Problem 49835. Decimal to Binary conversion for Large Integers

Created by Gifari Zulkarnaen

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{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Decimal integer, a base-10 number we normally use without fractional component, can be represented as </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Binary_number\"><w:r><w:t>binary</w:t></w:r></w:hyperlink><w:r><w:t>, a base-2 number composed either 0 or 1. The procedure to convert a decimal integer X to its binary equivalent is as follows:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Divide X by 2. The remainder (either 0 or 1) is the first binary value.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Divide the quotient of previous step by 2. The remainder is the next binary value.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Repeat the process until the quotient cannot be divided anymore and so last binary is found.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>As example, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>357_{10} \\equiv 10010101101_2</w:t></w:r></w:customXml><w:r><w:t> through process below:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>        </w:t></w:r><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"218\"/><w:attr w:name=\"width\" w:val=\"60\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Given a decimal string input x, build a function dectobin(x) that returns its binary equivalent in character array. Unlike built-in dec2bin function, your function should also work for large integers up to thousands number of digits.</w:t></w:r></w:p></w:body></w:document>","relationship":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/image","target":"/media/image1.gif","relationshipId":"rId1"}]},{"partUri":"/media/image1.gif","contentType":"image/gif","content":"https://upload.wikimedia.org/wikipedia/commons/d/d0/Decimal_to_Binary_Conversion.gif","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; "><div style="block-size: 436.9px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 218.45px; transform-origin: 407px 218.45px; vertical-align: baseline; "><div style="block-size: 41.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 20.8px; text-align: left; transform-origin: 384px 20.8px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">Decimal integer, a base-10 number we normally use without fractional component, can be represented as </span></span><a target='_blank' href = "https://en.wikipedia.org/wiki/Binary_number"><span style=""><span style="">binary</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">, a base-2 number composed either 0 or 1. The procedure to convert a decimal integer X to its binary equivalent is as follows:</span></span></div><ol style="block-size: 60px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 30px; transform-origin: 391px 30px; margin-top: 10px; margin-bottom: 20px; "><li style="block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; "><span style="block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">Divide X by 2. The remainder (either 0 or 1) is the first binary value.</span></span></li><li style="block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; "><span style="block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">Divide the quotient of previous step by 2. The remainder is the next binary value.</span></span></li><li style="block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; "><span style="block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">Repeat the process until the quotient cannot be divided anymore and so last binary is found.</span></span></li></ol><div style="block-size: 22.1px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11.05px; text-align: left; transform-origin: 384px 11.05px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">As example, </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" width="141.5" height="19.5" style="width: 141.5px; height: 19.5px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style=""> through process below:</span></span></div><div style="block-size: 223.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 111.8px; text-align: left; transform-origin: 384px 111.8px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">        </span></span><img class="imageNode" width="60" height="218" style="vertical-align: baseline;width: 60px;height: 218px" src="https://upload.wikimedia.org/wikipedia/commons/d/d0/Decimal_to_Binary_Conversion.gif" data-image-state="image-loaded"></div><div style="block-size: 41.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 20.8px; text-align: left; transform-origin: 384px 20.8px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">Given a decimal string input x, build a function dectobin(x) that returns its binary equivalent in character array. Unlike built-in dec2bin function, your function should also work for large integers up to thousands number of digits.</span></span></div></div></div>

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Problem 49835. Decimal to Binary conversion for Large Integers

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