{"kind":"Notebook","sha256":"71695e8830ede3fcf63ad601a81b089b978daa82e48b5cafa656784814e36d51","slug":"calculators","location":"/release/Lab2/Calculators.ipynb","dependencies":[],"frontmatter":{"title":"Calculators","kernelspec":{"name":"python3","display_name":"Python 3 (ipykernel)","language":"python"},"authors":[{"nameParsed":{"literal":"Chung Chan","given":"Chung","family":"Chan"},"name":"Chung Chan","affiliations":["City University of Hong Kong"],"id":"contributors-myst-generated-uid-0"}],"github":"https://github.com/dive4dec/cs1302_24a","keywords":[],"affiliations":[{"id":"City University of Hong Kong","name":"City University of Hong Kong"}],"thumbnail":"/~ccha23/cs1302_24a/build/pythagoras.dio-9b748f89d54f2baa09d24023fa7ce3c5.svg","exports":[{"format":"ipynb","filename":"Calculators.ipynb","url":"/~ccha23/cs1302_24a/build/Calculators-501bdfd677226d53f960f406455bdadb.ipynb"}]},"mdast":{"type":"root","children":[{"type":"block","kind":"notebook-content","data":{"slideshow":{"slide_type":"subslide"}},"children":[{"type":"paragraph","position":{"start":{"line":1,"column":1},"end":{"line":2,"column":1}},"children":[{"type":"text","value":"Run the following to load additional tools required for this lab.","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"ZueijJRCI5"},{"type":"break","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"QNlSCKsGLI"},{"type":"text","value":"In particular, the ","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"nyqNbUX3QM"},{"type":"inlineCode","value":"math","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"fRZOg3nQOe"},{"type":"text","value":" library provides many useful mathematical functions and constants.","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"yY4IU6Veg6"}],"key":"NmrGHiprwa"}],"key":"ixmxADtBYa"},{"type":"block","kind":"notebook-code","data":{"hide_input":false,"init_cell":true,"slideshow":{"slide_type":"-"}},"children":[{"type":"code","lang":"python","executable":true,"value":"import math\nfrom math import *\n\nimport jsxgraphs\nimport matplotlib.pyplot as plt\nimport numpy as np\nfrom ipywidgets import interact\n\n%matplotlib widget","key":"qduxkz0Fqu"},{"type":"output","id":"D6KgsyrGF3_tEi1gNTm-W","data":[],"key":"Emq5laFDCX"}],"key":"dE5AQMHfyH"},{"type":"block","kind":"notebook-content","data":{"slideshow":{"slide_type":"subslide"}},"children":[{"type":"paragraph","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"children":[{"type":"text","value":"The following code is a Python one-liner that creates a calculator.","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"L1SXMUsdfZ"}],"key":"EbBw5HoPeZ"}],"key":"RpdSkkpdrR"},{"type":"block","kind":"notebook-code","data":{"slideshow":{"slide_type":"-"}},"children":[{"type":"code","lang":"python","executable":true,"value":"eval(input())","key":"kk0HjMUjrz"},{"type":"output","id":"NaUAubgXoEbMOz4nsiBgO","data":[],"key":"v5j1yCvI0K"}],"key":"Rmxs6SMuGh"},{"type":"block","kind":"notebook-content","data":{"slideshow":{"slide_type":"fragment"}},"children":[{"type":"paragraph","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"children":[{"type":"text","value":"Evaluate the cell repeatedly with ","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"s7Q7CXUDx0"},{"type":"inlineCode","value":"Ctrl+Enter","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"rxKCOFL850"},{"type":"text","value":" to try some calculations below using this calculator:","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"BFeIR1mt7c"}],"key":"didk0dXqW3"},{"type":"list","ordered":true,"start":1,"spread":false,"position":{"start":{"line":3,"column":1},"end":{"line":8,"column":1}},"children":[{"type":"listItem","spread":true,"position":{"start":{"line":3,"column":1},"end":{"line":3,"column":1}},"children":[{"type":"span","position":{"start":{"line":3,"column":1},"end":{"line":3,"column":1}},"children":[{"type":"text","value":"2","key":"kYH4YBrMnc"},{"type":"superscript","children":[{"type":"text","value":"3","key":"sWfEqmFaZ6"}],"key":"ZJrJ033p9e"}],"key":"EtGvPnBBNw"},{"type":"text","value":" by entering ","position":{"start":{"line":3,"column":1},"end":{"line":3,"column":1}},"key":"piLdeLZjnZ"},{"type":"inlineCode","value":"2**3","position":{"start":{"line":3,"column":1},"end":{"line":3,"column":1}},"key":"C9UJcAqcfU"},{"type":"text","value":";","position":{"start":{"line":3,"column":1},"end":{"line":3,"column":1}},"key":"jLINmVingL"}],"key":"uD7b44R8PO"},{"type":"listItem","spread":true,"position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"children":[{"type":"inlineMath","value":"\\frac23","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"html":"<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac></mrow><annotation encoding=\"application/x-tex\">\\frac23</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1.1901em;vertical-align:-0.345em;\"></span><span class=\"mord\"><span class=\"mopen nulldelimiter\"></span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8451em;\"><span style=\"top:-2.655em;\"><span class=\"pstrut\" style=\"height:3em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3</span></span></span></span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"></span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"></span></span><span style=\"top:-3.394em;\"><span class=\"pstrut\" style=\"height:3em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2</span></span></span></span></span><span class=\"vlist-s\">​</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.345em;\"><span></span></span></span></span></span><span class=\"mclose nulldelimiter\"></span></span></span></span></span>","key":"VyGoJ6iWcd"},{"type":"text","value":" by entering ","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"sjwfPGOvcq"},{"type":"inlineCode","value":"2/3","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"h8eBkDW6jq"},{"type":"text","value":";","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"IJNlWyqODV"}],"key":"pwfZSnuSMq"},{"type":"listItem","spread":true,"position":{"start":{"line":5,"column":1},"end":{"line":5,"column":1}},"children":[{"type":"inlineMath","value":"\\left\\lceil\\frac32\\right\\rceil","position":{"start":{"line":5,"column":1},"end":{"line":5,"column":1}},"html":"<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mo fence=\"true\">⌈</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo fence=\"true\">⌉</mo></mrow><annotation encoding=\"application/x-tex\">\\left\\lceil\\frac32\\right\\rceil</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1.2em;vertical-align:-0.35em;\"></span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size1\">⌈</span></span><span class=\"mord\"><span class=\"mopen nulldelimiter\"></span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8451em;\"><span style=\"top:-2.655em;\"><span class=\"pstrut\" style=\"height:3em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2</span></span></span></span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"></span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"></span></span><span style=\"top:-3.394em;\"><span class=\"pstrut\" style=\"height:3em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3</span></span></span></span></span><span class=\"vlist-s\">​</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.345em;\"><span></span></span></span></span></span><span class=\"mclose nulldelimiter\"></span></span><span class=\"mclose delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size1\">⌉</span></span></span></span></span></span>","key":"Ba8PJRUZvP"},{"type":"text","value":" by entering ","position":{"start":{"line":5,"column":1},"end":{"line":5,"column":1}},"key":"dXuyW6Wj9w"},{"type":"inlineCode","value":"3//2","position":{"start":{"line":5,"column":1},"end":{"line":5,"column":1}},"key":"Sh9phNGMcL"},{"type":"text","value":";","position":{"start":{"line":5,"column":1},"end":{"line":5,"column":1}},"key":"Hx8TipYgoC"}],"key":"PKVNKSM9OX"},{"type":"listItem","spread":true,"position":{"start":{"line":6,"column":1},"end":{"line":6,"column":1}},"children":[{"type":"inlineMath","value":"3\\mod 2","position":{"start":{"line":6,"column":1},"end":{"line":6,"column":1}},"html":"<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mn>3</mn><mspace></mspace><mspace width=\"0.6667em\"/><mrow><mi mathvariant=\"normal\">m</mi><mi mathvariant=\"normal\">o</mi><mi mathvariant=\"normal\">d</mi></mrow><mtext> </mtext><mtext> </mtext><mn>2</mn></mrow><annotation encoding=\"application/x-tex\">3\\mod 2</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.6444em;\"></span><span class=\"mord\">3</span><span class=\"mspace allowbreak\"></span><span class=\"mspace\" style=\"margin-right:0.6667em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.6944em;\"></span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">mod</span></span></span><span class=\"mspace\" style=\"margin-right:0.1667em;\"></span><span class=\"mspace\" style=\"margin-right:0.1667em;\"></span><span class=\"mord\">2</span></span></span></span>","key":"CYaglaRyZX"},{"type":"text","value":" by entering ","position":{"start":{"line":6,"column":1},"end":{"line":6,"column":1}},"key":"yDfZyGHY06"},{"type":"inlineCode","value":"3%2","position":{"start":{"line":6,"column":1},"end":{"line":6,"column":1}},"key":"vDmmm6qwP6"},{"type":"text","value":";","position":{"start":{"line":6,"column":1},"end":{"line":6,"column":1}},"key":"e0DhueVH8j"}],"key":"p6XXJBqU7C"},{"type":"listItem","spread":true,"position":{"start":{"line":7,"column":1},"end":{"line":7,"column":1}},"children":[{"type":"inlineMath","value":"\\sqrt{2}","position":{"start":{"line":7,"column":1},"end":{"line":7,"column":1}},"html":"<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><msqrt><mn>2</mn></msqrt></mrow><annotation encoding=\"application/x-tex\">\\sqrt{2}</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1.04em;vertical-align:-0.1328em;\"></span><span 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and","position":{"start":{"line":7,"column":1},"end":{"line":7,"column":1}},"key":"Zp6LFloKTX"}],"key":"wuK4VQsoah"},{"type":"listItem","spread":true,"position":{"start":{"line":8,"column":1},"end":{"line":8,"column":1}},"children":[{"type":"inlineMath","value":"\\sin(\\pi/6)","position":{"start":{"line":8,"column":1},"end":{"line":8,"column":1}},"html":"<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi>sin</mi><mo>⁡</mo><mo stretchy=\"false\">(</mo><mi>π</mi><mi mathvariant=\"normal\">/</mi><mn>6</mn><mo stretchy=\"false\">)</mo></mrow><annotation encoding=\"application/x-tex\">\\sin(\\pi/6)</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"></span><span class=\"mop\">sin</span><span class=\"mopen\">(</span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">π</span><span class=\"mord\">/6</span><span class=\"mclose\">)</span></span></span></span>","key":"oyCSFz2gUV"},{"type":"text","value":" by entering ","position":{"start":{"line":8,"column":1},"end":{"line":8,"column":1}},"key":"LQWDw6EtUH"},{"type":"inlineCode","value":"sin(pi/6)","position":{"start":{"line":8,"column":1},"end":{"line":8,"column":1}},"key":"r3AqRuHe0F"},{"type":"text","value":";","position":{"start":{"line":8,"column":1},"end":{"line":8,"column":1}},"key":"fTCGq3KEQ5"}],"key":"bE40eYJoh0"}],"key":"Ya8agmel7D"}],"key":"JrdYA21573"},{"type":"block","kind":"notebook-content","data":{"slideshow":{"slide_type":"fragment"}},"children":[{"type":"paragraph","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"children":[{"type":"text","value":"For this lab, you will create different calculators. We will first show you a demo. Then, it will be your turn to create the calculators.","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"Vr7kXFgG1Q"}],"key":"aUn6tXEuD1"}],"key":"v9wni4ileg"},{"type":"block","kind":"notebook-content","data":{"slideshow":{"slide_type":"slide"}},"children":[{"type":"heading","depth":2,"position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"children":[{"type":"text","value":"Hypotenuse Calculator","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"AqP4hZvOJx"}],"identifier":"hypotenuse-calculator","label":"Hypotenuse Calculator","html_id":"hypotenuse-calculator","implicit":true,"key":"BA52g8V2yz"}],"key":"nw20wMit5E"},{"type":"block","kind":"notebook-content","data":{"slideshow":{"slide_type":"fragment"}},"children":[{"type":"proof","kind":"proposition","label":"pro:pythagorus","identifier":"pro:pythagorus","enumerated":true,"children":[{"type":"admonitionTitle","children":[{"type":"text","value":"Pythagoras Theorem","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"bLFCjG1mHj"}],"key":"O7jkogAC9i"},{"type":"paragraph","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"children":[{"type":"text","value":"By the Pythagoras theorem, given a right-angled triangle,","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"tjuXQJ6Qyh"}],"key":"kcQW0KZFy2"},{"type":"image","url":"/~ccha23/cs1302_24a/build/pythagoras.dio-9b748f89d54f2baa09d24023fa7ce3c5.svg","alt":"Right-angled triangle","position":{"start":{"line":6,"column":1},"end":{"line":6,"column":1}},"key":"SlDAmHFYPq","urlSource":"images/pythagoras.dio.svg"},{"type":"paragraph","position":{"start":{"line":8,"column":1},"end":{"line":8,"column":1}},"children":[{"type":"text","value":"the length of the hypotenuse is","position":{"start":{"line":8,"column":1},"end":{"line":8,"column":1}},"key":"D7rl1H384k"}],"key":"Hcp6rESSP4"},{"type":"math","identifier":"eq:hypotenuse","label":"eq:hypotenuse","html_id":"eq-hypotenuse","value":"c = \\sqrt{a^2 + b^2}","position":{"start":{"line":10,"column":1},"end":{"line":12,"column":1}},"html":"<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><semantics><mrow><mi>c</mi><mo>=</mo><msqrt><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></msqrt></mrow><annotation encoding=\"application/x-tex\">c = \\sqrt{a^2 + b^2}</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.4306em;\"></span><span class=\"mord mathnormal\">c</span><span class=\"mspace\" style=\"margin-right:0.2778em;\"></span><span class=\"mrel\">=</span><span class=\"mspace\" style=\"margin-right:0.2778em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:1.24em;vertical-align:-0.1777em;\"></span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.0623em;\"><span class=\"svg-align\" style=\"top:-3.2em;\"><span class=\"pstrut\" style=\"height:3.2em;\"></span><span class=\"mord\" style=\"padding-left:1em;\"><span class=\"mord\"><span class=\"mord mathnormal\">a</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7401em;\"><span style=\"top:-2.989em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2</span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mord\"><span class=\"mord mathnormal\">b</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7401em;\"><span style=\"top:-2.989em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2</span></span></span></span></span></span></span></span></span></span><span style=\"top:-3.0223em;\"><span class=\"pstrut\" style=\"height:3.2em;\"></span><span class=\"hide-tail\" style=\"min-width:1.02em;height:1.28em;\"><svg xmlns=\"http://www.w3.org/2000/svg\" width='400em' height='1.28em' viewBox='0 0 400000 1296' preserveAspectRatio='xMinYMin slice'><path d='M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z'/></svg></span></span></span><span class=\"vlist-s\">​</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1777em;\"><span></span></span></span></span></span></span></span></span></span>","enumerator":"1","key":"lZbGycDUmC"},{"type":"paragraph","position":{"start":{"line":14,"column":1},"end":{"line":14,"column":1}},"children":[{"type":"text","value":"where ","position":{"start":{"line":14,"column":1},"end":{"line":14,"column":1}},"key":"OjaSDVOtEE"},{"type":"inlineMath","value":"a","position":{"start":{"line":14,"column":1},"end":{"line":14,"column":1}},"html":"<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi>a</mi></mrow><annotation encoding=\"application/x-tex\">a</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.4306em;\"></span><span class=\"mord mathnormal\">a</span></span></span></span>","key":"bKeT1Ud8Vf"},{"type":"text","value":" and ","position":{"start":{"line":14,"column":1},"end":{"line":14,"column":1}},"key":"VdFgD6FCGs"},{"type":"inlineMath","value":"b","position":{"start":{"line":14,"column":1},"end":{"line":14,"column":1}},"html":"<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi>b</mi></mrow><annotation encoding=\"application/x-tex\">b</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.6944em;\"></span><span class=\"mord mathnormal\">b</span></span></span></span>","key":"eNgmz9KzSu"},{"type":"text","value":" are the lengths of the other sides of the triangle.","position":{"start":{"line":14,"column":1},"end":{"line":14,"column":1}},"key":"cUPoarcorJ"}],"key":"T4A5YQll97"}],"enumerator":"1","html_id":"pro-pythagorus","key":"FX7Hv29Ccu"}],"key":"Mn5WPjbbzu"},{"type":"block","kind":"notebook-content","data":{},"children":[{"type":"paragraph","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"children":[{"type":"text","value":"You can verify the theorem using the JSXGraph app 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c","key":"fO3gPpnu1M"},{"type":"caption","children":[{"type":"paragraph","children":[{"type":"captionNumber","kind":"code","label":"code:length_of_hypotenuse","identifier":"code:length_of_hypotenuse","html_id":"code-length-of-hypotenuse","enumerator":"1","children":[{"type":"text","value":"Program ","key":"UnmsCjN2Z0"},{"type":"text","value":"1","key":"dmaVEx7hkY"},{"type":"text","value":":","key":"IF4stPZWTB"}],"template":"Program %s:","key":"LG4O8IQonq"},{"type":"text","value":"A function that computes the length of 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np.isclose(length_of_hypotenuse(0, 0), 0)\nassert np.isclose(length_of_hypotenuse(3, 4), 5)\nassert np.isclose(length_of_hypotenuse(4, 7), 8.06225774829855)","key":"zX7HrNR6Um"},{"type":"output","id":"5jxrJFzlgYt0HYiIfDEFu","data":[],"key":"wKGEWS1r5D"}],"key":"pHap45FSwG"},{"type":"block","kind":"notebook-code","data":{"deletable":false,"editable":false,"nbgrader":{"cell_type":"code","checksum":"291ad430a53d236e2c00e62a50467c4d","grade":true,"grade_id":"htest-length_of_hypotenus","locked":true,"points":1,"schema_version":3,"solution":false,"task":false}},"children":[{"type":"code","lang":"python","executable":true,"value":"# hidden tests","key":"RedR5kQdhE"},{"type":"output","id":"ZlgKfaRWUQKBes7be95E6","data":[],"key":"u5gQQ2xGGD"}],"key":"R0waGL7T5v"},{"type":"block","kind":"notebook-content","data":{},"children":[{"type":"admonition","kind":"tip","class":"dropdown","children":[{"type":"admonitionTitle","children":[{"type":"text","value":"If you are curious about the hidden 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calculator","align":"center","key":"XAUDDWycuU","urlSource":"images/hypotenuse-calculator.gif"},{"type":"caption","children":[{"type":"paragraph","position":{"start":{"line":6,"column":1},"end":{"line":6,"column":1}},"children":[{"type":"captionNumber","kind":"figure","label":"fig:hypotenuse-calculator","identifier":"fig:hypotenuse-calculator","html_id":"fig-hypotenuse-calculator","enumerator":"1","children":[{"type":"text","value":"Figure ","key":"wiRkokoyUk"},{"type":"text","value":"1","key":"iC6NE9NEe9"},{"type":"text","value":":","key":"LMt5fwjIf9"}],"template":"Figure %s:","key":"ST5geetC3X"},{"type":"text","value":"Illustration of the hypotenuse calculator","position":{"start":{"line":6,"column":1},"end":{"line":6,"column":1}},"key":"pg5ClwKFAM"}],"key":"kivVBxXJcU"}],"key":"RgDiR5yBWM"}],"label":"fig:hypotenuse-calculator","identifier":"fig:hypotenuse-calculator","enumerator":"1","html_id":"fig-hypotenuse-calculator","key":"ylBZwtmeQ0"}],"key":"M4pKkLj5mc"},{"type":"block","kind":"notebook-code","data":{"code_folding":[],"slideshow":{"slide_type":"-"}},"children":[{"type":"code","lang":"python","executable":true,"value":"# hypotenuse calculator\n@interact(a=(0, 10, 1), b=(0, 10, 1))\ndef calculate_hypotenuse(a=3, b=4):\n    print('c: {:.2f}'.format(length_of_hypotenuse(a, b)))","key":"MqLPu4T7K9"},{"type":"output","id":"-LveVcUaT4s7W_H2UxX1a","data":[],"key":"NuGRXKSIa1"}],"key":"DoBGFDCQgB"},{"type":"block","kind":"notebook-content","data":{"slideshow":{"slide_type":"slide"}},"children":[{"type":"heading","depth":2,"position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"children":[{"type":"text","value":"Quadratic Equation","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"s7K4YKsrVy"}],"identifier":"quadratic-equation","label":"Quadratic Equation","html_id":"quadratic-equation","implicit":true,"key":"fmBzqbD653"}],"key":"v9HYWgzpbo"},{"type":"block","kind":"notebook-content","data":{"slideshow":{"slide_type":"subslide"}},"children":[{"type":"heading","depth":3,"position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"children":[{"type":"text","value":"Graphical Calculator for 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calculator","align":"center","key":"MrlTL8FAbM","urlSource":"images/plot_parabola.gif"},{"type":"caption","children":[{"type":"paragraph","position":{"start":{"line":6,"column":1},"end":{"line":6,"column":1}},"children":[{"type":"captionNumber","kind":"figure","label":"fig:parabola","identifier":"fig:parabola","html_id":"fig-parabola","enumerator":"2","children":[{"type":"text","value":"Figure ","key":"oKQyynTYuV"},{"type":"text","value":"2","key":"ZG8eeQdGtf"},{"type":"text","value":":","key":"FJD1vnC6wr"}],"template":"Figure %s:","key":"pLojGIHs1f"},{"type":"text","value":"Illustration of the parabola calculator","position":{"start":{"line":6,"column":1},"end":{"line":6,"column":1}},"key":"sRJCzX1pGM"}],"key":"FZK9iWJ3n7"}],"key":"POtYIHL9br"}],"label":"fig:parabola","identifier":"fig:parabola","enumerator":"2","html_id":"fig-parabola","key":"fDA14kMG21"}],"key":"hdhJztRmYn"},{"type":"block","kind":"notebook-content","data":{"slideshow":{"slide_type":"subslide"}},"children":[{"type":"proof","kind":"definition","label":"def:parabola","identifier":"def:parabola","enumerated":true,"children":[{"type":"admonitionTitle","children":[{"type":"text","value":"Parabola","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"klfcxlYmRL"}],"key":"U7cpouC1mL"},{"type":"paragraph","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"children":[{"type":"text","value":"The collection of points ","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"QVkpOmxt0d"},{"type":"inlineMath","value":"(x,y)","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"html":"<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mo stretchy=\"false\">(</mo><mi>x</mi><mo separator=\"true\">,</mo><mi>y</mi><mo stretchy=\"false\">)</mo></mrow><annotation encoding=\"application/x-tex\">(x,y)</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"></span><span class=\"mopen\">(</span><span class=\"mord mathnormal\">x</span><span class=\"mpunct\">,</span><span class=\"mspace\" style=\"margin-right:0.1667em;\"></span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y</span><span class=\"mclose\">)</span></span></span></span>","key":"gtYTqLFla4"},{"type":"text","value":" satisfying the following equation forms a ","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"aY5eU8GBgx"},{"type":"emphasis","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"children":[{"type":"text","value":"parabola","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"ZEBijI9wFt"}],"key":"zfox20MqGk"},{"type":"text","value":":","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"PMiRaMUK7l"}],"key":"fNEqyaB3cy"},{"type":"math","identifier":"eq:parabola","label":"eq:parabola","html_id":"eq-parabola","value":"y=ax^2+bx+c","position":{"start":{"line":6,"column":1},"end":{"line":8,"column":1}},"html":"<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><semantics><mrow><mi>y</mi><mo>=</mo><mi>a</mi><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mi>x</mi><mo>+</mo><mi>c</mi></mrow><annotation encoding=\"application/x-tex\">y=ax^2+bx+c</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.625em;vertical-align:-0.1944em;\"></span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y</span><span class=\"mspace\" style=\"margin-right:0.2778em;\"></span><span class=\"mrel\">=</span><span class=\"mspace\" style=\"margin-right:0.2778em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.9474em;vertical-align:-0.0833em;\"></span><span class=\"mord mathnormal\">a</span><span class=\"mord\"><span class=\"mord mathnormal\">x</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2</span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.7778em;vertical-align:-0.0833em;\"></span><span class=\"mord mathnormal\">b</span><span class=\"mord mathnormal\">x</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.4306em;\"></span><span class=\"mord mathnormal\">c</span></span></span></span></span>","enumerator":"2","key":"nd2wEQXIXh"},{"type":"paragraph","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"children":[{"type":"text","value":"where ","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"OSavw84Btu"},{"type":"inlineMath","value":"a","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"html":"<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi>a</mi></mrow><annotation encoding=\"application/x-tex\">a</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.4306em;\"></span><span class=\"mord mathnormal\">a</span></span></span></span>","key":"LfQUbtHbbm"},{"type":"text","value":", ","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"Y2WowZUSxN"},{"type":"inlineMath","value":"b","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"html":"<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi>b</mi></mrow><annotation encoding=\"application/x-tex\">b</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.6944em;\"></span><span class=\"mord mathnormal\">b</span></span></span></span>","key":"l3snOaM300"},{"type":"text","value":", and ","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"Wgc3ZkuYWN"},{"type":"inlineMath","value":"c","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"html":"<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi>c</mi></mrow><annotation encoding=\"application/x-tex\">c</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.4306em;\"></span><span class=\"mord mathnormal\">c</span></span></span></span>","key":"KtBkBJ38PG"},{"type":"text","value":" are real numbers called the ","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"FL0BQk31SW"},{"type":"emphasis","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"children":[{"type":"text","value":"coefficients","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"H6AlgbKh44"}],"key":"hpn4hkpgLB"},{"type":"text","value":".","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"wNEmqVDUuB"}],"key":"MM51RA2aBN"}],"enumerator":"1","html_id":"def-parabola","key":"KGqZoOzEzv"}],"key":"ftVZ9bQwMw"},{"type":"block","kind":"notebook-content","data":{},"children":[{"type":"paragraph","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"children":[{"type":"text","value":"The following plots the parabola with difference choices of coefficients.","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"ygkYI5aKgj"}],"key":"etXkX58dsj"}],"key":"UWX11m2dqt"},{"type":"block","kind":"notebook-code","data":{},"children":[{"type":"code","lang":"python","executable":true,"value":"jsxgraphs.parabola","key":"Euldeg9dDb"},{"type":"output","id":"8TDQPRzgRqYEIzbGT4A2I","data":[],"key":"O6TNHBMNgi"}],"key":"Wj0pStRUF0"},{"type":"block","kind":"notebook-content","data":{"slideshow":{"slide_type":"fragment"}},"children":[{"type":"exercise","label":"ex:parabola","identifier":"ex:parabola","enumerated":true,"children":[{"type":"paragraph","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"children":[{"type":"text","value":"Given the variables ","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"puPeFVRCdH"},{"type":"inlineCode","value":"x","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"ZKE3ZDmlvi"},{"type":"text","value":", 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class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi>x</mi></mrow><annotation encoding=\"application/x-tex\">x</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.4306em;\"></span><span class=\"mord mathnormal\">x</span></span></span></span>","key":"lzscg5dgEf"},{"type":"text","value":"-coordinate and the coefficients ","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"SVIF0hK6dQ"},{"type":"inlineMath","value":"a","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"html":"<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi>a</mi></mrow><annotation encoding=\"application/x-tex\">a</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.4306em;\"></span><span class=\"mord mathnormal\">a</span></span></span></span>","key":"aS8sA078QO"},{"type":"text","value":", ","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"bUK5jtC1HO"},{"type":"inlineMath","value":"b","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"html":"<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi>b</mi></mrow><annotation encoding=\"application/x-tex\">b</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.6944em;\"></span><span class=\"mord mathnormal\">b</span></span></span></span>","key":"tbS6XwoFEe"},{"type":"text","value":", and ","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"jtfyuRCBjZ"},{"type":"inlineMath","value":"c","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"html":"<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi>c</mi></mrow><annotation encoding=\"application/x-tex\">c</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.4306em;\"></span><span class=\"mord mathnormal\">c</span></span></span></span>","key":"fYk6bHwSxh"},{"type":"text","value":" respectively, assign ","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"SZockQghJ6"},{"type":"inlineCode","value":"y","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"sVB95aQXL1"},{"type":"text","value":" the corresponding ","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"htH9xOrA2s"},{"type":"inlineMath","value":"y","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"html":"<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi>y</mi></mrow><annotation encoding=\"application/x-tex\">y</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.625em;vertical-align:-0.1944em;\"></span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y</span></span></span></span>","key":"D8T161lGTJ"},{"type":"text","value":"-coordinate of the parabola ","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"aXkXcjsO1G"},{"type":"crossReference","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"children":[{"type":"text","value":"(","key":"RcIDc0x0MZ"},{"type":"text","value":"2","key":"N2C1ZPjCuB"},{"type":"text","value":")","key":"U52coNYvn4"}],"identifier":"eq:parabola","label":"eq:parabola","kind":"equation","template":"(%s)","enumerator":"2","resolved":true,"html_id":"eq-parabola","key":"HGL30XNIWv"},{"type":"text","value":".","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"H53LvZySir"}],"key":"wBkwVqFgMd"}],"enumerator":"2","html_id":"ex-parabola","key":"s6oTeY2GAe"}],"key":"Vw2FW6Xv0S"},{"type":"block","kind":"notebook-code","data":{"deletable":false,"nbgrader":{"cell_type":"code","checksum":"0c4ec83c059ff5e7eb8cce679873d361","grade":false,"grade_id":"get_y","locked":false,"schema_version":3,"solution":true,"task":false},"slideshow":{"slide_type":"-"}},"children":[{"type":"code","lang":"python","executable":true,"value":"def get_y(x, a, b, c):\n    # YOUR CODE HERE\n    raise NotImplementedError\n    return y","key":"bqkYyl1unG"},{"type":"output","id":"pflTlkNjCMa8JawYz94e_","data":[],"key":"E34XEqeTi0"}],"key":"aEI0K19iUD"},{"type":"block","kind":"notebook-content","data":{},"children":[{"type":"paragraph","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"children":[{"type":"text","value":"To test your code:","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"gLdJmxf8bp"}],"key":"bAKxwnnBNO"}],"key":"nkeR7nIRt9"},{"type":"block","kind":"notebook-code","data":{"code_folding":[],"deletable":false,"editable":false,"nbgrader":{"cell_type":"code","checksum":"baf7164d7d7a36ebda475ef4f4bb89b7","grade":true,"grade_id":"test-get_y","locked":true,"points":1,"schema_version":3,"solution":false,"task":false},"slideshow":{"slide_type":"fragment"}},"children":[{"type":"code","lang":"python","executable":true,"value":"# tests\nassert np.isclose(get_y(0, 0, 0, 0), 0)\nassert np.isclose(get_y(0, 1, 2, 1), 1)\nassert np.isclose(get_y(0, 2, 1, 2), 2)\nassert np.isclose(get_y(1.2, 2, 3, 4), 10.48)\nassert np.isclose(get_y(2, 3.3, 4, 5), 26.2)\nassert np.isclose(get_y(3, 4.4, 5, 6), 60.6)","key":"EqKg80G5zF"},{"type":"output","id":"Br-te3CpbQ_cXiQl4Wl5D","data":[],"key":"wh6KaMpBiX"}],"key":"JbsYXgk0L9"},{"type":"block","kind":"notebook-code","data":{"deletable":false,"editable":false,"nbgrader":{"cell_type":"code","checksum":"0adfafae7b0307eb4e3a7be0bd936147","grade":true,"grade_id":"htest-get_y","locked":true,"points":1,"schema_version":3,"solution":false,"task":false}},"children":[{"type":"code","lang":"python","executable":true,"value":"# hidden tests","key":"BSj3YMAkxl"},{"type":"output","id":"j3ivoARJ5Bp4Qf7isrCX7","data":[],"key":"RPArKola9k"}],"key":"IJvnUQDur1"},{"type":"block","kind":"notebook-content","data":{},"children":[{"type":"paragraph","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"children":[{"type":"text","value":"To run the graphical calculator illustrate in ","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"noLRBN4R8i"},{"type":"crossReference","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"children":[{"type":"text","value":"Figure ","key":"OXUoQISrjd"},{"type":"text","value":"2","key":"buSLHx6h9l"}],"identifier":"fig:parabola","label":"fig:parabola","kind":"figure","template":"Figure %s","enumerator":"2","resolved":true,"html_id":"fig-parabola","key":"zYplJWX4VJ"},{"type":"text","value":":","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"Wfgc80DGQN"}],"key":"emr8wHwOma"}],"key":"qHtHvD8aRV"},{"type":"block","kind":"notebook-code","data":{"code_folding":[],"slideshow":{"slide_type":"subslide"}},"children":[{"type":"code","lang":"python","executable":true,"value":"# graphical calculator for parabola\nfig, ax = plt.subplots()\nxmin, xmax, ymin, ymax, resolution = -10, 10, -10, 10, 50\nx = np.linspace(xmin, xmax, resolution)\nax.set_title(r\"$y=ax^2+bx+c$\")\nax.set_xlabel(r\"$x$\")\nax.set_ylabel(r\"$y$\")\nax.set_xlim([xmin, xmax])\nax.set_ylim([ymin, ymax])\nax.grid()\n(p,) = ax.plot(x, get_y(x, 0, 0, 0))\n\n\n@interact(a=(-10, 10, 1), b=(-10, 10, 1), c=(-10, 10, 1))\ndef plot_parabola(a, b, c):\n    p.set_ydata(get_y(x, a, b, c))","key":"L2QdMagEfd"},{"type":"output","id":"UvE9XXWR-YX5GpDnagheo","data":[],"key":"mKcV7yPXZo"}],"key":"NSqCGovZ6b"},{"type":"block","kind":"notebook-content","data":{"slideshow":{"slide_type":"slide"}},"children":[{"type":"heading","depth":3,"position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"children":[{"type":"text","value":"Quadratic Equation Solver","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"yuvWwsttJJ"}],"identifier":"quadratic-equation-solver","label":"Quadratic Equation 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quadratic equation solver","position":{"start":{"line":6,"column":1},"end":{"line":6,"column":1}},"key":"exoN3FY9SF"}],"key":"YyZbXpGQ5x"}],"key":"iXFVYUOWCF"}],"label":"fig:quadratic","identifier":"fig:quadratic","enumerator":"3","html_id":"fig-quadratic","key":"ZbEJutZGHJ"}],"key":"MoKgpvuAXP"},{"type":"block","kind":"notebook-content","data":{"slideshow":{"slide_type":"subslide"}},"children":[{"type":"proof","kind":"proposition","label":"quadratic","identifier":"quadratic","enumerated":true,"children":[{"type":"admonitionTitle","children":[{"type":"text","value":"quadratic equation","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"L1Y4MvKmkj"}],"key":"UNngezdYrv"},{"type":"paragraph","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"children":[{"type":"text","value":"For the quadratic equation","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"BJAz5j3Puy"}],"key":"CfcDUtnw5m"},{"type":"math","identifier":"eq:quadratic","label":"eq:quadratic","html_id":"eq-quadratic","value":"ax^2+bx+c=0,","position":{"start":{"line":6,"column":1},"end":{"line":8,"column":1}},"html":"<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><semantics><mrow><mi>a</mi><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mi>x</mi><mo>+</mo><mi>c</mi><mo>=</mo><mn>0</mn><mo separator=\"true\">,</mo></mrow><annotation encoding=\"application/x-tex\">ax^2+bx+c=0,</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.9474em;vertical-align:-0.0833em;\"></span><span class=\"mord mathnormal\">a</span><span class=\"mord\"><span class=\"mord mathnormal\">x</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2</span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.7778em;vertical-align:-0.0833em;\"></span><span class=\"mord mathnormal\">b</span><span class=\"mord mathnormal\">x</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.4306em;\"></span><span class=\"mord mathnormal\">c</span><span class=\"mspace\" style=\"margin-right:0.2778em;\"></span><span class=\"mrel\">=</span><span class=\"mspace\" style=\"margin-right:0.2778em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\"></span><span class=\"mord\">0</span><span class=\"mpunct\">,</span></span></span></span></span>","enumerator":"3","key":"rHoZKxFNkJ"},{"type":"paragraph","position":{"start":{"line":9,"column":1},"end":{"line":9,"column":1}},"children":[{"type":"text","value":"the ","position":{"start":{"line":9,"column":1},"end":{"line":9,"column":1}},"key":"xFbA3fwXwc"},{"type":"emphasis","position":{"start":{"line":9,"column":1},"end":{"line":9,"column":1}},"children":[{"type":"text","value":"roots","position":{"start":{"line":9,"column":1},"end":{"line":9,"column":1}},"key":"j8wYb8yavh"}],"key":"aq09QdoWka"},{"type":"text","value":" (solutions for ","position":{"start":{"line":9,"column":1},"end":{"line":9,"column":1}},"key":"CJA6sYijcx"},{"type":"inlineMath","value":"x","position":{"start":{"line":9,"column":1},"end":{"line":9,"column":1}},"html":"<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi>x</mi></mrow><annotation encoding=\"application/x-tex\">x</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.4306em;\"></span><span class=\"mord mathnormal\">x</span></span></span></span>","key":"ZZRgIgULOx"},{"type":"text","value":") are give by","position":{"start":{"line":9,"column":1},"end":{"line":9,"column":1}},"key":"W4OLN7PgH6"}],"key":"Wi4m489k5X"},{"type":"math","identifier":"eq:quadratic_roots","label":"eq:quadratic_roots","html_id":"eq-quadratic-roots","value":"\\frac{-b-\\sqrt{b^2-4ac}}{2a},\\frac{-b+\\sqrt{b^2-4ac}}{2a}.","position":{"start":{"line":11,"column":1},"end":{"line":13,"column":1}},"html":"<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><semantics><mrow><mfrac><mrow><mo>−</mo><mi>b</mi><mo>−</mo><msqrt><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>a</mi><mi>c</mi></mrow></msqrt></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac><mo separator=\"true\">,</mo><mfrac><mrow><mo>−</mo><mi>b</mi><mo>+</mo><msqrt><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>a</mi><mi>c</mi></mrow></msqrt></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac><mi mathvariant=\"normal\">.</mi></mrow><annotation encoding=\"application/x-tex\">\\frac{-b-\\sqrt{b^2-4ac}}{2a},\\frac{-b+\\sqrt{b^2-4ac}}{2a}.</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:2.2764em;vertical-align:-0.686em;\"></span><span class=\"mord\"><span class=\"mopen nulldelimiter\"></span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.5904em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"></span><span class=\"mord\"><span class=\"mord\">2</span><span class=\"mord mathnormal\">a</span></span></span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"></span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"></span></span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"></span><span class=\"mord\"><span class=\"mord\">−</span><span class=\"mord mathnormal\">b</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">−</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9134em;\"><span class=\"svg-align\" style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"></span><span class=\"mord\" style=\"padding-left:0.833em;\"><span class=\"mord\"><span class=\"mord mathnormal\">b</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7401em;\"><span style=\"top:-2.989em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2</span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">−</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mord\">4</span><span class=\"mord mathnormal\">a</span><span class=\"mord mathnormal\">c</span></span></span><span style=\"top:-2.8734em;\"><span class=\"pstrut\" style=\"height:3em;\"></span><span class=\"hide-tail\" style=\"min-width:0.853em;height:1.08em;\"><svg xmlns=\"http://www.w3.org/2000/svg\" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 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class=\"frac-line\" style=\"border-bottom-width:0.04em;\"></span></span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"></span><span class=\"mord\"><span class=\"mord\">−</span><span class=\"mord mathnormal\">b</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9134em;\"><span class=\"svg-align\" style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"></span><span class=\"mord\" style=\"padding-left:0.833em;\"><span class=\"mord\"><span class=\"mord mathnormal\">b</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7401em;\"><span style=\"top:-2.989em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2</span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">−</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mord\">4</span><span class=\"mord mathnormal\">a</span><span class=\"mord mathnormal\">c</span></span></span><span style=\"top:-2.8734em;\"><span class=\"pstrut\" style=\"height:3em;\"></span><span class=\"hide-tail\" style=\"min-width:0.853em;height:1.08em;\"><svg xmlns=\"http://www.w3.org/2000/svg\" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z'/></svg></span></span></span><span class=\"vlist-s\">​</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1266em;\"><span></span></span></span></span></span></span></span></span><span class=\"vlist-s\">​</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.686em;\"><span></span></span></span></span></span><span class=\"mclose nulldelimiter\"></span></span><span class=\"mord\">.</span></span></span></span></span>","enumerator":"4","key":"KeXMCQ3gKF"}],"enumerator":"2","html_id":"quadratic","key":"GxCexL1zcT"}],"key":"DWPngmFHPl"},{"type":"block","kind":"notebook-content","data":{"slideshow":{"slide_type":"fragment"}},"children":[{"type":"exercise","label":"ex:roots","identifier":"ex:roots","enumerated":true,"children":[{"type":"admonitionTitle","children":[{"type":"text","value":"roots","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"tHiiAVPEKE"}],"key":"wJL2cKthWZ"},{"type":"paragraph","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"children":[{"type":"text","value":"Assign to ","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"pPqcVVlw5N"},{"type":"inlineCode","value":"root1","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"glVD85ylKA"},{"type":"text","value":" and ","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"RJCS10kFXA"},{"type":"inlineCode","value":"root2","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"aXUZgqXTGq"},{"type":"text","value":" the values of the first and second roots in ","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"h6EHxBXTdT"},{"type":"crossReference","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"children":[{"type":"text","value":"(","key":"wJATqW54ue"},{"type":"text","value":"4","key":"E4MCSVYgyM"},{"type":"text","value":")","key":"zGxLfKF9uk"}],"identifier":"eq:quadratic_roots","label":"eq:quadratic_roots","kind":"equation","template":"(%s)","enumerator":"4","resolved":true,"html_id":"eq-quadratic-roots","key":"mV502ILaH0"},{"type":"text","value":" above respectively.","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"kQ8z8FnOj2"}],"key":"V61ZOxeudJ"},{"type":"admonition","kind":"caution","children":[{"type":"admonitionTitle","children":[{"type":"text","value":"Caution","key":"gMGhyZhzpJ"}],"key":"XFZCB1FIbg"},{"type":"paragraph","position":{"start":{"line":8,"column":1},"end":{"line":8,"column":1}},"children":[{"type":"text","value":"Return the roots in the correct order and pay attention to the associativity of the arithmetic operators.","position":{"start":{"line":8,"column":1},"end":{"line":8,"column":1}},"key":"W7a3qsgeZ8"}],"key":"R2veV0f0DP"}],"key":"tTD3tbzuLk"}],"enumerator":"3","html_id":"ex-roots","key":"TCOcZf5Qzd"}],"key":"lT3dOxpbwa"},{"type":"block","kind":"notebook-code","data":{"deletable":false,"nbgrader":{"cell_type":"code","checksum":"1db489f1469d915b70a815912ce37c13","grade":false,"grade_id":"get_roots","locked":false,"schema_version":3,"solution":true,"task":false},"slideshow":{"slide_type":"fragment"}},"children":[{"type":"code","lang":"python","executable":true,"value":"def get_roots(a, b, c):\n    # YOUR CODE HERE\n    raise NotImplementedError\n    return root1, root2","key":"bXQWYoFZnH"},{"type":"output","id":"Jy9wGHlpos5aIarfRu3YL","data":[],"key":"TauVwE1cnS"}],"key":"JB38bzgN4U"},{"type":"block","kind":"notebook-content","data":{},"children":[{"type":"paragraph","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"children":[{"type":"text","value":"To test your code:","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"zOOWH6siFu"}],"key":"NVUEDB1kvX"}],"key":"re9hyt8IIt"},{"type":"block","kind":"notebook-code","data":{"code_folding":[],"deletable":false,"editable":false,"nbgrader":{"cell_type":"code","checksum":"1d32bad676d5099e00b47a6f7b479c7b","grade":true,"grade_id":"test-get_roots","locked":true,"points":1,"schema_version":3,"solution":false,"task":false},"slideshow":{"slide_type":"fragment"}},"children":[{"type":"code","lang":"python","executable":true,"value":"# tests\nassert np.isclose(get_roots(1, 1, 0), (-1.0, 0.0)).all()\nassert np.isclose(get_roots(1, 2, 1), (-1.0, -1.0)).all()\nassert np.isclose(get_roots(2, 2, 1), (-0.5 - 0.5j, -0.5 + 0.5j)).all()","key":"JNRpzgJsI1"},{"type":"output","id":"T-puNZYkdkfsjTUmF7A9l","data":[],"key":"AOBHbayePe"}],"key":"G0Q1RXQcua"},{"type":"block","kind":"notebook-code","data":{"deletable":false,"editable":false,"nbgrader":{"cell_type":"code","checksum":"79a531007ec3cae77b0a47be0ba9710c","grade":true,"grade_id":"htest-get_roots","locked":true,"points":1,"schema_version":3,"solution":false,"task":false}},"children":[{"type":"code","lang":"python","executable":true,"value":"# hidden tests","key":"lPaPwf9qjw"},{"type":"output","id":"tcl3ASbS92MPdw8_dpH6k","data":[],"key":"HnIgjI9QzK"}],"key":"deFUxa7ULk"},{"type":"block","kind":"notebook-content","data":{},"children":[{"type":"paragraph","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"children":[{"type":"text","value":"To run the calculator illustrated in ","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"MkX7OAdFrZ"},{"type":"crossReference","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"children":[{"type":"text","value":"Figure ","key":"jjVw7XcMHK"},{"type":"text","value":"3","key":"zivu7NOY9R"}],"identifier":"fig:quadratic","label":"fig:quadratic","kind":"figure","template":"Figure %s","enumerator":"3","resolved":true,"html_id":"fig-quadratic","key":"QS1hlok8sF"},{"type":"text","value":":","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"RmcuYsmzg3"}],"key":"kv3bM85ho6"}],"key":"QmfrJ7lsXX"},{"type":"block","kind":"notebook-code","data":{"code_folding":[0],"slideshow":{"slide_type":"fragment"}},"children":[{"type":"code","lang":"python","executable":true,"value":"# quadratic equations solver\n@interact(a=(-10,10,1),b=(-10,10,1),c=(-10,10,1))\ndef quadratic_equation_solver(a=1,b=2,c=1):\n    print('Roots: {}, {}'.format(*get_roots(a,b,c)))","key":"TPjRjDHgCe"},{"type":"output","id":"fexlkJLeyhLbAQMi3vK37","data":[],"key":"t9lbjaSTkf"}],"key":"xuPBZuqXvH"},{"type":"block","kind":"notebook-content","data":{"slideshow":{"slide_type":"slide"}},"children":[{"type":"heading","depth":2,"position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"children":[{"type":"text","value":"Number Conversion","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"JgZ7CZTgga"}],"identifier":"number-conversion","label":"Number Conversion","html_id":"number-conversion","implicit":true,"key":"baM0Ekhnmj"}],"key":"Y9HCNbGGxH"},{"type":"block","kind":"notebook-content","data":{"slideshow":{"slide_type":"subslide"}},"children":[{"type":"heading","depth":3,"position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"children":[{"type":"text","value":"Byte-to-Decimal Calculator","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"j2WAg4NYlU"}],"identifier":"byte-to-decimal-calculator","label":"Byte-to-Decimal Calculator","html_id":"byte-to-decimal-calculator","implicit":true,"key":"YSqI88j70T"}],"key":"JLNhjDvJiB"},{"type":"block","kind":"notebook-content","data":{"slideshow":{"slide_type":"-"}},"children":[{"type":"container","kind":"figure","children":[{"type":"image","url":"/~ccha23/cs1302_24a/build/byte-to-decimal-b273dac0fdd85a6a984acb30d084b16e.gif","alt":"The byte-to-decimal calculator","align":"center","key":"xozRc0l7Lc","urlSource":"images/byte-to-decimal.gif"},{"type":"caption","children":[{"type":"paragraph","position":{"start":{"line":6,"column":1},"end":{"line":6,"column":1}},"children":[{"type":"captionNumber","kind":"figure","label":"fig:byte-to-decimal","identifier":"fig:byte-to-decimal","html_id":"fig-byte-to-decimal","enumerator":"4","children":[{"type":"text","value":"Figure ","key":"wjvxYskD2f"},{"type":"text","value":"4","key":"m6HnaVPzPN"},{"type":"text","value":":","key":"YjgU285pt0"}],"template":"Figure %s:","key":"WOzNw2cAUO"},{"type":"text","value":"Illustration of the byte-to-decimal calculator","position":{"start":{"line":6,"column":1},"end":{"line":6,"column":1}},"key":"iPvir9Ytqz"}],"key":"f9ulgmHiUR"}],"key":"M18ezczWU7"}],"label":"fig:byte-to-decimal","identifier":"fig:byte-to-decimal","enumerator":"4","html_id":"fig-byte-to-decimal","key":"eBpbuv7MmE"}],"key":"y6ZLKXxj5d"},{"type":"block","kind":"notebook-content","data":{"slideshow":{"slide_type":"subslide"}},"children":[{"type":"paragraph","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"children":[{"type":"text","value":"Denote a binary number stored as a byte (","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"iFrVa6cv1z"},{"type":"text","value":"8","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"f6RAws7bwS"},{"type":"text","value":"-bit) as","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"aB09XUX638"}],"key":"v9h9U7U3bE"},{"type":"math","value":"b_7\\circ b_6\\circ b_5\\circ b_4\\circ b_3\\circ b_2\\circ b_1\\circ b_0,","position":{"start":{"line":3,"column":1},"end":{"line":5,"column":1}},"html":"<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><semantics><mrow><msub><mi>b</mi><mn>7</mn></msub><mo>∘</mo><msub><mi>b</mi><mn>6</mn></msub><mo>∘</mo><msub><mi>b</mi><mn>5</mn></msub><mo>∘</mo><msub><mi>b</mi><mn>4</mn></msub><mo>∘</mo><msub><mi>b</mi><mn>3</mn></msub><mo>∘</mo><msub><mi>b</mi><mn>2</mn></msub><mo>∘</mo><msub><mi>b</mi><mn>1</mn></msub><mo>∘</mo><msub><mi>b</mi><mn>0</mn></msub><mo separator=\"true\">,</mo></mrow><annotation encoding=\"application/x-tex\">b_7\\circ b_6\\circ b_5\\circ b_4\\circ b_3\\circ b_2\\circ b_1\\circ b_0,</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"></span><span class=\"mord\"><span class=\"mord mathnormal\">b</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">7</span></span></span></span><span class=\"vlist-s\">​</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">∘</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"></span><span class=\"mord\"><span class=\"mord mathnormal\">b</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">6</span></span></span></span><span class=\"vlist-s\">​</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">∘</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"></span><span class=\"mord\"><span class=\"mord mathnormal\">b</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">5</span></span></span></span><span class=\"vlist-s\">​</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">∘</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"></span><span class=\"mord\"><span class=\"mord mathnormal\">b</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">4</span></span></span></span><span class=\"vlist-s\">​</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">∘</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"></span><span class=\"mord\"><span class=\"mord mathnormal\">b</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3</span></span></span></span><span class=\"vlist-s\">​</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">∘</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"></span><span class=\"mord\"><span class=\"mord mathnormal\">b</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2</span></span></span></span><span class=\"vlist-s\">​</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">∘</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"></span><span class=\"mord\"><span class=\"mord mathnormal\">b</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1</span></span></span></span><span class=\"vlist-s\">​</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">∘</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\"></span><span class=\"mord\"><span class=\"mord mathnormal\">b</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0</span></span></span></span><span class=\"vlist-s\">​</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span></span></span></span></span></span></span><span class=\"mpunct\">,</span></span></span></span></span>","enumerator":"5","key":"aAY8sQKz44"},{"type":"paragraph","position":{"start":{"line":6,"column":1},"end":{"line":6,"column":1}},"children":[{"type":"text","value":"where ","position":{"start":{"line":6,"column":1},"end":{"line":6,"column":1}},"key":"IKHlNI97gK"},{"type":"text","value":"∘","position":{"start":{"line":6,"column":1},"end":{"line":6,"column":1}},"key":"hBkr3DGoCN"},{"type":"text","value":" concatenates ","position":{"start":{"line":6,"column":1},"end":{"line":6,"column":1}},"key":"VcG75748JS"},{"type":"inlineMath","value":"b_i","position":{"start":{"line":6,"column":1},"end":{"line":6,"column":1}},"html":"<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><msub><mi>b</mi><mi>i</mi></msub></mrow><annotation encoding=\"application/x-tex\">b_i</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"></span><span class=\"mord\"><span class=\"mord mathnormal\">b</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i</span></span></span></span><span class=\"vlist-s\">​</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span></span></span></span></span></span></span></span></span></span>","key":"gDO9xeJtOV"},{"type":"text","value":"’s together into a binary string.","position":{"start":{"line":6,"column":1},"end":{"line":6,"column":1}},"key":"wdILMSrWlL"}],"key":"usxo5IGkBI"}],"key":"UhaUb8NUKH"},{"type":"block","kind":"notebook-content","data":{"slideshow":{"slide_type":"fragment"}},"children":[{"type":"paragraph","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"children":[{"type":"text","value":"The binary string can be converted to a decimal number by the formula","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"x52Co5pFGw"}],"key":"LZq5dfXZvj"},{"type":"math","value":"b_7\\cdot 2^7 + b_6\\cdot 2^6 + b_5\\cdot 2^5 + b_4\\cdot 2^4 + b_3\\cdot 2^3 + b_2\\cdot 2^2 + b_1\\cdot 2^1 + b_0\\cdot 2^0.","position":{"start":{"line":3,"column":1},"end":{"line":5,"column":1}},"html":"<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><semantics><mrow><msub><mi>b</mi><mn>7</mn></msub><mo>⋅</mo><msup><mn>2</mn><mn>7</mn></msup><mo>+</mo><msub><mi>b</mi><mn>6</mn></msub><mo>⋅</mo><msup><mn>2</mn><mn>6</mn></msup><mo>+</mo><msub><mi>b</mi><mn>5</mn></msub><mo>⋅</mo><msup><mn>2</mn><mn>5</mn></msup><mo>+</mo><msub><mi>b</mi><mn>4</mn></msub><mo>⋅</mo><msup><mn>2</mn><mn>4</mn></msup><mo>+</mo><msub><mi>b</mi><mn>3</mn></msub><mo>⋅</mo><msup><mn>2</mn><mn>3</mn></msup><mo>+</mo><msub><mi>b</mi><mn>2</mn></msub><mo>⋅</mo><msup><mn>2</mn><mn>2</mn></msup><mo>+</mo><msub><mi>b</mi><mn>1</mn></msub><mo>⋅</mo><msup><mn>2</mn><mn>1</mn></msup><mo>+</mo><msub><mi>b</mi><mn>0</mn></msub><mo>⋅</mo><msup><mn>2</mn><mn>0</mn></msup><mi mathvariant=\"normal\">.</mi></mrow><annotation encoding=\"application/x-tex\">b_7\\cdot 2^7 + b_6\\cdot 2^6 + b_5\\cdot 2^5 + b_4\\cdot 2^4 + b_3\\cdot 2^3 + b_2\\cdot 2^2 + b_1\\cdot 2^1 + b_0\\cdot 2^0.</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"></span><span class=\"mord\"><span class=\"mord mathnormal\">b</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">7</span></span></span></span><span class=\"vlist-s\">​</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">⋅</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.9474em;vertical-align:-0.0833em;\"></span><span class=\"mord\"><span class=\"mord\">2</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">7</span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"></span><span class=\"mord\"><span class=\"mord mathnormal\">b</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">6</span></span></span></span><span class=\"vlist-s\">​</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">⋅</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.9474em;vertical-align:-0.0833em;\"></span><span class=\"mord\"><span class=\"mord\">2</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">6</span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"></span><span class=\"mord\"><span class=\"mord mathnormal\">b</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">5</span></span></span></span><span class=\"vlist-s\">​</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">⋅</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.9474em;vertical-align:-0.0833em;\"></span><span class=\"mord\"><span class=\"mord\">2</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">5</span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"></span><span class=\"mord\"><span class=\"mord mathnormal\">b</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">4</span></span></span></span><span class=\"vlist-s\">​</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">⋅</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.9474em;vertical-align:-0.0833em;\"></span><span class=\"mord\"><span class=\"mord\">2</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">4</span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"></span><span class=\"mord\"><span class=\"mord mathnormal\">b</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3</span></span></span></span><span class=\"vlist-s\">​</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">⋅</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.9474em;vertical-align:-0.0833em;\"></span><span class=\"mord\"><span class=\"mord\">2</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3</span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"></span><span class=\"mord\"><span class=\"mord mathnormal\">b</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2</span></span></span></span><span class=\"vlist-s\">​</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">⋅</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.9474em;vertical-align:-0.0833em;\"></span><span class=\"mord\"><span class=\"mord\">2</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2</span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"></span><span class=\"mord\"><span class=\"mord mathnormal\">b</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1</span></span></span></span><span class=\"vlist-s\">​</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">⋅</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.9474em;vertical-align:-0.0833em;\"></span><span class=\"mord\"><span class=\"mord\">2</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1</span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"></span><span class=\"mord\"><span class=\"mord mathnormal\">b</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0</span></span></span></span><span class=\"vlist-s\">​</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">⋅</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.8641em;\"></span><span class=\"mord\"><span class=\"mord\">2</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0</span></span></span></span></span></span></span></span><span class=\"mord\">.</span></span></span></span></span>","enumerator":"6","key":"FbOmsZtikf"}],"key":"bDKnhOT3EK"},{"type":"block","kind":"notebook-content","data":{"slideshow":{"slide_type":"fragment"}},"children":[{"type":"paragraph","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"children":[{"type":"text","value":"E.g., the binary string ","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"pWbJHy12oC"},{"type":"inlineCode","value":"'11111111'","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"EZiq9MP1U4"},{"type":"text","value":" is the largest integer represented by a byte:","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"Xp3QmjDVJw"}],"key":"xQbNWZhWaS"},{"type":"math","value":"2^7+2^6+2^5+2^4+2^3+2^2+2^1+2^0=255=2^8-1.","position":{"start":{"line":3,"column":1},"end":{"line":5,"column":1}},"html":"<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><semantics><mrow><msup><mn>2</mn><mn>7</mn></msup><mo>+</mo><msup><mn>2</mn><mn>6</mn></msup><mo>+</mo><msup><mn>2</mn><mn>5</mn></msup><mo>+</mo><msup><mn>2</mn><mn>4</mn></msup><mo>+</mo><msup><mn>2</mn><mn>3</mn></msup><mo>+</mo><msup><mn>2</mn><mn>2</mn></msup><mo>+</mo><msup><mn>2</mn><mn>1</mn></msup><mo>+</mo><msup><mn>2</mn><mn>0</mn></msup><mo>=</mo><mn>255</mn><mo>=</mo><msup><mn>2</mn><mn>8</mn></msup><mo>−</mo><mn>1.</mn></mrow><annotation encoding=\"application/x-tex\">2^7+2^6+2^5+2^4+2^3+2^2+2^1+2^0=255=2^8-1.</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.9474em;vertical-align:-0.0833em;\"></span><span class=\"mord\"><span class=\"mord\">2</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">7</span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.9474em;vertical-align:-0.0833em;\"></span><span class=\"mord\"><span class=\"mord\">2</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">6</span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.9474em;vertical-align:-0.0833em;\"></span><span class=\"mord\"><span class=\"mord\">2</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">5</span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.9474em;vertical-align:-0.0833em;\"></span><span class=\"mord\"><span class=\"mord\">2</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">4</span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.9474em;vertical-align:-0.0833em;\"></span><span class=\"mord\"><span class=\"mord\">2</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3</span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.9474em;vertical-align:-0.0833em;\"></span><span class=\"mord\"><span class=\"mord\">2</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2</span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.9474em;vertical-align:-0.0833em;\"></span><span class=\"mord\"><span class=\"mord\">2</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1</span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.8641em;\"></span><span class=\"mord\"><span class=\"mord\">2</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0</span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2778em;\"></span><span class=\"mrel\">=</span><span class=\"mspace\" style=\"margin-right:0.2778em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.6444em;\"></span><span class=\"mord\">255</span><span class=\"mspace\" style=\"margin-right:0.2778em;\"></span><span class=\"mrel\">=</span><span class=\"mspace\" style=\"margin-right:0.2778em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.9474em;vertical-align:-0.0833em;\"></span><span class=\"mord\"><span class=\"mord\">2</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">8</span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">−</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.6444em;\"></span><span class=\"mord\">1.</span></span></span></span></span>","enumerator":"7","key":"TlrxWVUAMb"}],"key":"bRV1s1wpzY"},{"type":"block","kind":"notebook-content","data":{"slideshow":{"slide_type":"fragment"}},"children":[{"type":"exercise","label":"exercise-W45D8zOYbn","identifier":"exercise-w45d8zoybn","enumerated":true,"children":[{"type":"paragraph","position":{"start":{"line":3,"column":1},"end":{"line":3,"column":1}},"children":[{"type":"text","value":"Assign to ","position":{"start":{"line":3,"column":1},"end":{"line":3,"column":1}},"key":"WEfXF1vXgN"},{"type":"inlineCode","value":"decimal","position":{"start":{"line":3,"column":1},"end":{"line":3,"column":1}},"key":"iV2pD7Ti9F"},{"type":"text","value":" the ","position":{"start":{"line":3,"column":1},"end":{"line":3,"column":1}},"key":"JKJybZYOXJ"},{"type":"emphasis","position":{"start":{"line":3,"column":1},"end":{"line":3,"column":1}},"children":[{"type":"text","value":"integer","position":{"start":{"line":3,"column":1},"end":{"line":3,"column":1}},"key":"F9OE5bPexg"}],"key":"twUReiG8uf"},{"type":"text","value":" value represented by the binary sequence ","position":{"start":{"line":3,"column":1},"end":{"line":3,"column":1}},"key":"mqRsyYCVaj"},{"type":"inlineCode","value":"b7,b6,b5,b4,b3,b2,b1,b0","position":{"start":{"line":3,"column":1},"end":{"line":3,"column":1}},"key":"NdZ0UXZtQq"},{"type":"text","value":" of ","position":{"start":{"line":3,"column":1},"end":{"line":3,"column":1}},"key":"kr1kJxYvr0"},{"type":"emphasis","position":{"start":{"line":3,"column":1},"end":{"line":3,"column":1}},"children":[{"type":"text","value":"characters","position":{"start":{"line":3,"column":1},"end":{"line":3,"column":1}},"key":"bj8X9wbIL8"}],"key":"azstHiam5I"},{"type":"text","value":" ","position":{"start":{"line":3,"column":1},"end":{"line":3,"column":1}},"key":"MCyHVtix4a"},{"type":"inlineCode","value":"'0'","position":{"start":{"line":3,"column":1},"end":{"line":3,"column":1}},"key":"OYGilOXdD1"},{"type":"text","value":" or ","position":{"start":{"line":3,"column":1},"end":{"line":3,"column":1}},"key":"n5jdSdOdoV"},{"type":"inlineCode","value":"'1'","position":{"start":{"line":3,"column":1},"end":{"line":3,"column":1}},"key":"k7J1BHlfnY"},{"type":"text","value":".","position":{"start":{"line":3,"column":1},"end":{"line":3,"column":1}},"key":"IQohN9Y1RH"}],"key":"CBKSE2Wx7c"}],"enumerator":"4","html_id":"exercise-w45d8zoybn","key":"uh5HjqTjFh"}],"key":"jT5dD6xpnj"},{"type":"block","kind":"notebook-code","data":{"deletable":false,"nbgrader":{"cell_type":"code","checksum":"633bf6ad7d72799a2088df62acc03ff2","grade":false,"grade_id":"byte_to_decimal","locked":false,"schema_version":3,"solution":true,"task":false},"slideshow":{"slide_type":"fragment"}},"children":[{"type":"code","lang":"python","executable":true,"value":"def byte_to_decimal(b7, b6, b5, b4, b3, b2, b1, b0):\n    \"\"\"\n    Parameters\n    ----------\n    b7, ..., b0: single characters either '0' or '1'.\n    \"\"\"\n    # YOUR CODE HERE\n    raise NotImplementedError\n    return decimal","key":"b7PT023Smk"},{"type":"output","id":"KnY9EZcD7zQMiLMken3k_","data":[],"key":"Xe9zwzBOXq"}],"key":"ULOVR4Rqt4"},{"type":"block","kind":"notebook-content","data":{},"children":[{"type":"paragraph","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"children":[{"type":"text","value":"To test your code:","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"l9hotcKx3u"}],"key":"EGGg5hAAXv"}],"key":"r4nc8FA80C"},{"type":"block","kind":"notebook-code","data":{"code_folding":[0],"deletable":false,"editable":false,"nbgrader":{"cell_type":"code","checksum":"22ecacb91d8ae70a0541dca75c3737a9","grade":true,"grade_id":"test-byte_to_decimal","locked":true,"points":1,"schema_version":3,"solution":false,"task":false},"slideshow":{"slide_type":"fragment"}},"children":[{"type":"code","lang":"python","executable":true,"value":"# tests\ndef test_byte_to_decimal(decimal, b7, b6, b5, b4, b3, b2, b1, b0):\n    decimal_ = byte_to_decimal(b7, b6, b5, b4, b3, b2, b1, b0)\n    assert decimal == decimal_ and isinstance(decimal_, int)\n\n\ntest_byte_to_decimal(38, \"0\", \"0\", \"1\", \"0\", \"0\", \"1\", \"1\", \"0\")\ntest_byte_to_decimal(20, \"0\", \"0\", \"0\", \"1\", \"0\", \"1\", \"0\", \"0\")\ntest_byte_to_decimal(22, \"0\", \"0\", \"0\", \"1\", \"0\", \"1\", \"1\", \"0\")\ntest_byte_to_decimal(146, '1', '0', '0', '1', '0', '0', '1', '0')\ntest_byte_to_decimal(128, '1', '0', '0', '0', '0', '0', '0', '0')\ntest_byte_to_decimal(71, '0', '1', '0', '0', '0', '1', '1', '1')","key":"sLShhIDaSE"},{"type":"output","id":"Eh-cMVmuimwig2EUN2NWP","data":[],"key":"sHozKZXjzW"}],"key":"fokosjekcc"},{"type":"block","kind":"notebook-code","data":{"deletable":false,"editable":false,"nbgrader":{"cell_type":"code","checksum":"368a00935ff0f11755434b00e27eeaff","grade":true,"grade_id":"htest-byte_to_decimal","locked":true,"points":1,"schema_version":3,"solution":false,"task":false}},"children":[{"type":"code","lang":"python","executable":true,"value":"# hidden tests","key":"UfA8ozRENi"},{"type":"output","id":"u-2IGCJMKkO40C6-jOPsG","data":[],"key":"LglWMXx3yG"}],"key":"yOXiVU3Qs4"},{"type":"block","kind":"notebook-content","data":{},"children":[{"type":"paragraph","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"children":[{"type":"text","value":"To run the calculator illustrate in ","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"GictvkrmpR"},{"type":"crossReference","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"children":[{"type":"text","value":"Figure ","key":"zhq54y69fR"},{"type":"text","value":"4","key":"PG0EbV3m3d"}],"identifier":"fig:byte-to-decimal","label":"fig:byte-to-decimal","kind":"figure","template":"Figure %s","enumerator":"4","resolved":true,"html_id":"fig-byte-to-decimal","key":"BRcxRgQSil"},{"type":"text","value":":","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"lFxWetlIIj"}],"key":"v4P3dIbQWk"}],"key":"GY72Eksf2o"},{"type":"block","kind":"notebook-code","data":{"code_folding":[0]},"children":[{"type":"code","lang":"python","executable":true,"value":"# byte-to-decimal calculator\nbit = ['0', '1']\n\n\n@interact(b7=bit, b6=bit, b5=bit, b4=bit, b3=bit, b2=bit, b1=bit, b0=bit)\ndef convert_byte_to_decimal(b7, b6, b5, b4, b3, b2, b1, b0):\n    print('decimal:', byte_to_decimal(b7, b6, b5, b4, b3, b2, b1, b0))","key":"NZj2JrLnKi"},{"type":"output","id":"9PAXq3s5iYubm5UggX1FO","data":[],"key":"bdjaQtwljQ"}],"key":"E7uKxMYQkE"},{"type":"block","kind":"notebook-content","data":{"slideshow":{"slide_type":"subslide"}},"children":[{"type":"heading","depth":3,"position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"children":[{"type":"text","value":"Decimal-to-Byte Calculator","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"Ma1AEd5GWf"}],"identifier":"decimal-to-byte-calculator","label":"Decimal-to-Byte Calculator","html_id":"decimal-to-byte-calculator","implicit":true,"key":"dCo4adFM5k"}],"key":"jFD45VTOCw"},{"type":"block","kind":"notebook-content","data":{"slideshow":{"slide_type":"-"}},"children":[{"type":"container","kind":"figure","children":[{"type":"image","url":"/~ccha23/cs1302_24a/build/decimal-to-byte-170d5f683e6b6bca6dfb693303a02fab.gif","alt":"The decimal-to-byte calculator","align":"center","key":"HFbXZzMIE2","urlSource":"images/decimal-to-byte.gif"},{"type":"caption","children":[{"type":"paragraph","position":{"start":{"line":6,"column":1},"end":{"line":6,"column":1}},"children":[{"type":"captionNumber","kind":"figure","label":"fig:decimal-to-byte","identifier":"fig:decimal-to-byte","html_id":"fig-decimal-to-byte","enumerator":"5","children":[{"type":"text","value":"Figure ","key":"MVjuQdBO5x"},{"type":"text","value":"5","key":"PNr0INhl9O"},{"type":"text","value":":","key":"C5LprCXxvT"}],"template":"Figure %s:","key":"pyVJhAd8lC"},{"type":"text","value":"Illustration of the decimal-to-byte calculator","position":{"start":{"line":6,"column":1},"end":{"line":6,"column":1}},"key":"uo3U4JEXFk"}],"key":"W6VxWopyHm"}],"key":"sNzlqDupOg"}],"label":"fig:decimal-to-byte","identifier":"fig:decimal-to-byte","enumerator":"5","html_id":"fig-decimal-to-byte","key":"QNXF0AqLOg"}],"key":"TmrOL61KF6"},{"type":"block","kind":"notebook-content","data":{"slideshow":{"slide_type":"subslide"}},"children":[{"type":"exercise","label":"ex:decimal-to-byte","identifier":"ex:decimal-to-byte","enumerated":true,"children":[{"type":"paragraph","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"children":[{"type":"text","value":"Assign to ","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"PMYvQrbYXO"},{"type":"inlineCode","value":"byte","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"cfMtTfWlQZ"},{"type":"text","value":" a ","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"yEO3ijxinC"},{"type":"emphasis","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"children":[{"type":"text","value":"string of 8 bits","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"NXLKekBSc5"}],"key":"WIUzxVErbU"},{"type":"text","value":" that represents the value of ","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"pYAPDHhshv"},{"type":"inlineCode","value":"decimal","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"ycuSM3zOu1"},{"type":"text","value":", a non-negative decimal integer from ","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"Evb7VAL6e9"},{"type":"text","value":"0","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"IZfypiO9QW"},{"type":"text","value":" to ","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"u6gzfO3rcO"},{"type":"inlineMath","value":"2^8-1=255","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"html":"<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><msup><mn>2</mn><mn>8</mn></msup><mo>−</mo><mn>1</mn><mo>=</mo><mn>255</mn></mrow><annotation encoding=\"application/x-tex\">2^8-1=255</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8974em;vertical-align:-0.0833em;\"></span><span class=\"mord\"><span class=\"mord\">2</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">8</span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">−</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.6444em;\"></span><span class=\"mord\">1</span><span class=\"mspace\" style=\"margin-right:0.2778em;\"></span><span class=\"mrel\">=</span><span class=\"mspace\" style=\"margin-right:0.2778em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.6444em;\"></span><span class=\"mord\">255</span></span></span></span>","key":"jzWmpZkKm5"},{"type":"text","value":".","position":{"start":{"line":4,"column":1},"end":{"line":4,"column":1}},"key":"AqbBbw9IJR"}],"key":"S2p993CwkM"},{"type":"admonition","kind":"important","children":[{"type":"admonitionTitle","children":[{"type":"text","value":"Important","key":"mQE0RljLt3"}],"key":"CTLaA597JM"},{"type":"paragraph","position":{"start":{"line":8,"column":1},"end":{"line":8,"column":1}},"children":[{"type":"text","value":"Use the operators ","position":{"start":{"line":8,"column":1},"end":{"line":8,"column":1}},"key":"rprAEAk8Ax"},{"type":"inlineCode","value":"//","position":{"start":{"line":8,"column":1},"end":{"line":8,"column":1}},"key":"QDkKvPTact"},{"type":"text","value":" and ","position":{"start":{"line":8,"column":1},"end":{"line":8,"column":1}},"key":"ldvCBq595g"},{"type":"inlineCode","value":"%","position":{"start":{"line":8,"column":1},"end":{"line":8,"column":1}},"key":"RHPlvFgAA3"},{"type":"text","value":", but not the function ","position":{"start":{"line":8,"column":1},"end":{"line":8,"column":1}},"key":"K2aNpYiGfU"},{"type":"inlineCode","value":"int","position":{"start":{"line":8,"column":1},"end":{"line":8,"column":1}},"key":"CTT9A6h2ky"},{"type":"text","value":".","position":{"start":{"line":8,"column":1},"end":{"line":8,"column":1}},"key":"WjqHHfcpcy"}],"key":"x8ZOUjOL1U"}],"key":"xjYDLjXHhn"}],"enumerator":"5","html_id":"ex-decimal-to-byte","key":"V6OWAk1Z2L"}],"key":"NSNRbyiWqx"},{"type":"block","kind":"notebook-code","data":{"deletable":false,"nbgrader":{"cell_type":"code","checksum":"9b3e6e3653b1d63abe3861a80376b740","grade":false,"grade_id":"decimal_to_byte","locked":false,"schema_version":3,"solution":true,"task":false},"slideshow":{"slide_type":"-"}},"children":[{"type":"code","lang":"python","executable":true,"value":"def decimal_to_byte(decimal):\n    # YOUR CODE HERE\n    raise NotImplementedError\n    return byte","key":"VJYGTKSg3X"},{"type":"output","id":"ZuX-QA0pjA_dHBKupb7JD","data":[],"key":"ECpILnxCjV"}],"key":"ibTWruynkT"},{"type":"block","kind":"notebook-content","data":{},"children":[{"type":"paragraph","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"children":[{"type":"text","value":"To test your code:","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"b0Xfkih2Sv"}],"key":"orwp7qMr8w"}],"key":"VhrWG4R7Qw"},{"type":"block","kind":"notebook-code","data":{"code_folding":[0],"deletable":false,"editable":false,"nbgrader":{"cell_type":"code","checksum":"9c9637c807d290cf78e639b74c45f3fe","grade":true,"grade_id":"test-decimal_to_byte","locked":true,"points":1,"schema_version":3,"solution":false,"task":false},"slideshow":{"slide_type":"fragment"}},"children":[{"type":"code","lang":"python","executable":true,"value":"# tests\ndef test_decimal_to_byte(byte, decimal):\n    byte_ = decimal_to_byte(decimal)\n    assert byte == byte_ and isinstance(byte, str) and len(byte) == 8\n\n\ntest_decimal_to_byte(\"01100111\", 103)\ntest_decimal_to_byte(\"00000011\", 3)\ntest_decimal_to_byte(\"00011100\", 28)\ntest_decimal_to_byte('11011111', 223)\ntest_decimal_to_byte('00000100', 4)\ntest_decimal_to_byte('10011001', 153)\n\n\ndef test_decimal_to_byte(byte,decimal):\n    byte_ = decimal_to_byte(decimal)\n    correct = byte == byte_ and isinstance(byte, str) and len(byte) == 8\n    if not correct:\n        print(\n            f'{decimal} should be represented as the byte {byte}, not {byte_}.'\n        )\n    assert correct\n\n\ntest_decimal_to_byte('01100111', 103)\ntest_decimal_to_byte('00000011', 3)\ntest_decimal_to_byte('00011100', 28)","key":"GAYPNHiej7"},{"type":"output","id":"9H1lm3VyeniCiTdB6OJTz","data":[],"key":"BjmJqCmjwd"}],"key":"gA2oGIbEX7"},{"type":"block","kind":"notebook-code","data":{"deletable":false,"editable":false,"nbgrader":{"cell_type":"code","checksum":"7f8a949776449868af9155c44585aa19","grade":true,"grade_id":"htest-decimal_to_byte","locked":true,"points":1,"schema_version":3,"solution":false,"task":false}},"children":[{"type":"code","lang":"python","executable":true,"value":"# hidden tests","key":"QZsmL2Yyyf"},{"type":"output","id":"cyWETMdB-TKJNe9PAcT79","data":[],"key":"GckNGEP4gD"}],"key":"qwUs29CBZP"},{"type":"block","kind":"notebook-content","data":{},"children":[{"type":"paragraph","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"children":[{"type":"text","value":"To run the calculator illustrated in ","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"B0LFe372X0"},{"type":"crossReference","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"children":[{"type":"text","value":"Figure ","key":"VFqt0QvIUB"},{"type":"text","value":"5","key":"GzvIfwwNZT"}],"identifier":"fig:decimal-to-byte","label":"fig:decimal-to-byte","kind":"figure","template":"Figure %s","enumerator":"5","resolved":true,"html_id":"fig-decimal-to-byte","key":"vQmuZg1hGJ"},{"type":"text","value":":","position":{"start":{"line":1,"column":1},"end":{"line":1,"column":1}},"key":"okOHDNsddw"}],"key":"zARDQuyf7w"}],"key":"o8I3WMKVh9"},{"type":"block","kind":"notebook-code","data":{"code_folding":[0],"slideshow":{"slide_type":"fragment"}},"children":[{"type":"code","lang":"python","executable":true,"value":"# decimal-to-byte calculator\n@interact(decimal=(0, 255, 1))\ndef convert_decimal_to_byte(decimal=0):\n    print(\"byte:\", decimal_to_byte(decimal))","key":"b9Op5XYCzf"},{"type":"output","id":"pfntES4zyjNL-3PzlJla3","data":[],"key":"SduXl0KYiP"}],"key":"PRUTVkFjSd"}],"key":"yvAz6FiMar"},"references":{"cite":{"order":[],"data":{}}},"footer":{"navigation":{"prev":{"title":"Expressions and Arithmetic","url":"/expressions-and-arithmetic","group":"Lecture 2"},"next":{"title":"Symbolic Calculators","url":"/symbolic-calculators","group":"Lab 2"}}},"domain":"http://localhost:3000"}