\n\t\t\tvar suggestedNames = validation.unexpectedVariableName.split(jme.re.re_short_name);\n\t\t\tif(suggestedNames.length>3) {\n\t\t\t\tvar suggestion = [];\n\t\t\t\tfor(var i=1;i<suggestedNames.length;i+=2) {\n\t\t\t\t\tsuggestion.push(suggestedNames[i]);\n\t\t\t\t}\n\t\t\t\tsuggestion = suggestion.join('*');\n\t\t\t\tthis.giveWarning(R('part.jme.unexpected variable name suggestion',validation.unexpectedVariableName,suggestion));\n\t\t\t}\n\t\t\telse\n\t\t\t\tthis.giveWarning(R('part.jme.unexpected variable name', validation.unexpectedVariableName));\n\t\t}\n\t\tif( validation.failMinLength)\n\t\t{\n\t\t\tthis.giveWarning(this.settings.minLengthMessage);\n\t\t}\n\t\tif( validation.failMaxLength )\n\t\t{\n\t\t\tthis.giveWarning(this.settings.maxLengthMessage);\n\t\t}\n\t\tif( validation.failMustHave )\n\t\t{\n\t\t\tthis.giveWarning(this.settings.mustHaveMessage);\n\t\t\tif(this.settings.mustHaveShowStrings)\n\t\t\t{\n\t\t\t\tvar strings = this.settings.mustHave.map(function(x){return R('part.jme.must-have bits',x)});\n\t\t\t\tvar message = this.settings.mustHave.length==1 ? R('part.jme.must-have one',strings) : R('part.jme.must-have several',strings)\n\t\t\t\tthis.giveWarning(message);\n\t\t\t}\n\t\t}\n\t\tif( validation.failNotAllowed )\n\t\t{\n\t\t\tthis.giveWarning(this.settings.notAllowedMessage);\n\t\t\tif(this.settings.notAllowedShowStrings)\n\t\t\t{\n\t\t\t\tvar strings = this.settings.notAllowed.map(function(x){return R('part.jme.not-allowed bits',x)});\n\t\t\t\tvar message = this.settings.notAllowed.length==1 ? R('part.jme.not-allowed one',strings) : R('part.jme.not-allowed several',strings)\n\t\t\t\tthis.giveWarning(message);\n\t\t\t}\n\t\t}\n\t\treturn true;\n", "order": "instead"}}, "unitTests": [], "useCustomName": false, "customMarkingAlgorithm": "", "failureRate": 1, "notallowed": {"showStrings": true, "message": "<p>Brackets may not be used</p>", "strings": ["(", ")"], "partialCredit": 0}, "prompt": "<p>Enter a Boolean expression for all the common product terms in the&nbsp;above Karnaugh maps. Give the answer as a sum of products.</p>\n<p>Enter Boolean operators using the&nbsp;words \"and\", \"or\" and \"not\" (without the quotation marks, and remembering to use spaces to separate them). They will be displayed&nbsp;in mathematical notation.</p>\n<p>For example, to enter \"$a.\\bar{b}+c$\" then type \"a and not b or c\", this will display as \"$a \\land \\lnot b \\lor c$\"</p>", "customName": "", "checkVariableNames": false, "valuegenerators": [{"value": "", "name": "a"}, {"value": "", "name": "b"}, {"value": "", "name": "c"}, {"value": "", "name": "d"}], "showPreview": false}], "metadata": {"licence": "All rights reserved", "description": "<p>Development copy to test adding extra terms</p>"}, "functions": {"f": {"language": "jme", "parameters": [["p", "list"]], "type": "set", "definition": "// convert a cube to canonical set form using recursion\nif(abs(p)=1, //terminate on the last or only element of p\n    if(p[abs(p)-1]=2, //a \"don't care\" so include both 1 and 0\n    set(0,1),\n    if(p[abs(p)-1]=1,\n      set(1),\n      set(0)\n    )\n  ),\n//else\n    if(p[abs(p)-1]=2,\n      set(map(x*2,x,f(p[0..abs(p)-1]))) or set(map(x*2+1,x,f(p[0..abs(p)-1]))),\n    if(p[abs(p)-1]=1,\n      set(map(x*2+1,x,f(p[0..abs(p)-1]))),\n      set(map(x*2,x,f(p[0..abs(p)-1])))\n      )\n  )\n)"}, "usermap": {"language": "javascript", "parameters": [], "type": "html", "definition": "// draw a 4x4 Karnaugh map for a function given as a truth table\nfunction drawKmap(ctx,bits,literals)\n{\n\nctx.font = \"20px Arial\";ctx.textAlign=\"center\"; ctx.textBaseline=\"middle\";\n  ctx.lineWidth=2;\n\n//ctx.fillText(n,10,50);\nctx.beginPath();\nctx.moveTo(20,20);\nctx.lineTo(60,60);\nctx.stroke();\n\nctx.fillText(literals[0]+\" \"+literals[1],15,50);\nctx.fillText(literals[2]+\" \"+literals[3],50,10);\ngraycodebin=[\"00\",\"01\",\"11\",\"10\"];\nfor (ncol=0;ncol<=3;ncol++) {\n\tctx.fillText(graycodebin[ncol],80+ncol*40,40);\n\t}\n\nfor (nrow=0;nrow<=3;nrow++) {\n\tctx.fillText(graycodebin[nrow],40,80+nrow*40);\n\tfor (ncol=0;ncol<=3;ncol++) {\n\t\tctx.rect(60+ncol*40,60+nrow*40,40,40);\n\t\tctx.stroke();\n\t\tbitval=bits[nrow][ncol].toString();\n\t\tctx.fillText(bitval,80+ncol*40,80+nrow*40);\n\t\t}\n\t}\n\n}\n\nvar canv=document.createElement(\"canvas\");\ncanv.setAttribute(\"height\",\"250px\");\ncanv.setAttribute(\"width\",\"500px\");\nvar ctx = canv.getContext(\"2d\");\n\nquestion.signals.on('HTMLAttached',function(e) {\n  \n  // Create a Knockout.js observable\n  ko.computed(function(){\n  // Get the student's input string from part 0.\n  var studentString = question.parts[0].display.studentAnswer();\n    ctx.clearRect(0, 0, canv.width, canv.height);\n    drawKmap(ctx,studentString,['a','b','c','d'])\n  });\n});\n              \nreturn canv;"}, "draw2Kmapcanvas": {"language": "javascript", "parameters": [["bits", "list"], ["literals", "list"], ["bits2", "list"]], "type": "html", "definition": "// draw a 4x4 Karnaugh map for a function given as a truth table\nfunction drawKmap(ctx,bits,literals,legend)\n{\n\nctx.font = \"20px Arial\";ctx.textAlign=\"center\"; ctx.textBaseline=\"middle\";\n  ctx.lineWidth=2;\n\n//ctx.fillText(n,10,50);\nctx.beginPath();\nctx.moveTo(20,20);\nctx.lineTo(60,60);\nctx.stroke();\nctx.fillText(legend,140,240);\n\nctx.fillText(literals[0]+\" \"+literals[1],15,50);\nctx.fillText(literals[2]+\" \"+literals[3],50,10);\ngraycode=[0,1,3,2];\ngraycodebin=[\"00\",\"01\",\"11\",\"10\"];\nfor (ncol=0;ncol<=3;ncol++) {\n\tctx.fillText(graycodebin[ncol],80+ncol*40,40);\n\t}\n\nfor (nrow=0;nrow<=3;nrow++) {\n\tctx.fillText(graycodebin[nrow],40,80+nrow*40);\n\tfor (ncol=0;ncol<=3;ncol++) {\n\t\tctx.rect(60+ncol*40,60+nrow*40,40,40);\n\t\tctx.stroke();\n\t\tbitval=bits[graycode[nrow]*4+graycode[ncol]].toString();\n\t\tctx.fillText(bitval,80+ncol*40,80+nrow*40);\n\t\t}\n\t}\n\n}\n\n         function drawcanvas(ctx)\n         {\nvar num = 15;\nvar n = num.toString();\nctx.font = \"20px Arial\";ctx.textAlign=\"center\"; ctx.textBaseline=\"middle\";\n\nctx.fillText(n,10,50);\n\n\nfor (nrow=0;nrow<=3;nrow++) {\n\tctx.fillText(\"00\",40,80+nrow*40);\n\tfor (ncol=0;ncol<=3;ncol++) {\n\t\tctx.rect(60+ncol*40,60+nrow*40,40,40);\n\t\tctx.stroke();\n\t\tbitval=bits[nrow*4+ncol].toString();\n\t\tctx.fillText(bitval,80+ncol*40,80+nrow*40);\n\t\t}\n\t}\n\nctx.rect(0,0,400,300);\nctx.stroke();\n           \n           \n\t}\n\n\nvar canv=document.createElement(\"canvas\");\ncanv.setAttribute(\"height\",\"250px\");\ncanv.setAttribute(\"width\",\"600px\");\nvar ctx = canv.getContext(\"2d\");\n\n//literals=[\"a\",\"b\",\"c\",\"d\"];\ndrawKmap(ctx,bits,literals,'Y1');\nctx.save();\nctx.translate(320,0);\ndrawKmap(ctx,bits2,literals,'Y0');\nctx.restore();\n//drawcanvas(ctx)\nreturn canv;"}, "test": {"language": "jme", "parameters": [["args", "list"]], "type": "number", "definition": "args[0] or args[1]"}, "evalpterm": {"language": "jme", "parameters": [["c1", "list"], ["a", "boolean"], ["b", "boolean"], ["c", "boolean"], ["d", "boolean"]], "type": "boolean", "definition": "((c1[0]=1) and a or (c1[0]=0) and not a or (c1[0]=2)) and \n((c1[1]=1) and b or (c1[1]=0) and not b or (c1[1]=2)) and  \n((c1[2]=1) and c or (c1[2]=0) and not c or (c1[2]=2)) and  \n((c1[3]=1) and d or (c1[3]=0) and not d or (c1[3]=2))"}, "cubedist": {"language": "jme", "parameters": [["cube1", "list"], ["cube2", "list"]], "type": "number", "definition": "// find distance between two cubes using recursion\nif(abs(cube1)=0||abs(cube2)=0,\n  0,\n  if(cube1[0]=cube2[0],\n      cubedist(cube1[1..abs(cube1)], cube2[1..abs(cube2)]),\n      cubedist(cube1[1..abs(cube1)], cube2[1..abs(cube2)])+1\n  )\n)\n"}, "cubetotext": {"language": "jme", "parameters": [["cube", "list"], ["labels", "list"]], "type": "string", "definition": "// convert a cube to a formatted text string using recursion \n// fixed for bounding box problem 24-04-18\nif(abs(cube)=0,\n  [],\n  switch(cube[0]=0,\n      [\"$\\\\bbox[2pt]{\\\\bar{\"+labels[0]+\"}}$\"],\n    cube[0]=1,\n      [\"$\"+labels[0]+\"$\"],[]) + cubetotext(cube[1..abs(cube)],labels[1..abs(labels)]\n  )\n)\n"}, "mat2cube": {"language": "jme", "parameters": [["m", "matrix"]], "type": "list", "definition": "if(abs(list(m))=0,\n  [],\n  [m[0]*2]+mat2cube(m[1..abs(list(m))])\n  )"}}, "preamble": {"css": "", "js": ""}, "variablesTest": {"condition": "abs(list(f(c1)-union(union(f(c2),f(c3)),f(c4))))>0 and  //no redundant or duplicate terms\nabs(list(f(c2)-union(union(f(c1),f(c3)),f(c4))))>0 and \nabs(list(f(c3)-union(union(f(c2),f(c1)),f(c4))))>0 and \nabs(list(f(c4)-union(union(f(c2),f(c3)),f(c1))))>0 and \nabs(list((f(c1)-union(f(c3),f(c4))) and (f(c2)-union(f(c3),f(c4)))))=0 //no common terms except c3+c4\nand cubedist(c4,c3)>1 //common terms are prime", "maxRuns": 100}, "rulesets": {}, "tags": [], "statement": "<p>A three-output logic circuit is described by the following Karnaugh maps:-</p>\n<p>{draw2Kmapcanvas(truthtablesum,labels,truthtablesum2)}</p>\n<p></p>", "variables": {"c1": {"description": "", "definition": "shuffle([random(0..1),random(0..1),random(0..2),2])", "name": "c1", "templateType": "anything", "group": "Ungrouped variables"}, "dkmap1": {"description": "<p>Convert a 4-variable Boolean function from canonical (minterm) set to Karnaugh map matrix</p>\n<p>map(if((4*r+c) in canonicalsum,1,0),[r,c],product([0,1,3,2],[0,1,3,2]))</p>", "definition": "map(if((4*r+c) in canonicalsum,1,0),[r,c],product([0,1,3,2],[0,1,3,2]))", "name": "dkmap1", "templateType": "anything", "group": "Unused variables"}, "c4": {"description": "<p>common term</p>", "definition": "shuffle([random(0..1),random(0..1),random(0..1),2])", "name": "c4", "templateType": "anything", "group": "Unused variables"}, "truthtablesum2": {"description": "", "definition": "map(if(x in canonicalsum2,1,0),x,0..15)", "name": "truthtablesum2", "templateType": "anything", "group": "Ungrouped variables"}, "canonicalsum": {"description": "", "definition": "union(union(f(c1),f(c3)),f(c4))", "name": "canonicalsum", "templateType": "anything", "group": "Ungrouped variables"}, "canonicalsum2": {"description": "", "definition": "union(union(f(c2),f(c3)),f(c4))", "name": "canonicalsum2", "templateType": "anything", "group": "Ungrouped variables"}, "dkmap": {"description": "<p>Convert a 4-variable Boolean function from canonical (minterm) set to Karnaugh map matrix</p>", "definition": "map(if(x in canonicalsum,1,0),x,matrix(repeat([0,1,3,2],4))+4*transpose(matrix(repeat([0,1,3,2],4))))", "name": "dkmap", "templateType": "anything", "group": "Unused variables"}, "c3": {"description": "<p>common term</p>", "definition": "shuffle([random(0..1),random(0..1),random(0..2),2])", "name": "c3", "templateType": "anything", "group": "Ungrouped variables"}, "c2": {"description": "", "definition": "shuffle([random(0..1),random(0..1),random(0..2),2])\n", "name": "c2", "templateType": "anything", "group": "Ungrouped variables"}, "labels": {"description": "", "definition": "[ safe(\"a\"), safe(\"b\"), safe(\"c\"), safe(\"d\") ]", "name": "labels", "templateType": "list of strings", "group": "Ungrouped variables"}, "truthtablesum": {"description": "", "definition": "map(if(x in canonicalsum,1,0),x,0..15)", "name": "truthtablesum", "templateType": "anything", "group": "Ungrouped variables"}}, "advice": "<p>The functions are</p>\n<p>$Y1$={join([join(cubetotext(c1,labels),'.'),join(cubetotext(c3,labels),'.'),join(cubetotext(c4,labels),'.')],'+')}&nbsp;</p>\n<p>$Y0$={join([join(cubetotext(c2,labels),'.'),join(cubetotext(c3,labels),'.'),join(cubetotext(c4,labels),'.')],'+')}</p>\n<p>The common terms are {join([join(cubetotext(c3,labels),'.'),join(cubetotext(c4,labels),'.')],'+')}</p>", "ungrouped_variables": ["canonicalsum", "canonicalsum2", "c1", "c2", "c3", "labels", "truthtablesum", "truthtablesum2"], "type": "question"}, {"name": "PLA minimisation 2017", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Graeme Chester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/189/"}, {"name": "Fei Xia", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2603/"}], "statement": "<p><span style=\"line-height: 32px;\">A programmable logic array has to implement the following functions y0, y1 and y2:-</span></p>\n<p>y0 = {cset2textshuffled((y0),labels)}</p>\n<p>y1 = {cset2textshuffled((y1),labels)}</p>\n<p>y2 = {cset2textshuffled((y2),labels)}</p>\n<p><span style=\"line-height: 32px;\">Complete the table below with 0 or 1 in each box to program the corresponding AND-plane and OR-plane links in the PLA.(Hint: minimisation must be performed before entering the values).</span></p>\n<div data-jme-visible=\"true\">\n<p><span data-jme-visible=\"false\">y0={join(cubetotext(c0,labels),'.')+'+'+join(cubetotext(cboth,labels),'.')} &nbsp;{y0}</span></p>\n<p><span data-jme-visible=\"false\">y1={join(cubetotext(c1,labels),'.')+'+'+join(cubetotext(cboth2,labels),'.')} &nbsp;{y1}</span></p>\n<p><span data-jme-visible=\"false\">y2={join(cubetotext(cboth,labels),'.')+'+'+join(cubetotext(cboth2,labels),'.')} &nbsp;{y2}</span></p>\n</div>", "functions": {"mat2cube": {"parameters": [["m", "matrix"]], "language": "jme", "type": "list", "definition": "if(abs(list(m))=0,\n  [],\n  [m[0]*2]+mat2cube(m[1..abs(list(m))])\n  )"}, "reduce": {"parameters": [["lst", "list"]], "language": "javascript", "type": "list", "definition": "return lst.reduce(function(total,currentValue){return total.concat(currentValue);},[]);"}, "dec2bin": {"parameters": [["n", "number"], ["bitlen", "number"]], "language": "jme", "type": "list", "definition": "if(n>0||bitlen>0,\n  dec2bin(trunc(n/2),bitlen-1)+mod(n,2) ,\n    []\n    )\n  "}, "cset2text": {"parameters": [["cset", "set"], ["labels", "list"]], "language": "jme", "type": "string", "definition": "cubelist2text(map(dec2bin(x,len(labels)),x,cset),labels)"}, "cubetotext": {"parameters": [["cube", "list"], ["labels", "list"]], "language": "jme", "type": "string", "definition": "// convert a cube to a formatted text string using recursion \n// fixed for bounding box problem 24-04-18\nif(abs(cube)=0,\n  [],\n  switch(cube[0]=0,\n      [\"$\\\\bbox[2pt]{\\\\bar{\"+labels[0]+\"}}$\"],\n    cube[0]=1,\n      [\"$\"+labels[0]+\"$\"],[]) + cubetotext(cube[1..abs(cube)],labels[1..abs(labels)]\n  )\n)\n"}, "cset2textshuffled": {"parameters": [["cset", "set"], ["labels", "list"]], "language": "jme", "type": "string", "definition": "cubelist2text(shuffle(map(dec2bin(x,len(labels)),x,cset)),labels)"}, "f": {"parameters": [["p", "list"]], "language": "jme", "type": "set", "definition": "// convert a cube to canonical set form using recursion\nif(abs(p)=1, //terminate on the last or only element of p\n    if(p[abs(p)-1]=2, //a \"don't care\" so include both 1 and 0\n    set(0,1),\n    if(p[abs(p)-1]=1,\n      set(1),\n      set(0)\n    )\n  ),\n//else\n    if(p[abs(p)-1]=2,\n      set(map(x*2,x,f(p[0..abs(p)-1]))) or set(map(x*2+1,x,f(p[0..abs(p)-1]))),\n    if(p[abs(p)-1]=1,\n      set(map(x*2+1,x,f(p[0..abs(p)-1]))),\n      set(map(x*2,x,f(p[0..abs(p)-1])))\n      )\n  )\n)"}, "cubedist": {"parameters": [["cube1", "list"], ["cube2", "list"]], "language": "jme", "type": "number", "definition": "// find distance between two cubes using recursion\nif(abs(cube1)=0||abs(cube2)=0,\n  0,\n  if(cube1[0]=cube2[0],\n      cubedist(cube1[1..abs(cube1)], cube2[1..abs(cube2)]),\n      cubedist(cube1[1..abs(cube1)], cube2[1..abs(cube2)])+1\n  )\n)\n"}, "userpla1": {"parameters": [["inlabels", "list"], ["outlabels", "list"], ["pterms", "number"]], "language": "javascript", "type": "html", "definition": "function PLA(andplanearray, orplanearray, innames, outnames) {\n\t//need to add some error checking for row/columnn counts etc.\n\t// andplanearray=array(npterms,innames*2)\n\t// orplanearray=array(npterms,outnames)\n\tthis.andplane = andplanearray;\n\tthis.orplane = orplanearray;\n\tthis.inlabels = innames;\n\tthis.outlabels = outnames;\n\n\tthis.npterms = function() {\n\t\treturn this.andplane.length;\n\t};\n\n\tthis.ninputs = function() {\n\t\treturn this.inlabels.length;\n\t};\n\tthis.noutputs = function() {\n\t\treturn this.outlabels.length;\n\t};\n}\n\nfunction drawArrow(context, x, y, size) {\n//Draw arrow head with tip at x,y and orientation along positive x-axis\n\tcontext.beginPath();\n    context.moveTo(x, y);\n\tcontext.lineTo(x - size, y - size / 2);\n\tcontext.lineTo(x - size, y + size / 2);\n\tcontext.lineTo(x, y);\n\tcontext.fill();\n\t}\n\ndebugger;\nandplane = [[1, 0, 1, 1,0,1], [1, 1, 1, 0,0,0], [0, 1, 0, 1,0,1]];\norplane = [[1, 0], [0, 1], [1, 1]];\n//inlabels = [\"a\", \"b\",\"c\"];\n//outlabels = [\"y0\", \"y1\"];\n//pterms=3; maybe use to size the canvas, answer array length used otherwise\nvar myPLA = new PLA(andplane, orplane, inlabels, outlabels);\n\nconsole.log(myPLA);\n\nvar pitch = 40;\n\nvar canv=document.createElement(\"canvas\");\nvar canvH = pitch*pterms + 180;\nvar canvW = pitch*(2*inlabels.length+outlabels.length) + 180;\ncanv.setAttribute(\"height\",canvH+\"px\");\ncanv.setAttribute(\"width\",canvW+\"px\");\nvar ctx = canv.getContext(\"2d\");\n\nquestion.signals.on('HTMLAttached',function(e) {\n\n// Create a Knockout.js observable\nko.computed(function(){\n// Get the student's input string from part 0.\nvar studentPLA = question.parts[0].display.studentAnswer();\nvar studentPLAInputs = inlabels.length; \nvar studentPLAOutputs = outlabels.length; \n \nvar studentandp  = studentPLA.map(function(value,index) { return value.slice(0,studentPLAInputs*2); });\nvar studentorp   = studentPLA.map(function(value,index) { return value.slice(studentPLAInputs*2,studentPLAInputs*2+studentPLAOutputs); });\nvar myPLA = new PLA(studentandp, studentorp, inlabels, outlabels);\nctx.clearRect(0, 0, canv.width, canv.height);\ndrawPLA(ctx, myPLA, pitch);\n});\n});\n\t\t  \nreturn canv;\n\n\n\n\t\t\t\t\tfunction drawArrow(context, x, y, size,rotation) {\n\t\t\t\t\t\t//Draw arrow head with tip at x,y and orientation along positive x-axis\n\t\t\t\t\t\tcontext.save();\n\t\t\t\t\t\tcontext.lineWidth=3;\n\t\t\t\t\t\tcontext.translate(x, y);\n\t\t\t\t\t\tcontext.rotate(rotation);\n\t\t\t\t\t\tcontext.beginPath();\n\t\t\t\t\t\tcontext.moveTo(0, 0);\n\t\t\t\t\t\tcontext.lineTo( - size,  - size / 2);\n\t\t\t\t\t\tcontext.lineTo( - size,    size / 2);\n\t\t\t\t\t\tcontext.lineTo(0, 0);\n\t\t\t\t\t\tcontext.fill();\n\t\t\t\t\t\tcontext.restore();\n\t\t\t\t\t}\n\n\n\t\t\t\t\tfunction drawPLA(ctx, thePLA, pitch) {\n\t\t\t\t\t\tctx.lineWidth = 2;\n\t\t\t\t\t\tctx.font = (pitch / 2).toString() + \"px Arial\";\n\t\t\t\t\t\t//\t\t\t\t\t\tconsole.log((pitch / 2).toString());\n\t\t\t\t\t\tctx.textAlign = \"center\";\n\t\t\t\t\t\tctx.textBaseline = \"middle\";\n\t\t\t\t\t\tninputs = thePLA.ninputs();\n\t\t\t\t\t\tnoutputs = thePLA.noutputs();\n\t\t\t\t\t\tnpterms = thePLA.npterms();\n\t\t\t\t\t\t\n\t\t\t\t\t\t//i/o wires and labels\n\t\t\t\t\t\tfor (var ncol = 0; ncol < 2 * ninputs; ncol++) {\n\t\t\t\t\t\t\tctx.beginPath();\n\t\t\t\t\t\t\tctx.moveTo((ncol + 2) * pitch, (npterms + 1.5) * pitch);\n\t\t\t\t\t\t\tctx.lineTo((ncol + 2) * pitch, (npterms + 2  ) * pitch);\n\t\t\t\t\t\t\tctx.stroke();\n\t\t\t\t\t\t\tdrawArrow(ctx, (ncol + 2) * pitch, (npterms + 1.5) * pitch, pitch / 4, -Math.PI / 2);\n\n\t\t\t\t\t\t\tif (ncol % 2 == 0) {\n\t\t\t\t\t\t\t\tctx.fillText(thePLA.inlabels[ncol / 2], pitch * (ncol + 2), (npterms + 2.5) * pitch);\n\t\t\t\t\t\t\t} else {\n\t\t\t\t\t\t\t\tctx.fillText(thePLA.inlabels[(ncol - 1) / 2] + \"'\", pitch * (ncol + 2), (npterms + 2.5) * pitch);\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\n\t\t\t\t\t\tfor (var ncol = 0; ncol < noutputs; ncol++) {\n\t\t\t\t\t\t\tctx.beginPath();\n\t\t\t\t\t\t\tctx.moveTo(ncol * pitch + (2 * ninputs + 3.5) * pitch, (npterms + 1.5) * pitch);\n\t\t\t\t\t\t\tctx.lineTo(ncol * pitch + (2 * ninputs + 3.5) * pitch, (npterms + 2) * pitch);\n\t\t\t\t\t\t\tctx.stroke();\n\t\t\t\t\t\t\tctx.fillText(thePLA.outlabels[ncol], pitch * ncol + (2 * ninputs + 3.5) * pitch, (npterms + 2.5) * pitch);\n\t\t\t\t\t\t\tdrawArrow(ctx, ncol * pitch + (2 * ninputs + 3.5) * pitch, (npterms + 2) * pitch, pitch / 4, Math.PI / 2);\n\t\t\t\t\t\t}\n\n\t\t\t\t\t\t// AND plane cells\n\t\t\t\t\t\tfor (var nrow = 0; nrow < npterms; nrow++) {\n\n\t\t\t\t\t\t\tfor (var ncol = 0; ncol < 2 * ninputs; ncol++) {\n\t\t\t\t\t\t\tctx.beginPath();\n\t\t\t\t\t\t\t\tctx.rect((1.5 + ncol) * pitch, (1.5 + nrow) * pitch, pitch, pitch);\n\t\t\t\t\t\t\t\tctx.stroke();\n\t\t\t\t\t\t\t\tctx.fillText(thePLA.andplane[nrow][ncol].toString(), (2 + ncol) * pitch, (2 + nrow) * pitch);\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t// product term links\n\t\t\t\t\t\t\tctx.beginPath();\n\t\t\t\t\t\t\tctx.moveTo((2 * ninputs + 1.5) * pitch, (nrow + 2) * pitch);\n\t\t\t\t\t\t\tctx.lineTo((2 * ninputs + 3) * pitch, (nrow + 2) * pitch);\n\t\t\t\t\t\t\tctx.stroke();\n\t\t\t\t\t\t\tdrawArrow(ctx, (2 * ninputs + 3) * pitch, (nrow + 2) * pitch, pitch / 4, 0);\n\n\t\t\t\t\t\t\t// OR plane cells\n\t\t\t\t\t\t\tfor (var ncol = 0; ncol < noutputs; ncol++) {\n\t\t\t\t\t\t\tctx.beginPath();\n\t\t\t\t\t\t\t\tctx.rect((3 + 2 * ninputs + ncol) * pitch, (1.5 + nrow) * pitch, pitch, pitch);\n\t\t\t\t\t\t\t\tctx.stroke();\n\t\t\t\t\t\t\t\tctx.fillText(thePLA.orplane[nrow][ncol].toString(), (3.5 + 2 * ninputs + ncol) * pitch, (2 + nrow) * pitch);\n\t\t\t\t\t\t\t}\n\n\t\t\t\t\t\t}\n\n\t\t\t\t\t}\n"}, "cubelist2text": {"parameters": [["cubelist", "list"], ["labels", "list"]], "language": "jme", "type": "string", "definition": "join(map(join(cubetotext(x,labels),'.'),x,cubelist),'+')"}}, "metadata": {"description": "<p>Development versin for increasing size of PLA</p>", "licence": "All rights reserved"}, "advice": "<p>The common terms {join(cubetotext(cboth,labels),'.')} and {join(cubetotext(cboth2,labels),'.')} can be used to reduce the functions:-</p>\n<p>y0={join(cubetotext(c0,labels),'.')+'+'+join(cubetotext(cboth,labels),'.')}</p>\n<p>y1={join(cubetotext(c1,labels),'.')+'+'+join(cubetotext(cboth2,labels),'.')}</p>\n<p>y2={join(cubetotext(cboth,labels),'.')+'+'+join(cubetotext(cboth2,labels),'.')}</p>", "tags": [], "parts": [{"extendBaseMarkingAlgorithm": true, "allowFractions": false, "numColumns": "length(labels)*2+length(outlabels)", "marks": "9", "type": "matrix", "showFeedbackIcon": true, "prompt": "<p>{userpla1(labels,outlabels,terms)}</p>\n<p>Programming table (note that the columns are in the order: AND plane, OR plane)&nbsp;</p>", "correctAnswerFractions": false, "variableReplacements": [], "correctAnswer": "ans", "showCorrectAnswer": true, "markPerCell": false, "scripts": {"validate": {"order": "instead", "script": "debugger;\n// Use the built-in validation function to catch syntax errors and so on\nif(!Numbas.parts.MatrixEntryPart.prototype.validate.apply(this)) {\n  return false;\n}\nreturn true;"}, "mark": {"order": "instead", "script": "\t\t\t\t\tfunction PLA(andplanearray, orplanearray, innames, outnames) {\n\t\t\t\t\t\t//need to add some error checking for row/columnn counts etc.\n\t\t\t\t\t\t// andplanearray=array(npterms,innames*2)\n\t\t\t\t\t\t// orplanearray=array(npterms,outnames)\n\t\t\t\t\t\tthis.andplane = andplanearray;\n\t\t\t\t\t\tthis.orplane = orplanearray;\n\t\t\t\t\t\tthis.inlabels = innames;\n\t\t\t\t\t\tthis.outlabels = outnames;\n\n\t\t\t\t\t\tthis.npterms = function() {\n\t\t\t\t\t\t\treturn this.andplane.length;\n\t\t\t\t\t\t};\n\n\t\t\t\t\t\tthis.ninputs = function() {\n\t\t\t\t\t\t\treturn this.inlabels.length;\n\t\t\t\t\t\t};\n\t\t\t\t\t\tthis.noutputs = function() {\n\t\t\t\t\t\t\treturn this.outlabels.length;\n\t\t\t\t\t\t};\n\n\t\t\t\t\t\tthis.eval = function(invalues) {\n\t\t\t\t\t\t\tvar outvalues = new Array(this.noutputs());\n                          for (var ind = 0; ind < outvalues.length; ind++) {\n                            outvalues[ind] = 0;\n                          }\n                          //not supported in some browsers      outvalues.fill(0, 0, this.noutputs());\n\t\t\t\t\t\t\tfor (var nrow = 0; nrow < this.npterms(); nrow++) {\n\t\t\t\t\t\t\t\tvar ptout = 1;\n\t\t\t\t\t\t\t\tfor (var ncol = 0; ncol < this.ninputs(); ncol++) {\n\t\t\t\t\t\t\t\t\tif ((this.andplane[nrow][2 * ncol] == 1) && (invalues[ncol] == 0) || (this.andplane[nrow][2 * ncol + 1] == 1) && (invalues[ncol] == 1)) {\n\t\t\t\t\t\t\t\t\t\tptout = 0;\n\t\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t\tfor (var ncol = 0; ncol < this.noutputs(); ncol++) {\n\t\t\t\t\t\t\t\t\tif ((this.orplane[nrow][ncol] == 1) && (ptout == 1)) {\n\t\t\t\t\t\t\t\t\t\toutvalues[ncol] = 1;\n\t\t\t\t\t\t\t\t\t}\n\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\treturn outvalues;\n\t\t\t\t\t\t};\n\t\t\t\t\t}\n\ndebugger;\nthis.answered=true;\nvar studentPLA = this.studentAnswer;\nvar studentandp  = studentPLA.map(function(value,index) { return value.slice(0,8); });\nvar studentorp   = studentPLA.map(function(value,index) { return value.slice(8,11); });\nconsole.log('andplane ', studentandp);\nconsole.log('orplane ', studentorp);\nthePLA=new PLA(studentandp,studentorp,['a','b','c','d'],['y0','y1','y2']);\n\n//andplane = [[1, 0, 1, 1], [1, 1, 1, 0], [0, 1, 0, 1]];\n//orplane = [[1, 0], [0, 1], [1, 1], ];\n//inlabels = [\"a\", \"b\"];\n//outlabels = [\"y0\", \"y1\"];\n//thePLA = new PLA(andplane, orplane, inlabels, outlabels);\n\n\nvar y0set=[]; var y1set=[]; var y2set=[];\nfor (var aval=0;aval<2;aval++){\n\tfor (var bval=0;bval<2;bval++){\n    \tfor (var cval=0;cval<2;cval++){\n        \tfor (var dval=0;dval<2;dval++){\n    \t\t  var k=8*aval+4*bval+2*cval+dval;\n\t    \t  var y=thePLA.eval([aval,bval,cval,dval]);\n\t\t      if (y[0]==1) y0set.push(new Numbas.jme.types.TNum(k));\n\t\t      if (y[1]==1) y1set.push(new Numbas.jme.types.TNum(k));\n\t\t      if (y[2]==1) y2set.push(new Numbas.jme.types.TNum(k));\n            }\n        }\n\t}\n}\n\n//console.log('y0 ', y0set);\n//console.log('y1 ', y1set);\n//get the canonical set variables y0 y1\nvar variables = this.question.scope.variables;\nvar unwrap = Numbas.jme.unwrapValue;\nvar setmath = Numbas.setmath;\n\nvar y0ans=(unwrap(variables.y0));\nvar y1ans=unwrap((variables.y1));\nvar y2ans=unwrap((variables.y2));\nconsole.log('y0 ', y0set, y0ans);\nconsole.log('y1 ', y1set, y1ans);\nconsole.log('y2 ', y0set, y0ans);\n\n//compare the answers\nif (setmath.eq(y0set,y0ans)) {  this.addCredit(1.0/3,'Output y0 is correct. ');}\nelse{this.addCredit(0,'Output y0 is incorrect. ');\n};\n\nif (setmath.eq(y1set,y1ans)) {  this.addCredit(1.0/3,'Output y1 is correct. ');}\nelse{this.addCredit(0,'Output y1 is incorrect. ');\n};\n\nif (setmath.eq(y2set,y2ans)) {  this.addCredit(1.0/3,'Output y2 is correct. ');}\nelse{this.addCredit(0,'Output y2 is incorrect. ');\n};\n"}}, "variableReplacementStrategy": "originalfirst", "tolerance": 0, "numRows": "terms", "customMarkingAlgorithm": "", "allowResize": false, "unitTests": []}], "variable_groups": [], "preamble": {"js": "", "css": ""}, "rulesets": {}, "ungrouped_variables": ["c1", "c0", "cboth", "cboth2", "labels", "y0", "y1", "y2", "displayc", "ans", "test", "outlabels", "terms"], "variablesTest": {"condition": "//abs(list(f(c1)-f(cboth)))>0 and abs(list(f(cboth)-f(c1)))>0 and\n//abs(list(f(cboth)-f(c0)))>0 and abs(list(f(c0)-f(cboth)))>0 and\n//abs(list(f(c0)-f(c1)))>0 and abs(list(f(c1)-f(c0)))>0 and\n//cubedist(cboth,c0)>1 and cubedist(cboth,c1)>1\n\nabs(list(f(c1)-union(union(f(c0),f(cboth)),f(cboth2))))>0 and  //no redundant or duplicate terms\nabs(list(f(c0)-union(union(f(c1),f(cboth)),f(cboth2))))>0 and \nabs(list(f(cboth)-union(union(f(c0),f(c1)),f(cboth2))))>0 and \nabs(list(f(cboth2)-union(union(f(c0),f(cboth)),f(c1))))>0 and \nabs(list((f(c1)-union(f(cboth),f(cboth2))) and (f(c0)-union(f(cboth),f(cboth2)))))=0 and //no common terms except cboth,cboth2\ncubedist(cboth2,cboth)>1 //common terms are prime", "maxRuns": "40"}, "variables": {"y2": {"name": "y2", "definition": "union(f(cboth),f(cboth2))", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "cboth2": {"name": "cboth2", "definition": "shuffle([random(0..1),random(0..1),random(0..1),2])", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "c1": {"name": "c1", "definition": "shuffle([random(0..1),random(0..1),random(0..1),random(0..2)])", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "outlabels": {"name": "outlabels", "definition": "[ safe(\"y0\"), safe(\"y1\"), safe(\"y2\") ]", "group": "Ungrouped variables", "description": "", "templateType": "list of strings"}, "terms": {"name": "terms", "definition": "4", "group": "Ungrouped variables", "description": "", "templateType": "number"}, "test": {"name": "test", "definition": "matrix(reduce([[1,2],[2,3]]))", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "labels": {"name": "labels", "definition": "[ safe(\"a\"), safe(\"b\"), safe(\"c\"), safe(\"d\") ]", "group": "Ungrouped variables", "description": "", "templateType": "list of strings"}, "ans": {"name": "ans", "definition": "matrix(\n  reduce(map(switch(x=0,[0,1],x=1,[1,0],[0,0]),x,c0)    +[1,0,0] ),\n  reduce(map(switch(x=0,[0,1],x=1,[1,0],[0,0]),x,c1)    +[0,1,0] ),\n  reduce(map(switch(x=0,[0,1],x=1,[1,0],[0,0]),x,cboth) +[1,0,1] ),  \n  reduce(map(switch(x=0,[0,1],x=1,[1,0],[0,0]),x,cboth2)+[0,1,1] )\n)", "group": "Ungrouped variables", "description": "<p>map(if(x==2,0,1),x,c0)+[0,0],c1+[0,0],cboth+[1,1])matrix(</p>", "templateType": "anything"}, "y0": {"name": "y0", "definition": "union(f(c0),f(cboth))\n", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "y1": {"name": "y1", "definition": "union(f(c1),f(cboth2))", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "displayc": {"name": "displayc", "definition": "matrix(c0,c1,cboth)", "group": "Ungrouped variables", "description": "<p>Used to display lists in editor here, not used at run time</p>", "templateType": "anything"}, "c0": {"name": "c0", "definition": "shuffle([random(0..1),random(0..1),random(0..1),2])", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "cboth": {"name": "cboth", "definition": "shuffle([random(0..1),random(0..1),random(0..1),2])", "group": "Ungrouped variables", "description": "", "templateType": "anything"}}, "type": "question"}]}], "percentPass": "40", "metadata": {"licence": "All rights reserved", "description": ""}, "duration": 3600, "navigation": {"showresultspage": "oncompletion", "preventleave": true, "showfrontpage": true, "reverse": true, "allowregen": false, "onleave": {"action": "none", "message": ""}, "browse": true}, "type": "exam", "contributors": [{"name": "Graeme Chester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/189/"}, {"name": "Fei Xia", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2603/"}], "extensions": ["booleanlogic"], "custom_part_types": [], "resources": []}