2b:null 2c:["$","title",null,{"children":"Position numeral system | Roman Samec | Observable"}] 31:T50b,graphViz = (tree) => { if (tree instanceof BinaryTree) { let result = `digraph{`; let count = 0; let traverse = (root) => { if (root.node) { if (root.node.left.node) { //result += `${root.node.entry.key} [label=${root.node.entry.toString()}]\n`; result += `${root.node.left.node.entry.key} [label="${root.node.left.node.entry.toString()}" shape=${root.node.left.node.entry.shape}]\n`; result += `<${root.node.entry.key}> -> <${root.node.left.node.entry.key}>;\n`; traverse(root.node.left) } else { // result += 'null'+(++count)+'[shape = none, label=""];\n'; // result += `< ${root.node.toString()} > -> ${'null'+count} [arrowhead="tee"];\n`; } if (root.node.right.node) { result += `${root.node.right.node.entry.key} [label=${root.node.right.node.entry.toString()}]\n`; result += `<${root.node.entry.key}> -> <${root.node.right.node.entry.key}>;\n`; traverse(root.node.right); } else { // result += 'null'+(++count)+'[shape = none, label=""];\n'; // result += `< ${root.node.toString()} > -> ${'null'+count} [arrowhead="tee"];\n`; } } } traverse (tree) return result + "}" } }32:[] 2f:{"id":"6ae5f29817932e14","slug":"position-numeral-system","title":"Position numeral system","thumbnail":"f8dede634cb8b5e3c5c156176530e2cdb647b204906b8b62e40409782db16a3c","access_level":"public","create_time":"$D2021-10-28T16:41:37.213Z","update_time":"$D2022-07-23T10:41:01.468Z","view_time":null,"first_public_time":"$D2021-11-02T20:54:52.436Z","fork":{"id":"866c8c0dd5338d49","slug":"prime-numbers","title":"Prime numbers","owner":{"id":"4e8eb6188a86a7df","login":"rsamec","name":"Roman Samec"}},"stars":2,"starred":false,"owner":{"type":"team","id":"4e8eb6188a86a7df","login":"rsamec","name":"Roman Samec","avatar_url":"https://avatars-next.observableusercontent.com/4c48f0f4408a68e6e003e589591b7f0d1f94bed68ac1bb60eb91b7e498198ae5","tier":"starter_2024"},"version":3107,"publish_version":3107,"role":null,"authored":false,"authors":[{"type":"individual","id":"29741195570dd799","login":"rsamec","name":"Roman Samec","avatar_url":"https://avatars-next.observableusercontent.com/4c48f0f4408a68e6e003e589591b7f0d1f94bed68ac1bb60eb91b7e498198ae5","tier":null}],"members":[{"type":"individual","id":"29741195570dd799","login":"rsamec","name":"Roman Samec","avatar_url":"https://avatars-next.observableusercontent.com/4c48f0f4408a68e6e003e589591b7f0d1f94bed68ac1bb60eb91b7e498198ae5","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":1,"collection":null,"type":"notebook","body":{"title":"Position numeral system","cells":[{"id":0,"value":"# Position numeral system","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":2953,"value":"viewof inputNumber = Inputs.range([0,100000], {value: 928, step:1,label:\"Number\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2868,"value":"viewof inputBase = Inputs.select(new Map([['Binary',2],['Decimal',10]]),{value:10, label:\"Base of the num\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2989,"value":"### Decomposition\nA digit's value is the digit multiplied by the value of its place. ","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":3016,"value":"formatDecomposition(inputNumber,inputBase)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2871,"value":"draw(digitFactorsTree(inputNumber,inputBase))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2862,"value":"## Usage","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":3070,"value":"When you need to multiple two numbers, you decompose the digits of the second number (b) by its positions. The result is the sum of the multiplication results - the multiplication of the first number (a) * element of the decomposition of the second number (b).","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":3095,"value":"","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2413,"value":"viewof numbers= {\n const range = [1,100000]\n const inputs = [\n Inputs.range([...range], {value: 1111, step: 1, label:\"a\"}),\n Inputs.range([...range], {value: 11345, step:1, label:\"b\"}), \n ];\n const view = html`

${inputs}`;\n view.value = mergeInputs(inputs, []);\n return view;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":3087,"value":"formatDecomposition(numbers[1],10)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2198,"value":"formatMultipleNumbers(numbers[0],numbers[1])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2456,"value":"md`##### Utilities - decomposition`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2107,"value":"formatMultipleNumbers = (first, second) => {\n const borderTopStyle=\"border-top:1px solid black\";\n const array = decomposeNumberToArray(second, 10).map(\n (n, i, a) => n * first * Math.pow(10, a.length - (i + 1))\n );\n const inputNumbers = [first, second];\n return html`

\n${inputNumbers.map((n) => html.fragment`${n}
`)}\n${array.length > 1 ? array\n  .reverse()\n  .map((n, i) =>\n    i == 0\n      ? html.fragment`${n}
`\n      : html.fragment`${n}
`\n  ):''}\n${sum(array)}

`;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2028,"value":"formatDecomposition= (number, base) => {\n const array = decomposeNumberToArray(number,base);\n return tex`${decomposeNumberToArray(number,base).reduce((out, n,i,a) => out+= `${i!==0?' + ':''}(${n} * ${base}^{${a.length - (i+ 1)}})`,'')} = ${number}` \n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1974,"value":"composeArrayToNumber = (numberFactors, base) => {\n return sum(numberFactors.map((n,i,a) => n * Math.pow(base,a.length - (i+ 1))))\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1842,"value":"decomposeNumberToArray = (num,base) => {\n const digits = [];\n while (num > 0) {\n digits.push(num % base);\n num = Math.trunc(num / base);\n }\n //alternate\n //const digits = numbers[1].toString().split('').map(Number);\n return digits.reverse();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":49,"value":"digitFactorsTree = (num, base) => {\n const digits = decomposeNumberToArray(num, base);\n const sums = digits\n .map((v, i, a) => composeArrayToNumber(a.slice(a.length - (i + 1)), base))\n .reverse();\n return buildTree(\n digits.map((v, i, a) => [\n sums[i],\n v * Math.pow(base, a.length - (i + 1)), \n Math.pow(base, a.length - (i + 1)),\n v\n ]),\n 0,\n generatorFactory()\n );\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2372,"value":"sum = numbers => numbers.reduce((out,value) => out += value,0)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1296,"value":"multiple = numbers => numbers.reduce((out,value) => out *= value,1)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":61,"value":"function buildTree(factors, i, gen) {\n const current = factors[i];\n const next = factors[i + 1];\n return BT(\n new Entry(i === 0 ? current[0] : gen.next().value, current[0]),\n BT(\n new Entry(gen.next().value, `${current[3]} * ${current[2]}`, \"record\"),\n BT(),\n BT()\n ),\n next != null\n ? buildTree(factors, i + 1, gen)\n : BT(new Entry(gen.next().value, 0), BT(), BT())\n );\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":3106,"value":"","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2688,"value":"generatorFactory = () => { \n function* nextId() {\n let i = 1000;\n while (true) {\n yield i++;\n }\n }\n let gen = nextId();\n return gen;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":251,"value":"class Entry { \n constructor(key, value, shape) {\n this.key = key;\n this.value = value;\n this.shape = shape;\n }\n toString() {\n return this.value;\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":138,"value":"$31","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":145,"value":"draw = (tree) => dot`${graphViz(tree)}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":40,"value":"import {BT, BinaryTree} from \"@esperanc/binary-search-trees\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":134,"value":"dot = require(\"@observablehq/graphviz@0.2\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":682,"value":"import {html, svg} from \"@observablehq/htl\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":843,"value":"import {mergeInputs} from \"@mootari/observablehq-inputs-feature-73\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1552,"value":"import {cartesianPlane, segment, circle, square, rectangle, curves,lines, annotation, points, triangle} from \"@fengyfei/math-visualization\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2274,"value":"import {verticalStack,horizontalStack} from \"@rsamec/stacks\"","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W32","stdlib":"1","titling":"auto"}} 30:"$2f:body"