54 lines
No EOL
15 KiB
HTML
54 lines
No EOL
15 KiB
HTML
<!DOCTYPE html><html><head><meta content="text/html; charset=utf-8" http-equiv="Content-Type" /><meta content="width=device-width, initial-scale=1" name="viewport" /><!--replace-start-0--><!--replace-start-5--><!--replace-start-8--><title>Binary encoding - My Zettelkasten</title><!--replace-end-8--><!--replace-end-5--><!--replace-end-0--><link href="https://cdn.jsdelivr.net/npm/fomantic-ui@2.8.7/dist/semantic.min.css" rel="stylesheet" /><link href="https://fonts.googleapis.com/css?family=Merriweather|Libre+Franklin|Roboto+Mono&display=swap" rel="stylesheet" /><!--replace-start-1--><!--replace-start-4--><!--replace-start-7--><link href="https://raw.githubusercontent.com/srid/neuron/master/assets/neuron.svg" rel="icon" /><meta content="We know that everything going on in a computer is the manipulation of binary digits. Thus all data must ultimately reduce to binary numbers manipulated through logic circuits." name="description" /><meta content="Binary encoding" property="og:title" /><meta content="My Zettelkasten" property="og:site_name" /><meta content="article" property="og:type" /><meta content="Binary_encoding" property="neuron:zettel-id" /><meta content="Binary_encoding" property="neuron:zettel-slug" /><meta content="binary" property="neuron:zettel-tag" /><script type="application/ld+json">[]</script><style type="text/css">body{background-color:#eeeeee !important;font-family:"Libre Franklin", serif !important}body .ui.container{font-family:"Libre Franklin", serif !important}body h1, h2, h3, h4, h5, h6, .ui.header, .headerFont{font-family:"Merriweather", sans-serif !important}body code, pre, tt, .monoFont{font-family:"Roboto Mono","SFMono-Regular","Menlo","Monaco","Consolas","Liberation Mono","Courier New", monospace !important}body div.z-index p.info{color:#808080}body div.z-index ul{list-style-type:square;padding-left:1.5em}body div.z-index .uplinks{margin-left:0.29999em}body .zettel-content h1#title-h1{background-color:rgba(33,133,208,0.1)}body nav.bottomPane{background-color:rgba(33,133,208,2.0e-2)}body div#footnotes{border-top-color:#2185d0}body p{line-height:150%}body img{max-width:100%}body .deemphasized{font-size:0.94999em}body .deemphasized:hover{opacity:1}body .deemphasized:not(:hover){opacity:0.69999}body .deemphasized:not(:hover) a{color:#808080 !important}body div.container.universe{padding-top:1em}body div.zettel-view ul{padding-left:1.5em;list-style-type:square}body div.zettel-view .pandoc .highlight{background-color:#ffff00}body div.zettel-view .pandoc .ui.disabled.fitted.checkbox{margin-right:0.29999em;vertical-align:middle}body div.zettel-view .zettel-content .metadata{margin-top:1em}body div.zettel-view .zettel-content .metadata div.date{text-align:center;color:#808080}body div.zettel-view .zettel-content h1{padding-top:0.2em;padding-bottom:0.2em;text-align:center}body div.zettel-view .zettel-content h2{border-bottom:solid 1px #4682b4;margin-bottom:0.5em}body div.zettel-view .zettel-content h3{margin:0px 0px 0.4em 0px}body div.zettel-view .zettel-content h4{opacity:0.8}body div.zettel-view .zettel-content div#footnotes{margin-top:4em;border-top-style:groove;border-top-width:2px;font-size:0.9em}body div.zettel-view .zettel-content div#footnotes ol > li > p:only-of-type{display:inline;margin-right:0.5em}body div.zettel-view .zettel-content aside.footnote-inline{width:30%;padding-left:15px;margin-left:15px;float:right;background-color:#d3d3d3}body div.zettel-view .zettel-content .overflows{overflow:auto}body div.zettel-view .zettel-content code{margin:auto auto auto auto;font-size:100%}body div.zettel-view .zettel-content p code, li code, ol code{padding:0.2em 0.2em 0.2em 0.2em;background-color:#f5f2f0}body div.zettel-view .zettel-content pre{overflow:auto}body div.zettel-view .zettel-content dl dt{font-weight:bold}body div.zettel-view .zettel-content blockquote{background-color:#f9f9f9;border-left:solid 10px #cccccc;margin:1.5em 0px 1.5em 0px;padding:0.5em 10px 0.5em 10px}body div.zettel-view .zettel-content.raw{background-color:#dddddd}body .ui.label.zettel-tag{color:#000000}body .ui.label.zettel-tag a{color:#000000}body nav.bottomPane ul.backlinks > li{padding-bottom:0.4em;list-style-type:disc}body nav.bottomPane ul.context-list > li{list-style-type:lower-roman}body .footer-version img{-webkit-filter:grayscale(100%);-moz-filter:grayscale(100%);-ms-filter:grayscale(100%);-o-filter:grayscale(100%);filter:grayscale(100%)}body .footer-version img:hover{-webkit-filter:grayscale(0%);-moz-filter:grayscale(0%);-ms-filter:grayscale(0%);-o-filter:grayscale(0%);filter:grayscale(0%)}body .footer-version, .footer-version a, .footer-version a:visited{color:#808080}body .footer-version a{font-weight:bold}body .footer-version{margin-top:1em !important;font-size:0.69999em}@media only screen and (max-width: 768px){body div#zettel-container{margin-left:0.4em !important;margin-right:0.4em !important}}body span.zettel-link-container span.zettel-link a{color:#2185d0;font-weight:bold;text-decoration:none}body span.zettel-link-container span.zettel-link a:hover{background-color:rgba(33,133,208,0.1)}body span.zettel-link-container span.extra{color:auto}body span.zettel-link-container.errors{border:solid 1px #ff0000}body span.zettel-link-container.errors span.zettel-link a:hover{text-decoration:none !important;cursor:not-allowed}body [data-tooltip]:after{font-size:0.69999em}body div.tag-tree div.node{font-weight:bold}body div.tag-tree div.node a.inactive{color:#555555}body .tree.flipped{-webkit-transform:rotate(180deg);-moz-transform:rotate(180deg);-ms-transform:rotate(180deg);-o-transform:rotate(180deg);transform:rotate(180deg)}body .tree{overflow:auto}body .tree ul.root{padding-top:0px;margin-top:0px}body .tree ul{position:relative;padding:1em 0px 0px 0px;white-space:nowrap;margin:0px auto 0px auto;text-align:center}body .tree ul::after{content:"";display:table;clear:both}body .tree ul:last-child{padding-bottom:0.1em}body .tree li{display:inline-block;vertical-align:top;text-align:center;list-style-type:none;position:relative;padding:1em 0.5em 0em 0.5em}body .tree li::before{content:"";position:absolute;top:0px;right:50%;border-top:solid 2px #cccccc;width:50%;height:1.19999em}body .tree li::after{content:"";position:absolute;top:0px;right:50%;border-top:solid 2px #cccccc;width:50%;height:1.19999em}body .tree li::after{right:auto;left:50%;border-left:solid 2px #cccccc}body .tree li:only-child{padding-top:0em}body .tree li:only-child::after{display:none}body .tree li:only-child::before{display:none}body .tree li:first-child::before{border-style:none;border-width:0px}body .tree li:first-child::after{border-radius:5px 0px 0px 0px}body .tree li:last-child::after{border-style:none;border-width:0px}body .tree li:last-child::before{border-right:solid 2px #cccccc;border-radius:0px 5px 0px 0px}body .tree ul ul::before{content:"";position:absolute;top:0px;left:50%;border-left:solid 2px #cccccc;width:0px;height:1.19999em}body .tree li div.forest-link{border:solid 2px #cccccc;padding:0.2em 0.29999em 0.2em 0.29999em;text-decoration:none;display:inline-block;border-radius:5px 5px 5px 5px;color:#333333;position:relative;top:2px}body .tree.flipped li div.forest-link{-webkit-transform:rotate(180deg);-moz-transform:rotate(180deg);-ms-transform:rotate(180deg);-o-transform:rotate(180deg);transform:rotate(180deg)}</style><script
|
||
async=""
|
||
id="MathJax-script"
|
||
src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"
|
||
></script>
|
||
<link
|
||
href="https://cdnjs.cloudflare.com/ajax/libs/prism/1.23.0/themes/prism.min.css"
|
||
rel="stylesheet"
|
||
/><link rel="preconnect" href="https://fonts.googleapis.com" /><link
|
||
rel="preconnect"
|
||
href="https://fonts.gstatic.com"
|
||
crossorigin
|
||
/><link
|
||
href="https://fonts.googleapis.com/css2?family=IBM+Plex+Mono:ital,wght@0,100;0,200;0,300;0,400;0,500;0,600;0,700;1,100;1,200;1,300;1,400;1,500;1,600;1,700&family=IBM+Plex+Sans+Condensed:ital,wght@0,100;0,200;0,300;0,400;0,500;0,600;0,700;1,100;1,200;1,300;1,400;1,500;1,600;1,700&family=IBM+Plex+Sans:ital,wght@0,100;0,200;0,300;0,400;0,500;0,600;0,700;1,100;1,200;1,300;1,400;1,500;1,600;1,700&family=IBM+Plex+Serif:ital,wght@0,100;0,200;0,300;0,400;0,500;0,600;0,700;1,100;1,200;1,300;1,400;1,500;1,600;1,700&display=swap"
|
||
rel="stylesheet"
|
||
/>
|
||
<script src="https://cdnjs.cloudflare.com/ajax/libs/prism/1.23.0/components/prism-core.min.js"></script>
|
||
<script src="https://cdnjs.cloudflare.com/ajax/libs/prism/1.23.0/plugins/autoloader/prism-autoloader.min.js"></script>
|
||
<style>
|
||
body .ui.container,
|
||
body ul {
|
||
font-family: "IBM Plex Sans" !important;
|
||
}
|
||
body blockquote {
|
||
border-left-width: 3px !important;
|
||
font-style: italic;
|
||
}
|
||
.headerFont,
|
||
.ui.header,
|
||
body h1,
|
||
h2,
|
||
h3,
|
||
h4,
|
||
h5,
|
||
h6 {
|
||
font-family: "IBM Plex Sans Condensed" !important;
|
||
}
|
||
body p {
|
||
line-height: 1.4;
|
||
}
|
||
.monoFont,
|
||
body code,
|
||
pre,
|
||
tt {
|
||
font-family: "IBM Plex Mono" !important;
|
||
font-size: 12px !important;
|
||
line-height: 1.4 !important;
|
||
}
|
||
</style>
|
||
<!--replace-end-7--><!--replace-end-4--><!--replace-end-1--></head><body><div class="ui fluid container universe"><!--replace-start-2--><!--replace-start-3--><!--replace-start-6--><div class="ui text container" id="zettel-container" style="position: relative"><div class="zettel-view"><article class="ui raised attached segment zettel-content"><div class="pandoc"><h1 id="title-h1">Binary encoding</h1><p>We know that everything going on in a computer is the manipulation of binary digits. Thus all data must ultimately reduce to binary numbers manipulated through logic circuits.</p><p><em>Encoding</em> is the process of establishing a correspondence between sets of binary numbers and sets of symbols that are representative of a given type of data. For certain fundamental data types, for example alphanumeric characters and colours, there are agreed standards of encoding such that, for example, that <code>111111</code> (binary) and <code>3F</code> (hex) always corresponds to the character <code>?</code>. The reverse is obviously <em>decoding</em>: deriving the data/ symbol from the binary format.</p><blockquote><p>An encoding system maps each symbol to a unique sequence of bits. A computer then interprets that sequence of bits and displays the apppropriate symbol to the user.</p></blockquote><p>The length of the binary number (sometimes called the <em>word length</em>) corresponding to 8-bit, 16-bit, 32-bit etc. that is used to represent a given data set is determined by the number of variations that you require to capture the entire range of the dataset:</p><blockquote><p>An <span class="math inline">\(n\)</span>-bit binary system can encode <span class="math inline">\(2^n\)</span> different things</p></blockquote><p>For example, say we know that there are 18 levels to a computer game. To encode a reference for each level we would need a binary number that is capable of at least 18 total variations. In this instance a 32-bit (<span class="math inline">\(2^{5}\)</span> ) number would be best because the next smallest (16-bit) would not be sufficient. Our levels would have representations as follows:</p><pre><code class="language-none">00001 (1)
|
||
00010 (2)
|
||
00011 (3)
|
||
00100 (4)
|
||
...</code></pre><h2 id="related-points">Related points</h2><p>Think about when you open a file format in a text editor that cannot decode it. For example trying to open a Word document in VSCode. The mangled letters it displays is the encoded binary data. When you open the file in Word, the decoding is applied and it resembles what you would expect.</p><p>When we save a file, the different file extensions denote different formats and these are encoding formats. For example if you save an image file as <code>.png</code> rather than <code>.jpg</code>, you are applying a different encoding algorithm to the data that compresses the raw binary data in a different way.</p></div></article><nav class="ui attached segment deemphasized backlinksPane" id="neuron-backlinks-pane"><h3 class="ui header">Backlinks</h3><ul class="backlinks"><li><span class="zettel-link-container cf"><span class="zettel-link"><a href="Twos_complement.html">Two’s complement</a></span></span><ul class="context-list" style="zoom: 85%;"><li class="item"><div class="pandoc"><p>Two’s complement divides the available word length (see <span class="zettel-link-container cf"><span class="zettel-link" title="Zettel: Binary encoding"><a href="Binary_encoding.html">binary encoding</a></span></span>) into two subsets: one for negative integrs and one for positive integers.</p></div></li></ul></li><li><span class="zettel-link-container cf"><span class="zettel-link"><a href="Signed_and_unsigned_numbers.html">Signed and unsigned numbers</a></span></span><ul class="context-list" style="zoom: 85%;"><li class="item"><div class="pandoc"><p><span class="zettel-link-container cf"><span class="zettel-link"><a href="Twos_complement.html">Two’s complement</a></span></span>, <span class="zettel-link-container cf"><span class="zettel-link"><a href="Binary_encoding.html">Binary encoding</a></span></span>, <span class="zettel-link-container cf"><span class="zettel-link"><a href="Signed_magnitude_representation.html">Signed magnitude representation</a></span></span></p></div></li></ul></li><li><span class="zettel-link-container cf"><span class="zettel-link"><a href="Memory_addresses.html">Memory addresses</a></span></span><ul class="context-list" style="zoom: 85%;"><li class="item"><div class="pandoc"><p>By itself, the the data is meaningless but we know from <span class="zettel-link-container cf"><span class="zettel-link" title="Zettel: Binary encoding"><a href="Binary_encoding.html">binary encoding</a></span></span> that the binary data will correspond to some meaningful data, such as a character or a colour, depending on the encoding scheme used. The above table could correspond to the characters for ‘A’, ‘B’ and ‘C’ in the ASCII encoding scheme:</p></div></li></ul></li><li><span class="zettel-link-container cf"><span class="zettel-link"><a href="Binary_encoding_of_text.html">Text encoding</a></span></span><ul class="context-list" style="zoom: 85%;"><li class="item"><div class="pandoc"><p>Text encoding is an applied instance of <span class="zettel-link-container cf"><span class="zettel-link" title="Zettel: Binary encoding"><a href="Binary_encoding.html">binary encoding</a></span></span>.</p></div></li></ul></li></ul></nav><nav class="ui attached segment deemphasized bottomPane" id="neuron-tags-pane"><div><span class="ui basic label zettel-tag" title="Tag">binary</span></div></nav><nav class="ui bottom attached icon compact inverted menu blue" id="neuron-nav-bar"><!--replace-start-9--><!--replace-end-9--><a class="right item" href="impulse.html" title="Open Impulse"><i class="wave square icon"></i></a></nav></div></div><!--replace-end-6--><!--replace-end-3--><!--replace-end-2--><div class="ui center aligned container footer-version"><div class="ui tiny image"><a href="https://neuron.zettel.page"><img alt="logo" src="https://raw.githubusercontent.com/srid/neuron/master/assets/neuron.svg" title="Generated by Neuron 1.9.35.3" /></a></div></div></div></body></html> |