e39465ad2f
new file: Files/flashplayer_32_sa.exe
new file: favicon.ico
new file: globe.gif
new file: imgs/download.png
new file: imgs/zuck.jpg
new file: index.html
new file: other.ico
new file: script.js
new file: site.webmanifest
new file: sitemap.html
new file: styles/backround.css
new file: styles/border.css
new file: styles/fonts/Titillium_Web/OFL.txt
new file: styles/fonts/Titillium_Web/TitilliumWeb-Black.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Bold.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-BoldItalic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-ExtraLight.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-ExtraLightItalic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Italic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Light.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-LightItalic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Regular.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-SemiBold.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-SemiBoldItalic.ttf
new file: styles/fonts/webfontkit-20221027-163353/generator_config.txt
new file: styles/fonts/webfontkit-20221027-163353/specimen_files/grid_12-825-55-15.css
new file: styles/fonts/webfontkit-20221027-163353/specimen_files/specimen_stylesheet.css
new file: styles/fonts/webfontkit-20221027-163353/stylesheet.css
new file: styles/fonts/webfontkit-20221027-163353/titilliumweb-extralight-demo.html
new file: styles/fonts/webfontkit-20221027-163353/titilliumweb-extralight-webfont.woff
new file: styles/fonts/webfontkit-20221027-163353/titilliumweb-extralight-webfont.woff2
new file: styles/fonts/webfontkit-20221027-165950/generator_config.txt
new file: styles/fonts/webfontkit-20221027-165950/specimen_files/grid_12-825-55-15.css
new file: styles/fonts/webfontkit-20221027-165950/specimen_files/specimen_stylesheet.css
new file: styles/fonts/webfontkit-20221027-165950/stylesheet.css
new file: styles/fonts/webfontkit-20221027-165950/titilliumweb-bold-demo.html
new file: styles/fonts/webfontkit-20221027-165950/titilliumweb-bold-webfont.woff
new file: styles/fonts/webfontkit-20221027-165950/titilliumweb-bold-webfont.woff2
new file: styles/style.css
new file: tools/2048/.gitignore
new file: tools/2048/.jshintrc
new file: tools/2048/CONTRIBUTING.md
new file: tools/2048/LICENSE.txt
new file: tools/2048/README.md
new file: tools/2048/Rakefile
new file: tools/2048/favicon.ico
new file: tools/2048/index.html
new file: tools/2048/js/animframe_polyfill.js
new file: tools/2048/js/application.js
new file: tools/2048/js/bind_polyfill.js
new file: tools/2048/js/classlist_polyfill.js
new file: tools/2048/js/game_manager.js
new file: tools/2048/js/grid.js
new file: tools/2048/js/html_actuator.js
new file: tools/2048/js/keyboard_input_manager.js
new file: tools/2048/js/local_storage_manager.js
new file: tools/2048/js/tile.js
new file: tools/2048/meta/apple-touch-icon.png
new file: tools/webretro/cores/neocd_libretro.js
new file: tools/webretro/cores/neocd_libretro.wasm
new file: tools/webretro/cores/nestopia_libretro.js
new file: tools/webretro/cores/nestopia_libretro.wasm
new file: tools/webretro/cores/o2em_libretro.js
new file: tools/webretro/cores/o2em_libretro.wasm
new file: tools/webretro/cores/opera_libretro.js
new file: tools/webretro/cores/opera_libretro.wasm
1175 lines
42 KiB
HTML
1175 lines
42 KiB
HTML
<!DOCTYPE html>
|
|
<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
|
|
|
|
<!-- Mirrored from www.mathsisfun.com/numbers/bases.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:45:25 GMT -->
|
|
<head>
|
|
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
|
|
|
|
|
|
|
|
<!-- #BeginEditable "doctitle" -->
|
|
<title>Number Bases</title>
|
|
<script src="images/number-odometer.js" type="text/javascript"></script>
|
|
<link rel="stylesheet" type="text/css" href="../stylejs.css">
|
|
<!-- #EndEditable -->
|
|
<meta name="keywords" content="math, maths, mathematics, school, homework, education">
|
|
<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
|
|
<meta name="HandheldFriendly" content="true">
|
|
<meta name="referrer" content="always">
|
|
<link rel="preload" href="../images/style/font-champ-bold.ttf" as="font" type="font/ttf" crossorigin="">
|
|
<link rel="preload" href="../style4.css" as="style">
|
|
<link rel="preload" href="../main4.js" as="script">
|
|
<link rel="stylesheet" href="../style4.css">
|
|
<script src="../main4.js" defer="defer"></script>
|
|
<!-- Global site tag (gtag.js) - Google Analytics -->
|
|
<script async="" src="https://www.googletagmanager.com/gtag/js?id=UA-29771508-1"></script>
|
|
<script>
|
|
window.dataLayer = window.dataLayer || [];
|
|
function gtag(){dataLayer.push(arguments);}
|
|
gtag('js', new Date());
|
|
gtag('config', 'UA-29771508-1');
|
|
</script>
|
|
</head>
|
|
|
|
<body id="bodybg">
|
|
|
|
<div id="stt"></div>
|
|
<div id="adTop"></div>
|
|
<header>
|
|
<div id="hdr"></div>
|
|
<div id="tran"></div>
|
|
<div id="adHide"></div>
|
|
<div id="cookOK"></div>
|
|
</header>
|
|
|
|
<div class="mid">
|
|
|
|
<nav>
|
|
<div id="menuWide" class="menu"></div>
|
|
<div id="logo"><a href="../index.html"><img src="../images/style/logo.svg" alt="Math is Fun"></a></div>
|
|
|
|
<div id="search" role="search"></div>
|
|
<div id="linkto"></div>
|
|
|
|
<div id="menuSlim" class="menu"></div>
|
|
<div id="menuTiny" class="menu"></div>
|
|
</nav>
|
|
|
|
<div id="extra"></div>
|
|
|
|
<article id="content" role="main">
|
|
|
|
<!-- #BeginEditable "Body" -->
|
|
|
|
|
|
<h1 class="center">Number Bases</h1>
|
|
|
|
|
|
<h2>Base 10</h2>
|
|
|
|
<p>We use "Base 10" every day ... it is our <a href="../place-value.html">Decimal Number System</a>.</p>
|
|
<p>It has 10 digits:</p>
|
|
<p class="center larger">0
|
|
1 2 3 4 5 6 7 8 9</p>
|
|
We count like this:
|
|
|
|
|
|
|
|
<div class="simple">
|
|
|
|
<table style="border: 0; margin:auto;">
|
|
<tbody>
|
|
<tr>
|
|
<td> </td>
|
|
<td class="large" align="right">0</td>
|
|
<td> </td>
|
|
<td>Start at 0 </td>
|
|
</tr>
|
|
<tr>
|
|
<td>•</td>
|
|
<td class="large" align="right">1</td>
|
|
<td> </td>
|
|
<td>Then 1</td>
|
|
</tr>
|
|
<tr>
|
|
<td>••</td>
|
|
<td class="large" align="right">2</td>
|
|
<td> </td>
|
|
<td>Then 2</td>
|
|
</tr>
|
|
<tr>
|
|
<td> </td>
|
|
<td class="large" align="right">⋮</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>•••••••••</td>
|
|
<td class="large" align="right">9</td>
|
|
<td> </td>
|
|
<td>Up to 9</td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••</td>
|
|
<td class="large" align="right"><span class="hilite">1</span>0</td>
|
|
<td> </td>
|
|
<td>Start back at 0 again, but add 1 on the left</td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••<br>
|
|
•</td>
|
|
<td class="large" align="right">11</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••<br>
|
|
••</td>
|
|
<td class="large" align="right">12</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td> </td>
|
|
<td class="large" align="right">⋮</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••<br>
|
|
•••••••••</td>
|
|
<td class="large" align="right">19</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••<br>
|
|
••••••••••</td>
|
|
<td class="large" align="right"><span class="hilite">2</span>0</td>
|
|
<td> </td>
|
|
<td>Start back at 0 again, but add 1 on the left</td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••<br>
|
|
••••••••••<br>
|
|
•</td>
|
|
<td class="large" align="right">21</td>
|
|
<td> </td>
|
|
<td>And so on!</td>
|
|
</tr>
|
|
</tbody></table></div>
|
|
<p class="large"> </p>
|
|
<p class="large">But there are other bases!</p>
|
|
|
|
|
|
<h2><a href="../binary-number-system.html">Binary</a> (Base 2) has only 2 digits: 0 and 1</h2>
|
|
|
|
<p>We count like this:</p>
|
|
<div class="simple">
|
|
|
|
<table style="border: 0; margin:auto;">
|
|
<tbody>
|
|
<tr>
|
|
<td> </td>
|
|
<td class="large" align="right">0</td>
|
|
<td> </td>
|
|
<td>Start at 0 </td>
|
|
</tr>
|
|
<tr>
|
|
<td>•</td>
|
|
<td class="large" align="right">1</td>
|
|
<td> </td>
|
|
<td>Then 1</td>
|
|
</tr>
|
|
<tr>
|
|
<td>••</td>
|
|
<td class="large" align="right"><span class="hilite">1</span>0</td>
|
|
<td> </td>
|
|
<td>Start back at 0 again, but add 1 on the left</td>
|
|
</tr>
|
|
<tr>
|
|
<td>•••</td>
|
|
<td class="large" align="right">11</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••</td>
|
|
<td class="large" align="right"><span class="hilite">1</span>00</td>
|
|
<td> </td>
|
|
<td>start back at 0 again, and add one to the number on the left...<br>
|
|
... but that number is already at 1 so it also goes back to 0 ...<br>
|
|
... and 1 is added to the <i>next position</i> on the left</td>
|
|
</tr>
|
|
<tr>
|
|
<td>•••••</td>
|
|
<td class="large" align="right">101</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••</td>
|
|
<td class="large" align="right">110</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>•••••••</td>
|
|
<td class="large" align="right">111</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••</td>
|
|
<td class="large" align="right"><span class="hilite">1</span>000</td>
|
|
<td> </td>
|
|
<td>Start back at 0 again (for all 3 digits),<br>
|
|
add 1 on the left</td>
|
|
</tr>
|
|
<tr>
|
|
<td>•••••••••</td>
|
|
<td class="large" align="right">1001</td>
|
|
<td> </td>
|
|
<td>And so on!</td>
|
|
</tr>
|
|
</tbody></table>
|
|
</div>
|
|
<p>See how it is done in this little demonstration (press play):</p>
|
|
<script>numberodometerMain(2);</script>
|
|
<p class="center">Also try Decimal, and try other bases like 3 or 4.<br>
|
|
It will help you understand how all these different bases work.</p>
|
|
|
|
|
|
<h2>Ternary (Base 3) has 3 digits: 0, 1 and 2</h2>
|
|
|
|
<p>We count like this:</p>
|
|
<div class="simple">
|
|
|
|
<table style="border: 0; margin:auto;">
|
|
<tbody>
|
|
<tr>
|
|
<td> </td>
|
|
<td class="large" align="right">0</td>
|
|
<td> </td>
|
|
<td>Start at 0 </td>
|
|
</tr>
|
|
<tr>
|
|
<td>•</td>
|
|
<td class="large" align="right">1</td>
|
|
<td> </td>
|
|
<td>Then 1</td>
|
|
</tr>
|
|
<tr>
|
|
<td>••</td>
|
|
<td class="large" align="right">2</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>•••</td>
|
|
<td class="large" align="right"><span class="hilite">1</span>0</td>
|
|
<td> </td>
|
|
<td>Start back at 0 again, but add 1 on the left</td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••</td>
|
|
<td class="large" align="right">11</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>•••••</td>
|
|
<td class="large" align="right">12</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••</td>
|
|
<td class="large" align="right"><span class="hilite">2</span>0</td>
|
|
<td> </td>
|
|
<td>Start back at 0 again, but add 1 on the left</td>
|
|
</tr>
|
|
<tr>
|
|
<td>•••••••</td>
|
|
<td class="large" align="right">21</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••</td>
|
|
<td class="large" align="right">22</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>•••••••••</td>
|
|
<td class="large" align="right"><span class="hilite">1</span>00</td>
|
|
<td> </td>
|
|
<td>start back at 0 again, and add one to the number on the left...<br>
|
|
... but that number is already at 2 so it also goes back to 0 ...<br>
|
|
... and 1 is added to the <i>next position</i> on the left</td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••</td>
|
|
<td class="large" align="right">101</td>
|
|
<td> </td>
|
|
<td>And so on!</td>
|
|
</tr>
|
|
</tbody></table>
|
|
|
|
|
|
<h2>Quaternary (Base 4) has 4 digits: 0, 1, 2 and 3</h2>
|
|
|
|
<p>We count like this:</p>
|
|
<div class="simple">
|
|
|
|
<table style="border: 0; margin:auto;">
|
|
<tbody>
|
|
<tr>
|
|
<td> </td>
|
|
<td class="large" align="right">0</td>
|
|
<td> </td>
|
|
<td>Start at 0 </td>
|
|
</tr>
|
|
<tr>
|
|
<td>•</td>
|
|
<td class="large" align="right">1</td>
|
|
<td> </td>
|
|
<td>Then 1</td>
|
|
</tr>
|
|
<tr>
|
|
<td>••</td>
|
|
<td class="large" align="right">2</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>•••</td>
|
|
<td class="large" align="right">3</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••</td>
|
|
<td class="large" align="right"><span class="hilite">1</span>0</td>
|
|
<td> </td>
|
|
<td>Start back at 0 again, but add 1 on the left</td>
|
|
</tr>
|
|
<tr>
|
|
<td>•••••</td>
|
|
<td class="large" align="right">11</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••</td>
|
|
<td class="large" align="right">12</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>•••••••</td>
|
|
<td class="large" align="right">13</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••</td>
|
|
<td class="large" align="right"><span class="hilite">2</span>0</td>
|
|
<td> </td>
|
|
<td>Start back at 0 again, but add 1 on the left</td>
|
|
</tr>
|
|
<tr>
|
|
<td>•••••••••</td>
|
|
<td class="large" align="right">21</td>
|
|
<td> </td>
|
|
<td>And so on!</td>
|
|
</tr>
|
|
</tbody></table>
|
|
</div>
|
|
</div>
|
|
|
|
|
|
<h2>Quinary (Base 5) has 5 digits: 0, 1, 2, 3 and 4</h2>
|
|
|
|
<p>We count like this:</p>
|
|
<div class="simple">
|
|
|
|
<table style="border: 0; margin:auto;">
|
|
<tbody>
|
|
<tr>
|
|
<td> </td>
|
|
<td class="large" align="right">0</td>
|
|
<td> </td>
|
|
<td>Start at 0 </td>
|
|
</tr>
|
|
<tr>
|
|
<td>•</td>
|
|
<td class="large" align="right">1</td>
|
|
<td> </td>
|
|
<td>Then 1</td>
|
|
</tr>
|
|
<tr>
|
|
<td>••</td>
|
|
<td class="large" align="right">2</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>•••</td>
|
|
<td class="large" align="right">3</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••</td>
|
|
<td class="large" align="right">4</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>•••••</td>
|
|
<td class="large" align="right"><span class="hilite">1</span>0</td>
|
|
<td> </td>
|
|
<td>Start back at 0 again, but add 1 on the left</td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••</td>
|
|
<td class="large" align="right">11</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>•••••••</td>
|
|
<td class="large" align="right">12</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••</td>
|
|
<td class="large" align="right">13</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>•••••••••</td>
|
|
<td class="large" align="right">14</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••</td>
|
|
<td class="large" align="right"><span class="hilite">2</span>0</td>
|
|
<td> </td>
|
|
<td>Start back at 0 again, but add 1 on the left</td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••<br>
|
|
•</td>
|
|
<td class="large" align="right">21</td>
|
|
<td> </td>
|
|
<td>And so on!</td>
|
|
</tr>
|
|
</tbody></table>
|
|
</div>
|
|
|
|
|
|
<h2>Senary (Base 6) has 6 digits: 0, 1, 2, 3, 4 and 5</h2>
|
|
|
|
<p>We count like this:</p>
|
|
<div class="simple">
|
|
|
|
<table style="border: 0; margin:auto;">
|
|
<tbody>
|
|
<tr>
|
|
<td> </td>
|
|
<td class="large" align="right">0</td>
|
|
<td> </td>
|
|
<td>Start at 0 </td>
|
|
</tr>
|
|
<tr>
|
|
<td>•</td>
|
|
<td class="large" align="right">1</td>
|
|
<td> </td>
|
|
<td>Then 1</td>
|
|
</tr>
|
|
<tr>
|
|
<td>••</td>
|
|
<td class="large" align="right">2</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>•••</td>
|
|
<td class="large" align="right">3</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••</td>
|
|
<td class="large" align="right">4</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>•••••</td>
|
|
<td class="large" align="right">5</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••</td>
|
|
<td class="large" align="right"><span class="hilite">1</span>0</td>
|
|
<td> </td>
|
|
<td>Start back at 0 again, but add 1 on the left</td>
|
|
</tr>
|
|
<tr>
|
|
<td>•••••••</td>
|
|
<td class="large" align="right">11</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••</td>
|
|
<td class="large" align="right">12</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>•••••••••</td>
|
|
<td class="large" align="right">13</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••</td>
|
|
<td class="large" align="right">14</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••<br>
|
|
•</td>
|
|
<td class="large" align="right">15</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••<br>
|
|
••</td>
|
|
<td class="large" align="right"><span class="hilite">2</span>0</td>
|
|
<td> </td>
|
|
<td>Start back at 0 again, but add 1 on the left</td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••<br>
|
|
•••</td>
|
|
<td class="large" align="right">21</td>
|
|
<td> </td>
|
|
<td>And so on!</td>
|
|
</tr>
|
|
</tbody></table>
|
|
</div>
|
|
|
|
|
|
<h2>Septenary (Base 7) has 7 digits: 0, 1, 2, 3, 4 5 and 6</h2>
|
|
|
|
<p>We count like this:</p>
|
|
<div class="simple">
|
|
|
|
<table style="border: 0; margin:auto;">
|
|
<tbody>
|
|
<tr>
|
|
<td> </td>
|
|
<td class="large" align="right">0</td>
|
|
<td> </td>
|
|
<td>Start at 0 </td>
|
|
</tr>
|
|
<tr>
|
|
<td>•</td>
|
|
<td class="large" align="right">1</td>
|
|
<td> </td>
|
|
<td>Then 1</td>
|
|
</tr>
|
|
<tr>
|
|
<td>••</td>
|
|
<td class="large" align="right">2</td>
|
|
<td> </td>
|
|
<td>Then 2</td>
|
|
</tr>
|
|
<tr>
|
|
<td> </td>
|
|
<td class="large" align="right">⋮</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••</td>
|
|
<td class="large" align="right">6</td>
|
|
<td> </td>
|
|
<td>Up to 6</td>
|
|
</tr>
|
|
<tr>
|
|
<td>•••••••</td>
|
|
<td class="large" align="right"><span class="hilite">1</span>0</td>
|
|
<td> </td>
|
|
<td>Start back at 0 again, but add 1 on the left</td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••</td>
|
|
<td class="large" align="right">11</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>•••••••••</td>
|
|
<td class="large" align="right">12</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td> </td>
|
|
<td class="large" align="right">⋮</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••<br>
|
|
•••</td>
|
|
<td class="large" align="right">16</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••<br>
|
|
••••</td>
|
|
<td class="large" align="right"><span class="hilite">2</span>0</td>
|
|
<td> </td>
|
|
<td>Start back at 0 again, but add 1 on the left</td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••<br>
|
|
•••••</td>
|
|
<td class="large" align="right">21</td>
|
|
<td> </td>
|
|
<td>And so on!</td>
|
|
</tr>
|
|
</tbody></table>
|
|
</div>
|
|
|
|
|
|
<h2>Octal (Base 8) has 8 digits</h2>
|
|
|
|
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/paws-8.svg" alt="2 paws 8" height="108" width="200"></p>
|
|
<p>If Dogs ruled the world they might use base-8 instead of decimal:</p>
|
|
<p class="center larger">0
|
|
1 2 3 4 5 6 7</p>
|
|
<div style="clear:both">
|
|
</div>
|
|
<div class="simple">
|
|
|
|
<table style="border: 0; margin:auto;">
|
|
<tbody>
|
|
<tr>
|
|
<td> </td>
|
|
<td class="large" align="right">0</td>
|
|
<td> </td>
|
|
<td>Start at 0 </td>
|
|
</tr>
|
|
<tr>
|
|
<td>•</td>
|
|
<td class="large" align="right">1</td>
|
|
<td> </td>
|
|
<td>Then 1</td>
|
|
</tr>
|
|
<tr>
|
|
<td>••</td>
|
|
<td class="large" align="right">2</td>
|
|
<td> </td>
|
|
<td>Then 2</td>
|
|
</tr>
|
|
<tr>
|
|
<td> </td>
|
|
<td class="large" align="right">⋮</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>•••••••</td>
|
|
<td class="large" align="right">7</td>
|
|
<td> </td>
|
|
<td>Up to 7</td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••</td>
|
|
<td class="large" align="right"><span class="hilite">1</span>0</td>
|
|
<td> </td>
|
|
<td>Start back at 0 again, but add 1 on the left</td>
|
|
</tr>
|
|
<tr>
|
|
<td>•••••••••</td>
|
|
<td class="large" align="right">11</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••</td>
|
|
<td class="large" align="right">12</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td> </td>
|
|
<td class="large" align="right">⋮</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••<br>
|
|
•••••</td>
|
|
<td class="large" align="right">17</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••<br>
|
|
••••••</td>
|
|
<td class="large" align="right"><span class="hilite">2</span>0</td>
|
|
<td> </td>
|
|
<td>Start back at 0 again, but add 1 on the left</td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••<br>
|
|
•••••••</td>
|
|
<td class="large" align="right">21</td>
|
|
<td> </td>
|
|
<td>And so on!</td>
|
|
</tr>
|
|
</tbody></table>
|
|
</div>
|
|
|
|
|
|
<h2>Nonary (Base 9) has 9 digits:</h2>
|
|
|
|
<p class="center larger">0
|
|
1 2 3 4 5 6 7 8</p>
|
|
<p>We count like this:</p>
|
|
<div class="simple">
|
|
|
|
<table style="border: 0; margin:auto;">
|
|
<tbody>
|
|
<tr>
|
|
<td> </td>
|
|
<td class="large" align="right">0</td>
|
|
<td> </td>
|
|
<td>Start at 0 </td>
|
|
</tr>
|
|
<tr>
|
|
<td>•</td>
|
|
<td class="large" align="right">1</td>
|
|
<td> </td>
|
|
<td>Then 1</td>
|
|
</tr>
|
|
<tr>
|
|
<td>••</td>
|
|
<td class="large" align="right">2</td>
|
|
<td> </td>
|
|
<td>Then 2</td>
|
|
</tr>
|
|
<tr>
|
|
<td> </td>
|
|
<td class="large" align="right">⋮</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••</td>
|
|
<td class="large" align="right">8</td>
|
|
<td> </td>
|
|
<td>Up to 8</td>
|
|
</tr>
|
|
<tr>
|
|
<td>•••••••••</td>
|
|
<td class="large" align="right"><span class="hilite">1</span>0</td>
|
|
<td> </td>
|
|
<td>Start back at 0 again, but add 1 on the left</td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••</td>
|
|
<td class="large" align="right">11</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••<br>
|
|
•</td>
|
|
<td class="large" align="right">12</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td> </td>
|
|
<td class="large" align="right">⋮</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••<br>
|
|
•••••••</td>
|
|
<td class="large" align="right">18</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••<br>
|
|
••••••••</td>
|
|
<td class="large" align="right"><span class="hilite">2</span>0</td>
|
|
<td> </td>
|
|
<td>Start back at 0 again, but add 1 on the left</td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••<br>
|
|
•••••••••</td>
|
|
<td class="large" align="right">21</td>
|
|
<td> </td>
|
|
<td>And so on!</td>
|
|
</tr>
|
|
</tbody></table>
|
|
</div>
|
|
|
|
|
|
<h2>Decimal (Base 10) has 10 digits:</h2>
|
|
|
|
<p class="center larger">0
|
|
1 2 3 4 5 6 7 8 9</p>
|
|
<p>Well ... we talked about this at the start but here it is again:</p>
|
|
<div class="simple">
|
|
|
|
<table style="border: 0; margin:auto;">
|
|
<tbody>
|
|
<tr>
|
|
<td> </td>
|
|
<td class="large" align="right">0</td>
|
|
<td> </td>
|
|
<td>Start at 0 </td>
|
|
</tr>
|
|
<tr>
|
|
<td>•</td>
|
|
<td class="large" align="right">1</td>
|
|
<td> </td>
|
|
<td>Then 1</td>
|
|
</tr>
|
|
<tr>
|
|
<td>••</td>
|
|
<td class="large" align="right">2</td>
|
|
<td> </td>
|
|
<td>Then 2</td>
|
|
</tr>
|
|
<tr>
|
|
<td> </td>
|
|
<td class="large" align="right">⋮</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>•••••••••</td>
|
|
<td class="large" align="right">9</td>
|
|
<td> </td>
|
|
<td>Up to 9</td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••</td>
|
|
<td class="large" align="right"><span class="hilite">1</span>0</td>
|
|
<td> </td>
|
|
<td>Start back at 0 again, but add 1 on the left</td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••<br>
|
|
•</td>
|
|
<td class="large" align="right">11</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••<br>
|
|
••</td>
|
|
<td class="large" align="right">12</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td> </td>
|
|
<td class="large" align="right">⋮</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••<br>
|
|
•••••••••</td>
|
|
<td class="large" align="right">19</td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••<br>
|
|
••••••••••</td>
|
|
<td class="large" align="right"><span class="hilite">2</span>0</td>
|
|
<td> </td>
|
|
<td>Start back at 0 again, but add 1 on the left</td>
|
|
</tr>
|
|
<tr>
|
|
<td>••••••••••<br>
|
|
••••••••••<br>
|
|
•</td>
|
|
<td class="large" align="right">21</td>
|
|
<td> </td>
|
|
<td>And so on!</td>
|
|
</tr>
|
|
</tbody></table>
|
|
</div>
|
|
|
|
|
|
<h2>Undecimal (Base 11)</h2>
|
|
|
|
<p>Undecimal (Base 11) needs one more digit than Decimal, so "A" is used, like this:</p>
|
|
|
|
<table style="border: 0;">
|
|
<tbody>
|
|
<tr style="text-align:center;">
|
|
<th>Decimal:</th>
|
|
<td style="width:21px;">0</td>
|
|
<td style="width:21px;">1</td>
|
|
<td style="width:21px;">2</td>
|
|
<td style="width:21px;">3</td>
|
|
<td style="width:21px;">4</td>
|
|
<td style="width:21px;">5</td>
|
|
<td style="width:22px;">6</td>
|
|
<td style="width:20px;">7</td>
|
|
<td style="width:21px;">8</td>
|
|
<td style="width:21px;">9</td>
|
|
<td style="width:21px;">10</td>
|
|
<td style="width:21px;">11</td>
|
|
<td style="width:21px;">12</td>
|
|
<td style="width:21px;">...</td>
|
|
</tr>
|
|
<tr style="text-align:center;">
|
|
<th>Undecimal:</th>
|
|
<td style="width:21px;">0</td>
|
|
<td style="width:21px;">1</td>
|
|
<td style="width:21px;">2</td>
|
|
<td style="width:21px;">3</td>
|
|
<td style="width:21px;">4</td>
|
|
<td style="width:21px;">5</td>
|
|
<td style="width:22px;">6</td>
|
|
<td style="width:20px;">7</td>
|
|
<td style="width:21px;">8</td>
|
|
<td style="width:21px;">9</td>
|
|
<td style="width:21px;"><b>A</b></td>
|
|
<td style="width:21px;">10</td>
|
|
<td style="width:21px;">11</td>
|
|
<td style="width:21px;">...</td>
|
|
</tr>
|
|
</tbody></table>
|
|
|
|
|
|
<h2>Duodecimal (Base 12)</h2>
|
|
|
|
<p>Duodecimal (Base 12) needs two more digits than Decimal, so "A" and "B" are used:</p>
|
|
|
|
<table style="border: 0;">
|
|
<tbody>
|
|
<tr style="text-align:center;">
|
|
<th>Decimal:</th>
|
|
<td style="width:21px;">0</td>
|
|
<td style="width:21px;">1</td>
|
|
<td style="width:21px;">2</td>
|
|
<td style="width:21px;">3</td>
|
|
<td style="width:21px;">4</td>
|
|
<td style="width:21px;">5</td>
|
|
<td style="width:21px;">6</td>
|
|
<td style="width:21px;">7</td>
|
|
<td style="width:21px;">8</td>
|
|
<td style="width:21px;">9</td>
|
|
<td style="width:21px;">10</td>
|
|
<td style="width:21px;">11</td>
|
|
<td style="width:21px;">12</td>
|
|
<td style="width:21px;">13</td>
|
|
<td style="width:21px;">...</td>
|
|
</tr>
|
|
<tr style="text-align:center;">
|
|
<th>Duodecimal:</th>
|
|
<td style="width:21px;">0</td>
|
|
<td style="width:21px;">1</td>
|
|
<td style="width:21px;">2</td>
|
|
<td style="width:21px;">3</td>
|
|
<td style="width:21px;">4</td>
|
|
<td style="width:21px;">5</td>
|
|
<td style="width:21px;">6</td>
|
|
<td style="width:21px;">7</td>
|
|
<td style="width:21px;">8</td>
|
|
<td style="width:21px;">9</td>
|
|
<td style="width:21px;"><b>A</b></td>
|
|
<td style="width:21px;"><b>B</b></td>
|
|
<td style="width:21px;">10</td>
|
|
<td style="width:21px;">11</td>
|
|
<td style="width:21px;">...</td>
|
|
</tr>
|
|
</tbody></table>
|
|
|
|
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/paws-16.svg" alt="4 paws make 16" height="108" width="200"></p>
|
|
<h2>Hexadecimal (Base 16)</h2>
|
|
|
|
|
|
<p>Dogs might understand hexadecimal well.</p>
|
|
<p>It uses the digits <b>0 to 9</b>, then the six letters <b>A to F</b>, like this:</p>
|
|
<div style="clear:both">
|
|
|
|
</div>
|
|
<table style="border: 0;">
|
|
<tbody>
|
|
<tr style="text-align:center;">
|
|
<th>Decimal:</th>
|
|
<td style="width:21px;">0</td>
|
|
<td style="width:21px;">1</td>
|
|
<td style="width:21px;">2</td>
|
|
<td style="width:21px;">3</td>
|
|
<td style="width:21px;">4</td>
|
|
<td style="width:21px;">5</td>
|
|
<td style="width:21px;">6</td>
|
|
<td style="width:21px;">7</td>
|
|
<td style="width:21px;">8</td>
|
|
<td style="width:21px;">9</td>
|
|
<td style="width:21px;">10</td>
|
|
<td style="width:21px;">11</td>
|
|
<td style="width:21px;">12</td>
|
|
<td style="width:21px;">13</td>
|
|
<td style="width:21px;">14</td>
|
|
<td style="width:21px;">15</td>
|
|
<td style="width:21px;">16</td>
|
|
<td style="width:21px;">17</td>
|
|
<td style="width:21px;">...</td>
|
|
</tr>
|
|
<tr style="text-align:center;">
|
|
<th>Hexadecimal:</th>
|
|
<td style="width:21px;">0</td>
|
|
<td style="width:21px;">1</td>
|
|
<td style="width:21px;">2</td>
|
|
<td style="width:21px;">3</td>
|
|
<td style="width:21px;">4</td>
|
|
<td style="width:21px;">5</td>
|
|
<td style="width:21px;">6</td>
|
|
<td style="width:21px;">7</td>
|
|
<td style="width:21px;">8</td>
|
|
<td style="width:21px;">9</td>
|
|
<td style="width:21px;"><b>A</b></td>
|
|
<td style="width:21px;"><b>B</b></td>
|
|
<td style="width:21px;"><b>C</b></td>
|
|
<td style="width:21px;"><b>D</b></td>
|
|
<td style="width:21px;"><b>E</b></td>
|
|
<td style="width:21px;"><b>F</b></td>
|
|
<td style="width:21px;">10</td>
|
|
<td style="width:21px;">11</td>
|
|
<td style="width:21px;">...</td>
|
|
</tr>
|
|
</tbody></table>
|
|
|
|
|
|
<h2>Vigesimal (Base 20)</h2>
|
|
|
|
<p>With vigesimal, the convention is that <b>I</b> is not used because it looks like <b>1</b>, so <b>J</b>=18 and <b>K</b>=19, as in this table:</p>
|
|
|
|
<table style="border: 0;">
|
|
<tbody>
|
|
<tr style="text-align:center;">
|
|
<th>Decimal:</th>
|
|
<td style="width:21px;">0</td>
|
|
<td style="width:21px;">1</td>
|
|
<td style="width:21px;">2</td>
|
|
<td style="width:21px;">3</td>
|
|
<td style="width:21px;">4</td>
|
|
<td style="width:21px;">5</td>
|
|
<td style="width:21px;">6</td>
|
|
<td style="width:21px;">7</td>
|
|
<td style="width:21px;">8</td>
|
|
<td style="width:21px;">9</td>
|
|
<td style="width:21px;">10</td>
|
|
<td style="width:21px;">11</td>
|
|
<td style="width:21px;">12</td>
|
|
<td style="width:21px;">13</td>
|
|
<td style="width:21px;">14</td>
|
|
<td style="width:21px;">15</td>
|
|
<td style="width:21px;">16</td>
|
|
<td style="width:21px;">17</td>
|
|
<td style="width:21px;">18</td>
|
|
<td style="width:21px;">19</td>
|
|
<td style="width:21px;">20</td>
|
|
<td style="width:21px;">...</td>
|
|
</tr>
|
|
<tr style="text-align:center;">
|
|
<th>Vigesimal:</th>
|
|
<td style="width:21px;">0</td>
|
|
<td style="width:21px;">1</td>
|
|
<td style="width:21px;">2</td>
|
|
<td style="width:21px;">3</td>
|
|
<td style="width:21px;">4</td>
|
|
<td style="width:21px;">5</td>
|
|
<td style="width:21px;">6</td>
|
|
<td style="width:21px;">7</td>
|
|
<td style="width:21px;">8</td>
|
|
<td style="width:21px;">9</td>
|
|
<td style="width:21px;"><b>A</b></td>
|
|
<td style="width:21px;"><b>B</b></td>
|
|
<td style="width:21px;"><b>C</b></td>
|
|
<td style="width:21px;"><b>D</b></td>
|
|
<td style="width:21px;"><b>E</b></td>
|
|
<td style="width:21px;"><b>F</b></td>
|
|
<td style="width:21px;"><b>G</b></td>
|
|
<td style="width:21px;"><b>H</b></td>
|
|
<td style="width:21px;"><b>J</b></td>
|
|
<td style="width:21px;"><b>K</b></td>
|
|
<td style="width:21px;">10</td>
|
|
<td style="width:21px;">...</td>
|
|
</tr>
|
|
</tbody></table>
|
|
|
|
|
|
<h2>Sexagesimal (Base 60)</h2>
|
|
|
|
<p>Sexagesimal works like clockwork!</p>
|
|
<p>There are no special codes, just the numbers 0 to 59, like we use with hours and minutes.</p>
|
|
<iframe src="../measure/iclock-write.html" scrolling="no" style="width:252px; height:102px; overflow:hidden; margin:auto; display:block; border: none;"></iframe>
|
|
<p>The main advantage is that 60 can be evenly divided by 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30, which makes it easy for us to divide up hours and minutes.</p>
|
|
|
|
|
|
<h2>More About Bases</h2>
|
|
|
|
<div class="words">
|
|
<p>The Number Base is also called the <b>Radix</b></p>
|
|
</div>
|
|
|
|
|
|
<h2>How to Show the Base</h2>
|
|
|
|
<p>To show what base a number has, put the base in the lower right like this:</p>
|
|
<p class="center"><span class="largest"><b>101<sub>2</sub></b></span><b><sub><br>
|
|
</sub></b>This shows that is in Base 2 (Binary)</p>
|
|
<p class="center"><span class="largest"><b>314<sub>8</sub></b></span><b><sub><br>
|
|
</sub></b>This shows that is in Base 8 (Octal)</p>
|
|
<p> </p>
|
|
|
|
<div class="related">
|
|
<a href="../base-conversion-method.html">Base Conversion Method</a>
|
|
<a href="../hexadecimals.html">Hexadecimal</a>
|
|
</div>
|
|
<!-- #EndEditable -->
|
|
|
|
</article>
|
|
|
|
<div id="adend" class="centerfull noprint"></div>
|
|
<footer id="footer" class="centerfull noprint"></footer>
|
|
<div id="copyrt">Copyright © 2022 Rod Pierce</div>
|
|
|
|
</div>
|
|
</body><!-- #EndTemplate -->
|
|
<!-- Mirrored from www.mathsisfun.com/numbers/bases.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:45:26 GMT -->
|
|
</html> |