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		<title>5 Technology Stories from digg.com</title>
		<link>http://hockeyplaya55.wordpress.com/2009/04/29/5-technology-stories-from-diggcom/</link>
		<comments>http://hockeyplaya55.wordpress.com/2009/04/29/5-technology-stories-from-diggcom/#comments</comments>
		<pubDate>Wed, 29 Apr 2009 20:00:47 +0000</pubDate>
		<dc:creator>hockeyplaya55</dc:creator>
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		<description><![CDATA[1) Facebook vs MySpace   http://www.techcrunch.com/wp-content/uploads/2009/04/fb-vs-myspace.jpg I think this is significant because people can see which is more popular 2) Largest windmill  http://i.gizmodo.com/5223801/this-thing-is-just-too-damn-huge-to-be-realbut-it-is I think this is significant because it&#8217;s the worlds largest windmill being assembled 3) World Wildlife  Federation    http://www.flickr.com/photos/32895514@N02/3472074417/sizes/l/ 4) Scarpar Powerboard   http://i.gizmodo.com/5204650/scarpar-powerboard-is-the-closest-alternative-to-the-hoverboard 5) HD wallpapers  http://www.smashingapps.com/2009/04/12/35-colorful-and-inspiring-examples-of-high-definition-wallpapers.html<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=hockeyplaya55.wordpress.com&amp;blog=4734180&amp;post=28&amp;subd=hockeyplaya55&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>1) Facebook vs MySpace   <a href="http://www.techcrunch.com/wp-content/uploads/2009/04/fb-vs-myspace.jpg">http://www.techcrunch.com/wp-content/uploads/2009/04/fb-vs-myspace.jpg</a></p>
<p>I think this is significant because people can see which is more popular</p>
<p>2) Largest windmill  <a href="http://i.gizmodo.com/5223801/this-thing-is-just-too-damn-huge-to-be-realbut-it-is">http://i.gizmodo.com/5223801/this-thing-is-just-too-damn-huge-to-be-realbut-it-is</a></p>
<p>I think this is significant because it&#8217;s the worlds largest windmill being assembled</p>
<p>3) World Wildlife  Federation    <a href="http://www.flickr.com/photos/32895514@N02/3472074417/sizes/l/">http://www.flickr.com/photos/32895514@N02/3472074417/sizes/l/</a></p>
<p>4) Scarpar Powerboard   <a href="http://i.gizmodo.com/5204650/scarpar-powerboard-is-the-closest-alternative-to-the-hoverboard">http://i.gizmodo.com/5204650/scarpar-powerboard-is-the-closest-alternative-to-the-hoverboard</a></p>
<p>5) HD wallpapers  <a href="http://www.smashingapps.com/2009/04/12/35-colorful-and-inspiring-examples-of-high-definition-wallpapers.html">http://www.smashingapps.com/2009/04/12/35-colorful-and-inspiring-examples-of-high-definition-wallpapers.html</a></p>
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		<title>Internet Privacy Concerns</title>
		<link>http://hockeyplaya55.wordpress.com/2009/03/02/internet-privacy-concerns/</link>
		<comments>http://hockeyplaya55.wordpress.com/2009/03/02/internet-privacy-concerns/#comments</comments>
		<pubDate>Mon, 02 Mar 2009 19:12:42 +0000</pubDate>
		<dc:creator>hockeyplaya55</dc:creator>
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		<description><![CDATA[With Google Latitude, you can: See where your friends are and what they are up to Quickly contact them with SMS, IM, or a phone call Control what your location is and who gets to see it Enjoy Google Latitude on your phone, PC, or both. From your mobile phone &#8211; View your friends&#8217; locations [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=hockeyplaya55.wordpress.com&amp;blog=4734180&amp;post=24&amp;subd=hockeyplaya55&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>With Google Latitude, you can:</p>
<ul>
<li>See where your friends are and what they are up to</li>
<li>Quickly contact them with SMS, IM, or a phone call</li>
<li>Control what your location is and who gets to see it</li>
</ul>
<p>Enjoy Google Latitude on your phone, PC, or both.</p>
<p><strong>From your mobile phone</strong> &#8211; View your friends&#8217; locations and status messages and share yours with them</p>
<p><strong>From your computer</strong> &#8211; View your friends&#8217; locations and status messages on a full screen even without a compatible phone or data plan</p>
<p>Facebook founder <a href="http://blog.facebook.com/blog.php?post=54434097130"><strong>Mark Zuckerberg</strong> has responded</a> to the privacy concerns raised in <a href="http://consumerist.com/5150175/facebooks-new-terms-of-service-we-can-do-anything-we-want-with-your-content-forever">this post by Consumerist</a>.  The post pointed out that a change Facebook made to its <a href="http://www.facebook.com/terms.php">terms of service</a> left the impression that the social network could keep and use copies of user content (e.g. photos, notes, and personal information) in perpetuity even if users removed the information and closed their accounts.</p>
<p>&#8220;One of the questions about our new terms of use is whether Facebook can use this information forever,&#8221; Zuckerberg wrote.  But, oddly, he did not answer that question.  Instead he opted for a rather roundabout explanation: if you send a friend a message via Facebook&#8217;s e-mail system, Facebook must create mutliple copies of that message &#8212; one for your &#8220;sent&#8221; message box and one for your friend&#8217;s inbox. That way, if you leave Facebook, the copy your friend has would not be deleted. Fair enough.</p>
<p>The implication is that, by extension, Facebook also keeps copies of all your other information, too. </p>
<p>But the e-mail example has a major hole in it. Copying content makes sense for e-mails, where the medium itself depends on messages being copied. The thing is, Facebook users generally do not &#8216;send&#8217; other types of content to one another, including photographs. Rather, they post them on their own profiles for others to stop by and see. There&#8217;s no obvious reason that Facebook would need to perpetually store multiple copies of photographs &#8212; because, as far as the user is concerned, they appear only in one place.</p>
<p>Plus, Zuckerberg seems to underestimate his users&#8217; understanding of e-mail.  My guess is most Facebook users don&#8217;t think that if they close an e-mail account that all the e-mails they&#8217;ve ever sent will disappear.  Frankly, it&#8217;s not e-mails that are at issue here; it&#8217;s this other, more personal category of content &#8212; the stuff that people post within their own digital walls.</p>
<p>Zuckerberg goes on to write that despite the presence of &#8220;overly formal and protective&#8221; language that Facebook uses to cop eternal rights to your content (a slightly condescending formulation, if you ask me), &#8220;In reality, we wouldn&#8217;t share your information in a way you wouldn&#8217;t want. The trust you place in us as a safe place to share information is the most important part of what makes Facebook work.&#8221;</p>
<p>Facebook should at least get credit for announcing the terms-of-service changes in this <a href="http://blog.facebook.com/blog.php?post=50531412130">Feb. 4 blog post</a>, even though it drew no specific attention to the content ownership amendments, focusing instead on new prohibitions against harassment and providing false information.</p>
<p>And, truth be told, I doubt the company has any nefarious plans to sell all your old photos to the government, or spill out your archived wall postings into the public domain.  But you&#8217;d think one of the biggest social media companies in the world &#8212; one that&#8217;s dealt with outrage over <a href="http://articles.latimes.com/2007/nov/21/business/fi-facebook21">privacy issues before</a> &#8212; would have taken steps to avoid a publicity stink bomb like this.  Step one: proactively explain to its tens of millions of users exactly what these types of changes mean.</p>
<p>In that vein, it seems dubious that users will accept Zuckerberg&#8217;s entreaty to &#8216;just trust us&#8217; when, in his response to user confusion and suspicion, he has skirted the very question that he would have us believe he is addressing. </p>
<p>Users still don&#8217;t know why or whether Facebook keeps all their content on file without their explicit permission.  Not just messages, but &#8220;photos, text, link, audio, video, designs, ads and anything else that you post on or through the Facebook Service.&#8221;</p>
<p>Its aight. My image on social network sites is cool there are no concerns</p>
<p>I do think that employers can and should use the internet to research possible hires and current employees</p>
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		<title>Binary Tutorial Part 2</title>
		<link>http://hockeyplaya55.wordpress.com/2008/12/16/binary-tutorial-part-2/</link>
		<comments>http://hockeyplaya55.wordpress.com/2008/12/16/binary-tutorial-part-2/#comments</comments>
		<pubDate>Tue, 16 Dec 2008 17:43:21 +0000</pubDate>
		<dc:creator>hockeyplaya55</dc:creator>
				<category><![CDATA[Uncategorized]]></category>

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		<description><![CDATA[Binary Tutorial Part 2               There are Binary number stuff and ya there are numbers and stuff involved so here. These are tables and words that describe this binary number stuff.   The number system that you use is base 10 (since people have 10 fingers, this works out well for them). When you [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=hockeyplaya55.wordpress.com&amp;blog=4734180&amp;post=20&amp;subd=hockeyplaya55&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="text-decoration:underline;"><span style="font-size:small;"><span style="font-family:Times New Roman;">Binary Tutorial Part 2</span></span></span></strong></p>
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="text-decoration:underline;"><span style="text-decoration:none;"><span style="font-size:small;font-family:Times New Roman;"> </span></span></span></strong></p>
<p class="MsoNormal" style="margin:0;"><span style="font-size:small;"><span style="font-family:Times New Roman;"><span>            </span>There are Binary number stuff and ya there are numbers and stuff involved so here. These are tables and words that describe this binary number stuff.</span></span></p>
<p class="MsoNormal" style="margin:0;"><span style="font-size:small;font-family:Times New Roman;"> </span></p>
<div>
<table class="MsoNormalTable" style="width:202.25pt;" border="0" cellspacing="0" cellpadding="0" width="270">
<tbody>
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<td style="width:200.55pt;background-color:transparent;border:#ece9d8;padding:0;" width="267" valign="top">
<p class="para" style="margin:0 0 7.5pt;"><span style="font-size:small;"><span style="color:#666666;font-family:Georgia;">The number system that you use is </span><span class="term1"><span style="font-family:Georgia;"><strong>base 10</strong></span></span><span style="color:#666666;font-family:Georgia;"> (since people have 10 fingers, this works out well for them). When you write the number 1853, for example it means:</span></span></p>
<p class="para" style="text-align:center;margin:0 0 7.5pt;" align="center"><span style="color:#666666;font-family:Georgia;"></span></p>
<p class="para" style="margin:0 0 7.5pt;"><span style="color:#666666;font-family:Georgia;"><span style="font-size:small;">Each digit (0-9) within a base 10 number is multiplied by the power of ten corresponding to its position. Notice that each digit place has 10 times the value of the digit place to the right of it. But you knew all this, of course.</span></span></p>
<h3 style="margin:11.25pt 0 3.75pt;"><a name="binary"></a><span style="font-size:medium;color:#009900;">Binary Numbers </span></h3>
<p class="para" style="margin:0 0 7.5pt;"><span style="font-size:small;"><span style="color:#666666;font-family:Georgia;">But what of the poor computer, which has no fingers to count on? Base 10 is not convenient for a fingerless computer to use. What computers DO have, are electrical circuits, which are either <strong><em><span style="font-family:Georgia;">on</span></em></strong> or <strong><em><span style="font-family:Georgia;">off</span></em></strong>. Just two states to work with. So the natural number system for use in an electronic computer is </span><span class="term1"><span style="font-family:Georgia;"><strong>base 2</strong></span></span><span style="color:#666666;font-family:Georgia;"> (called the </span><span class="term1"><span style="font-family:Georgia;"><strong>binary</strong></span></span><span style="color:#666666;font-family:Georgia;"> number system). Unlike you who have ten digits to calculate with (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), the computer has only two digits (0 and 1) with which it must do everything. So, in a computer’s memory, a tiny transistor that is <strong><em><span style="font-family:Georgia;">on</span></em></strong> (conducting a current) might represent a 1, while a transistor that is <strong><em><span style="font-family:Georgia;">off</span></em></strong> would represent a 0 (zero). </span></span></p>
<p class="para" style="margin:0 0 7.5pt;"><span style="color:#666666;font-family:Georgia;"><span style="font-size:small;">The binary number 11100111101, for example, means:</span></span></p>
<p class="para" style="text-align:center;margin:0 0 7.5pt;" align="center"><span style="color:#666666;font-family:Georgia;"></span></p>
<p class="para" style="margin:0 0 7.5pt;"><span style="color:#666666;font-family:Georgia;"><span style="font-size:small;">Ah! So they are the same number!</span></span></p>
<p class="para" style="text-align:center;margin:0 0 7.5pt;" align="center"><span style="color:#666666;font-family:Georgia;"><span style="font-size:small;">1853 (base 10)  =  11100111101 (base 2) </span></span></p>
<p class="para" style="margin:0 0 7.5pt;"><span style="color:#666666;font-family:Georgia;"><span style="font-size:small;">Notice that each binary digit position in the base 2 number has <strong><em><span style="font-family:Georgia;">2</span></em></strong> times the value of the binary digit position to the right of it (since this is base 2; remember how base 10 worked).</span></span></p>
<p class="para" style="margin:0 0 7.5pt;"><a name="bit"></a><span style="font-size:small;"><span style="color:#666666;font-family:Georgia;">It gets cumbersome saying “binary digit” all the time, so the shorter term “bit” was invented. A </span><span class="term1"><span style="font-family:Georgia;"><strong>bit</strong></span></span><span style="color:#666666;font-family:Georgia;"> is one <strong><span style="font-family:Georgia;">b</span></strong>inary dig<strong><span style="font-family:Georgia;">it</span></strong>. A bit can hold either a 1 or a 0 (zero). A string of bits can hold larger numbers (just as you use strings of base 10 digits to represent numbers larger than 9).</span></span></p>
<div>
<table class="MsoNormalTable" style="width:262.5pt;" border="1" cellspacing="0" cellpadding="0" width="350">
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<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;" colspan="2">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#006600;font-family:&quot;"><span style="font-size:small;">Binary Representation of Numbers </span></span></strong></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#006600;font-family:&quot;"><span style="font-size:small;">Base 10</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#006600;font-family:&quot;"><span style="font-size:small;">Base 2</span></span></strong></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">0</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">00000000</span></span></strong></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">1</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">00000001</span></span></strong></p>
</td>
</tr>
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<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">2</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">00000010</span></span></strong></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">3</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">00000011</span></span></strong></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">4</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">00000100</span></span></strong></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">5</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">00000101</span></span></strong></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">&#8230;</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">&#8230;</span></span></strong></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">65</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">01000001</span></span></strong></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">66</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">01000010</span></span></strong></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">67</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">01000011</span></span></strong></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">&#8230;</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">&#8230;</span></span></strong></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">254</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">11111110</span></span></strong></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">255</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">11111111</span></span></strong></p>
</td>
</tr>
</tbody>
</table>
</div>
<p class="para" style="margin:0 0 7.5pt;"><span style="color:#666666;font-family:Georgia;"><span style="font-size:small;"> </span></span></p>
<p class="para" style="margin:0 0 7.5pt;"><span style="color:#666666;font-family:Georgia;"><span style="font-size:small;">A particularly handy size chunk of computer memory happens to be 8 bits long. This size chunk of memory can be used to represent any number from zero (00000000) to 255 (11111111). Why does 11111111 (base 2) equal 255 (base 10)? Because it means:</span></span></p>
<p class="para" style="text-align:center;margin:0 0 7.5pt;" align="center"><span style="color:#666666;font-family:Georgia;"><span style="font-size:small;">1 x 128  +  1 x 64  +  1 x 32  +  1 x 16  + <br />
1 x 8  +  1 x 4  +  1 x 2  +  1 x 1  =  255</span></span></p>
<p class="para" style="margin:0 0 7.5pt;"><span style="color:#666666;font-family:Georgia;"><span style="font-size:small;">And why is this a handy size chunk of memory? Because if we want to represent all of the characters of the English alphabet, 8 digits is the first power of 2 that gives you enough possibilities to do this (a 4-bit long chunk can only hold numbers from zero to 7&#8230;not enough). </span></span></p>
<p class="para" style="margin:0 0 7.5pt;"><a name="byte"></a><span style="font-size:small;"><span style="color:#666666;font-family:Georgia;">We have a special name for a chunk of memory that is 8 bits long: it is called a </span><span class="term1"><span style="font-family:Georgia;"><strong>byte</strong></span></span><span style="color:#666666;font-family:Georgia;">. This is the basic unit we use to measure computer memory size. (A chunk of memory 4 bits long is called a “nybble,” but you don&#8217;t need to know that for the test.)</span></span></p>
<p class="para" style="margin:0 0 7.5pt;"><a name="ascii"></a><span style="font-size:small;"><span style="color:#666666;font-family:Georgia;">Text characters are represented in computer memory as numbers. How? You need a scheme for equating letters to numbers. The system used is called the </span><span class="term1"><span style="font-family:Georgia;"><strong>ASCII</strong></span></span><span style="color:#666666;font-family:Georgia;"> code (</span><span class="term1"><span style="font-family:Georgia;"><strong>American Standard Code for Information Interchange</strong></span></span><span style="color:#666666;font-family:Georgia;">). The capital letter <strong><span style="font-family:Georgia;">A</span></strong> is represented by the number <strong><span style="font-family:Georgia;">65</span></strong> in the ASCII code (<strong><span style="font-family:Georgia;">65</span></strong> is <strong><span style="font-family:Georgia;">01000001</span></strong> in binary). The first 65 ASCII codes (0 through 64) are used for an assortment of Control characters and special characters, so capital <strong><span style="font-family:Georgia;">A</span></strong> ended up at 65. Capital <strong><span style="font-family:Georgia;">B</span></strong> is <strong><span style="font-family:Georgia;">66</span></strong> (<strong><span style="font-family:Georgia;">01000010</span></strong>) and so on. </span></span></p>
<div>
<table class="MsoNormalTable" style="width:300pt;" border="1" cellspacing="0" cellpadding="0" width="400">
<tbody>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;" colspan="3">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#006600;font-family:&quot;"><span style="font-size:small;">ASCII Representation of Characters (just a sample) </span></span></strong></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#006600;font-family:&quot;"><span style="font-size:small;">Character</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#006600;font-family:&quot;"><span style="font-size:small;">Base 10 </span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#006600;font-family:&quot;"><span style="font-size:small;">Base 2</span></span></strong></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">(return)</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">13</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">00001101</span></span></strong></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">(space)</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">32</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">00100000</span></span></strong></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">!</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">33</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">00100001</span></span></strong></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">1</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">49</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">00110001</span></span></strong></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">2</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">50</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">00110010</span></span></strong></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">@</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">64</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">01000000</span></span></strong></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">A</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">65</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">01000001</span></span></strong></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">B</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">66</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">01000010</span></span></strong></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">C</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">67</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">01000011</span></span></strong></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">a</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">97</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">01100001</span></span></strong></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">b</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">98</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">01100010</span></span></strong></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">c</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">99</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">01100011</span></span></strong></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">(delete)</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">127</span></span></strong></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:1.5pt;">
<p class="MsoNormal" style="text-align:center;margin:0;" align="center"><strong><span style="color:#666666;font-family:&quot;"><span style="font-size:small;">01111111</span></span></strong></p>
</td>
</tr>
</tbody>
</table>
</div>
<p class="para" style="margin:0 0 7.5pt;"><span style="color:#666666;font-family:Georgia;"><span style="font-size:small;"> </span></span></p>
<p class="para" style="margin:0 0 7.5pt;"><span style="color:#666666;font-family:Georgia;"><span style="font-size:small;">How does the computer know whether the <strong><span style="font-family:Georgia;">01000001</span></strong> in a byte of memory is the number <strong><span style="font-family:Georgia;">65</span></strong> or the letter <strong><span style="font-family:Georgia;">A</span></strong>? Because an application program keeps track of what it put where in memory, so MS Word knows that a given byte where it has stored text contains numbers that represent letters.</span><a name="kilo"></a></span></p>
</td>
<td style="width:1.7pt;background-color:transparent;border:#ece9d8;padding:0;" width="2" valign="top">
<p class="MsoNormal" style="margin:0;"><span style="color:#666666;font-family:Georgia;"><span style="font-size:small;"> </span></span></p>
</td>
</tr>
</tbody>
</table>
</div>
<p class="MsoNormal" style="margin:0;"><span style="font-size:small;font-family:Times New Roman;">Now that the charts tell stuff it’s now time to look at more charts on how to convert Hexadecimal to base 10, here is the Hexadecimal system of system stuff.</span></p>
<p class="MsoNormal" style="margin:0;"><span style="font-size:small;font-family:Times New Roman;"> </span></p>
<p class="MsoNormal" style="margin:0;"><span style="color:black;font-family:Verdana;"><span style="font-size:small;">Hexadecimal System uses 16 digits:</p>
<p><strong>0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F</strong></p>
<p>And thus the <strong>base</strong> is <strong>16</strong>.</p>
<p>Hexadecimal numbers are compact and easy to read.<br />
It is very easy to convert numbers from binary system to hexadecimal system and vice-versa, every nibble (4 bits) can be converted to a hexadecimal digit using this table:</p>
<p></span><a name="hextable"><span style="font-size:small;"> </span></a><span style="font-size:small;"> </span></span></p>
<table class="MsoNormalTable" border="0" cellspacing="10" cellpadding="0">
<tbody>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<table class="MsoNormalTable" border="1" cellpadding="0">
<tbody>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><strong><span style="font-size:10pt;color:black;font-family:Verdana;">Decimal<br />
(base 10)</span></strong><span style="font-size:10pt;color:black;font-family:Verdana;"></span></td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><strong><span style="font-size:10pt;color:black;font-family:Verdana;">Binary<br />
(base 2)</span></strong><span style="font-size:10pt;color:black;font-family:Verdana;"></span></td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><strong><span style="font-size:10pt;color:black;font-family:Verdana;">Hexadecimal<br />
(base 16)</span></strong><span style="font-size:10pt;color:black;font-family:Verdana;"></span></td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">0</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">0000</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">0</span></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">1</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">0001</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">1</span></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">2</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">0010</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">2</span></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">3</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">0011</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">3</span></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">4</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">0100</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">4</span></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">5</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">0101</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">5</span></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">6</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">0110</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">6</span></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">7</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">0111</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">7</span></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">8</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">1000</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">8</span></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">9</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">1001</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">9</span></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">10</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">1010</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">A</span></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">11</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">1011</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">B</span></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">12</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">1100</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">C</span></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">13</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">1101</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">D</span></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">14</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">1110</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">E</span></p>
</td>
</tr>
<tr>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">15</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">1111</span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;">F</span></p>
</td>
</tr>
</tbody>
</table>
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;"></span></p>
</td>
<td style="background-color:transparent;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="font-size:10pt;color:black;font-family:Verdana;"></span></p>
</td>
</tr>
</tbody>
</table>
<p class="MsoNormal" style="margin:0;"><span style="color:black;font-family:Verdana;"></p>
<p><span style="font-size:small;">There is a convention to add <strong>&#8220;h&#8221;</strong> in the end of a hexadecimal number, this way we can determine that 5Fh is a hexadecimal number with decimal value of 95.<br />
We also add <strong>&#8220;0&#8243;</strong> (zero) in the beginning of hexadecimal numbers that begin with a letter (A..F), for example <strong>0E120h</strong>.</p>
<p>The hexadecimal number <strong>1234h</strong> is equal to decimal value of 4660:</p>
<p></span></span></p>
<p class="MsoNormal" style="margin:0;"><span style="color:black;font-family:Verdana;"><span style="font-size:small;">If you want to learn how to convert decimals into hexadecimals all u do is divide, here are a lot of charts.</span></span></p>
<ol type="1">
<li class="MsoNormal"><span style="font-family:Arial;"><span style="font-size:small;">Divide the decimal number by 16.   Treat the division as an integer division.   </span></span></li>
<li class="MsoNormal"><span style="font-family:Arial;"><span style="font-size:small;">Write down the remainder (in hexadecimal). </span></span></li>
<li class="MsoNormal"><span style="font-family:Arial;"><span style="font-size:small;">Divide the result again by 16.  Treat the division as an integer division.   </span></span></li>
<li class="MsoNormal"><span style="font-family:Arial;"><span style="font-size:small;">Repeat step 2 and 3 until result is 0. </span></span></li>
<li class="MsoNormal"><span style="font-family:Arial;"><span style="font-size:small;">The hex value is the digit sequence of the remainders from the last to first. </span></span></li>
</ol>
<table class="MsoNormalTable" style="border:1.5pt outset;" border="1" cellpadding="0">
<tbody>
<tr>
<td style="background:#cccc66;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">HEXADECIMAL</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">0</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">1</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">2</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">3</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">4</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">5</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">6</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">7</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">8</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">9</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">A</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">B</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">C</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">D</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">E</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">F</span></span></p>
</td>
</tr>
<tr>
<td style="background:#cccc66;border:#ece9d8;padding:.75pt;">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">DECIMAL</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">0</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">1</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">2</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">3</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">4</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">5</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">6</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">7</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">8</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">9</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">10</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">11</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">12</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">13</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">14</span></span></p>
</td>
<td style="width:22.5pt;background-color:transparent;border:#ece9d8;padding:.75pt;" width="30">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">15</span></span></p>
</td>
</tr>
</tbody>
</table>
<p class="MsoNormal" style="margin:0;"><span style="font-size:small;"><strong><span style="color:#cc0000;font-family:Arial;">Example 1 <br />
</span></strong><span style="color:#003333;font-family:Arial;">Convert the number <strong>1128</strong> DECIMAL to HEXADECIMAL</span></span></p>
<table class="MsoNormalTable" style="width:393pt;border:black 1pt outset;" border="1" cellspacing="0" cellpadding="0" width="524">
<tbody>
<tr>
<td style="background:#cccccc;width:183.75pt;border:black 1pt inset;padding:1.5pt;" width="245">
<p class="MsoNormal" style="margin:0;"><span style="font-size:small;"><strong><span style="color:#003333;font-family:Arial;">NOTES</span></strong><span style="color:#003333;font-family:Arial;"></span></span></p>
</td>
<td style="background:#cccccc;width:79.5pt;border:black 1pt inset;padding:1.5pt;" width="106">
<p class="MsoNormal" style="margin:0;"><span style="font-size:small;"><strong><span style="color:#003333;font-family:Arial;">DIVISION</span></strong><span style="color:#003333;font-family:Arial;"></span></span></p>
</td>
<td style="background:#cccccc;width:84pt;border:black 1pt inset;padding:1.5pt;" width="112">
<p class="MsoNormal" style="margin:0;"><span style="font-size:small;"><strong><span style="color:#003333;font-family:Arial;">RESULT</span></strong><span style="color:#003333;font-family:Arial;"></span></span></p>
</td>
<td style="background:#cccccc;width:113.25pt;border:black 1pt inset;padding:1.5pt;" width="151">
<p class="MsoNormal" style="margin:0;"><span style="font-size:small;"><strong><span style="color:#003333;font-family:Arial;">REMAINDER (in HEXADECIMAL)</span></strong><span style="color:#003333;font-family:Arial;"></span></span></p>
</td>
</tr>
<tr>
<td style="width:183.75pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="245">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">Start by dividing the number by 16.  </p>
<p>In this case, 1128 divided by 16 is 70.5.  So the integer division result is 70 (throw out anything after the decimal point).</p>
<p>The remainder is (70.5 &#8211; 70) multiplied with 16; or (0.5 times 16), which is 8.</span></span></td>
<td style="width:79.5pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="106">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">1128 / 16</span></span></p>
</td>
<td style="width:84pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="112">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">70</span></span></p>
</td>
<td style="width:113.25pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="151">
<p class="MsoNormal" style="margin:0;"><span style="font-size:small;"><strong><span style="color:#003333;font-family:Arial;">8</span></strong><span style="color:#003333;font-family:Arial;"></span></span></p>
</td>
</tr>
<tr>
<td style="width:183.75pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="245">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">Then, divide the result again by 16 </p>
<p>(the number 70 on the DIVISION column  comes from the previous RESULT). </span></span></p>
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">In this case, 70/16=4.375.  So the integer division result is 4 (throw out anything after the decimal point)</span></span></p>
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">The remainder is (0.375 multiplied with 16, which is 6.</span></span></p>
</td>
<td style="width:79.5pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="106">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">70 / 16</span></span></p>
</td>
<td style="width:84pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="112">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">4</span></span></p>
</td>
<td style="width:113.25pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="151">
<p class="MsoNormal" style="margin:0;"><span style="font-size:small;"><strong><span style="color:#003333;font-family:Arial;">6</span></strong><span style="color:#003333;font-family:Arial;"></span></span></p>
</td>
</tr>
<tr>
<td style="width:183.75pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="245">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">Repeat.   Note here that 4/16=0.25.  So the integer division result is 0. </span></span></p>
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">The remainder is (0.25-0) multiplied with 16, which is 4.</span></span></p>
</td>
<td style="width:79.5pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="106">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">4 / 16</span></span></p>
</td>
<td style="width:84pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="112">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">0</span></span></p>
</td>
<td style="width:113.25pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="151">
<p class="MsoNormal" style="margin:0;"><span style="font-size:small;"><strong><span style="color:#003333;font-family:Arial;">4</span></strong><span style="color:#003333;font-family:Arial;"></span></span></p>
</td>
</tr>
<tr>
<td style="width:183.75pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="245">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">Stop because the result is already 0 (0 divided by 16 will always be 0)</span></span></p>
</td>
<td style="width:79.5pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="106">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;"> </span></span></p>
</td>
<td style="width:84pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="112">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;"> </span></span></p>
</td>
<td style="width:113.25pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="151">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;"> </span></span></p>
</td>
</tr>
<tr>
<td style="background:#ccffff;width:183.75pt;border:black 1pt inset;padding:1.5pt;" width="245">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">Well, here is the answer. These numbers come from the REMAINDER column values (read from bottom to top)</span></span></p>
</td>
<td style="background:#ccffff;width:79.5pt;border:black 1pt inset;padding:1.5pt;" width="106">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;"> </span></span></p>
</td>
<td style="background:#ccffff;width:84pt;border:black 1pt inset;padding:1.5pt;" width="112">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;"> </span></span></p>
</td>
<td style="background:#ccffff;width:113.25pt;border:black 1pt inset;padding:1.5pt;" width="151">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">468</span></span></p>
</td>
</tr>
</tbody>
</table>
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">Side note: You can get the remainder of a division using the <strong>Modulus</strong> or <strong>%</strong> operator.  Ie: 1128%16=8.  <br />
</span></span><strong><span style="color:#cc0000;font-family:Arial;"><br />
<span style="font-size:small;">Example 2 </span></span></strong><strong><span style="color:#0099cc;font-family:Arial;"><br />
</span></strong><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">Convert the number <strong>256</strong> DECIMAL to HEXADECIMAL</span></span></p>
<table class="MsoNormalTable" style="width:343.5pt;border:black 1pt outset;" border="1" cellspacing="0" cellpadding="0" width="458">
<tbody>
<tr>
<td style="background:#cccccc;width:66.75pt;border:black 1pt inset;padding:1.5pt;" width="89">
<p class="MsoNormal" style="margin:0;"><span style="font-size:small;"><strong><span style="color:#003333;font-family:Arial;">DIVISION</span></strong><span style="color:#003333;font-family:Arial;"></span></span></p>
</td>
<td style="background:#cccccc;width:62.25pt;border:black 1pt inset;padding:1.5pt;" width="83">
<p class="MsoNormal" style="margin:0;"><span style="font-size:small;"><strong><span style="color:#003333;font-family:Arial;">RESULT</span></strong><span style="color:#003333;font-family:Arial;"></span></span></p>
</td>
<td style="background:#cccccc;width:130.5pt;border:black 1pt inset;padding:1.5pt;" width="174">
<p class="MsoNormal" style="margin:0;"><span style="font-size:small;"><strong><span style="color:#003333;font-family:Arial;">REMAINDER (in HEX)</span></strong><span style="color:#003333;font-family:Arial;"></span></span></p>
</td>
</tr>
<tr>
<td style="width:66.75pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="89">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">256 / 16</span></span></p>
</td>
<td style="width:62.25pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="83">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">16</span></span></p>
</td>
<td style="width:130.5pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="174">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">0</span></span></p>
</td>
</tr>
<tr>
<td style="width:66.75pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="89">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">16 / 16</span></span></p>
</td>
<td style="width:62.25pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="83">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">1</span></span></p>
</td>
<td style="width:130.5pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="174">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">0</span></span></p>
</td>
</tr>
<tr>
<td style="width:66.75pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="89">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">1 / 16</span></span></p>
</td>
<td style="width:62.25pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="83">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">0</span></span></p>
</td>
<td style="width:130.5pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="174">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">1</span></span></p>
</td>
</tr>
<tr>
<td style="width:66.75pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="89">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;"> </span></span></p>
</td>
<td style="width:62.25pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="83">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;"> </span></span></p>
</td>
<td style="width:130.5pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="174">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;"> </span></span></p>
</td>
</tr>
<tr>
<td style="background:#ccffff;width:66.75pt;border:black 1pt inset;padding:1.5pt;" width="89">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">ANSWER</span></span></p>
</td>
<td style="background:#ccffff;width:62.25pt;border:black 1pt inset;padding:1.5pt;" width="83">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;"> </span></span></p>
</td>
<td style="background:#ccffff;width:130.5pt;border:black 1pt inset;padding:1.5pt;" width="174">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">100</span></span></p>
</td>
</tr>
</tbody>
</table>
<p class="MsoNormal" style="margin:0;"><strong><span style="color:#cc0000;font-family:Arial;"><br />
<span style="font-size:small;">Example 3<br />
</span></span></strong><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">Convert the number <strong>921</strong> DECIMAL to HEXADECIMAL</span></span></p>
<table class="MsoNormalTable" style="width:343.5pt;border:black 1pt outset;" border="1" cellspacing="0" cellpadding="0" width="458">
<tbody>
<tr>
<td style="background:#cccccc;width:79.5pt;border:black 1pt inset;padding:1.5pt;" width="106">
<p class="MsoNormal" style="margin:0;"><span style="font-size:small;"><strong><span style="color:#003333;font-family:Arial;">DIVISION</span></strong><span style="color:#003333;font-family:Arial;"></span></span></p>
</td>
<td style="background:#cccccc;width:84pt;border:black 1pt inset;padding:1.5pt;" width="112">
<p class="MsoNormal" style="margin:0;"><span style="font-size:small;"><strong><span style="color:#003333;font-family:Arial;">RESULT</span></strong><span style="color:#003333;font-family:Arial;"></span></span></p>
</td>
<td style="background:#cccccc;width:165pt;border:black 1pt inset;padding:1.5pt;" width="220">
<p class="MsoNormal" style="margin:0;"><span style="font-size:small;"><strong><span style="color:#003333;font-family:Arial;">REMAINDER (in HEX)</span></strong><span style="color:#003333;font-family:Arial;"></span></span></p>
</td>
</tr>
<tr>
<td style="width:79.5pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="106">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">921 / 16</span></span></p>
</td>
<td style="width:84pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="112">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">57</span></span></p>
</td>
<td style="width:165pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="220">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">9</span></span></p>
</td>
</tr>
<tr>
<td style="width:79.5pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="106">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">57 / 16</span></span></p>
</td>
<td style="width:84pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="112">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">3</span></span></p>
</td>
<td style="width:165pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="220">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">9</span></span></p>
</td>
</tr>
<tr>
<td style="width:79.5pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="106">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">3 / 16</span></span></p>
</td>
<td style="width:84pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="112">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">0</span></span></p>
</td>
<td style="width:165pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="220">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">3</span></span></p>
</td>
</tr>
<tr>
<td style="width:79.5pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="106">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;"> </span></span></p>
</td>
<td style="width:84pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="112">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;"> </span></span></p>
</td>
<td style="width:165pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="220">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;"> </span></span></p>
</td>
</tr>
<tr>
<td style="background:#ccffff;width:79.5pt;border:black 1pt inset;padding:1.5pt;" width="106">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">ANSWER</span></span></p>
</td>
<td style="background:#ccffff;width:84pt;border:black 1pt inset;padding:1.5pt;" width="112">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;"> </span></span></p>
</td>
<td style="background:#ccffff;width:165pt;border:black 1pt inset;padding:1.5pt;" width="220">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">399</span></span></p>
</td>
</tr>
</tbody>
</table>
<p class="MsoNormal" style="margin:0;"><strong><span style="color:#cc0000;font-family:Arial;"><br />
<span style="font-size:small;">Example 4<br />
</span></span></strong><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">Convert the number <strong>188</strong> DECIMAL to HEXADECIMAL</span></span></p>
<table class="MsoNormalTable" style="width:344.25pt;border:black 1pt outset;" border="1" cellspacing="0" cellpadding="0" width="459">
<tbody>
<tr>
<td style="background:#cccccc;width:79.5pt;border:black 1pt inset;padding:1.5pt;" width="106">
<p class="MsoNormal" style="margin:0;"><span style="font-size:small;"><strong><span style="color:#003333;font-family:Arial;">DIVISION</span></strong><span style="color:#003333;font-family:Arial;"></span></span></p>
</td>
<td style="background:#cccccc;width:84pt;border:black 1pt inset;padding:1.5pt;" width="112">
<p class="MsoNormal" style="margin:0;"><span style="font-size:small;"><strong><span style="color:#003333;font-family:Arial;">RESULT</span></strong><span style="color:#003333;font-family:Arial;"></span></span></p>
</td>
<td style="background:#cccccc;width:165.75pt;border:black 1pt inset;padding:1.5pt;" width="221">
<p class="MsoNormal" style="margin:0;"><span style="font-size:small;"><strong><span style="color:#003333;font-family:Arial;">REMAINDER<br />
(in HEX)</span></strong><span style="color:#003333;font-family:Arial;"></span></span></td>
</tr>
<tr>
<td style="width:79.5pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="106">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">188 / 16</span></span></p>
</td>
<td style="width:84pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="112">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">11</span></span></p>
</td>
<td style="width:165.75pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="221">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">C (12 decimal)</span></span></p>
</td>
</tr>
<tr>
<td style="width:79.5pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="106">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">11 / 16</span></span></p>
</td>
<td style="width:84pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="112">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">0</span></span></p>
</td>
<td style="width:165.75pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="221">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">B (11 decimal)</span></span></p>
</td>
</tr>
<tr>
<td style="width:79.5pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="106">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;"> </span></span></p>
</td>
<td style="width:84pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="112">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;"> </span></span></p>
</td>
<td style="width:165.75pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="221">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;"> </span></span></p>
</td>
</tr>
<tr>
<td style="background:#ccffff;width:79.5pt;border:black 1pt inset;padding:1.5pt;" width="106">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">ANSWER</span></span></p>
</td>
<td style="background:#ccffff;width:84pt;border:black 1pt inset;padding:1.5pt;" width="112">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;"> </span></span></p>
</td>
<td style="background:#ccffff;width:165.75pt;border:black 1pt inset;padding:1.5pt;" width="221">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">BC</span></span></p>
</td>
</tr>
</tbody>
</table>
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">Note that here, the answer would not be 1112, but BC.  Remember to write down the remainder in hex, not decimal.</span></span></p>
<p class="MsoNormal" style="margin:0;"><strong><span style="color:#cc0000;font-family:Arial;"><br />
<span style="font-size:small;">Example 5<br />
</span></span></strong><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">Convert the number <strong>590</strong> DECIMAL to HEXADECIMAL</span></span></p>
<table class="MsoNormalTable" style="width:344.25pt;border:black 1pt outset;" border="1" cellspacing="0" cellpadding="0" width="459">
<tbody>
<tr>
<td style="background:#cccccc;width:79.5pt;border:black 1pt inset;padding:1.5pt;" width="106">
<p class="MsoNormal" style="margin:0;"><span style="font-size:small;"><strong><span style="color:#003333;font-family:Arial;">DIVISION</span></strong><span style="color:#003333;font-family:Arial;"></span></span></p>
</td>
<td style="background:#cccccc;width:84pt;border:black 1pt inset;padding:1.5pt;" width="112">
<p class="MsoNormal" style="margin:0;"><span style="font-size:small;"><strong><span style="color:#003333;font-family:Arial;">RESULT</span></strong><span style="color:#003333;font-family:Arial;"></span></span></p>
</td>
<td style="background:#cccccc;width:165.75pt;border:black 1pt inset;padding:1.5pt;" width="221">
<p class="MsoNormal" style="margin:0;"><span style="font-size:small;"><strong><span style="color:#003333;font-family:Arial;">REMAINDER<br />
(HEX)</span></strong><span style="color:#003333;font-family:Arial;"></span></span></td>
</tr>
<tr>
<td style="width:79.5pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="106">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">590 / 16</span></span></p>
</td>
<td style="width:84pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="112">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">36</span></span></p>
</td>
<td style="width:165.75pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="221">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">E (14 decimal)</span></span></p>
</td>
</tr>
<tr>
<td style="width:79.5pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="106">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">36 / 16</span></span></p>
</td>
<td style="width:84pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="112">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">2</span></span></p>
</td>
<td style="width:165.75pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="221">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">4 (4 decimal)</span></span></p>
</td>
</tr>
<tr>
<td style="width:79.5pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="106">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">2 / 16</span></span></p>
</td>
<td style="width:84pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="112">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">0</span></span></p>
</td>
<td style="width:165.75pt;background-color:transparent;border:black 1pt inset;padding:1.5pt;" width="221">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">2 (2 decimal)</span></span></p>
</td>
</tr>
<tr>
<td style="background:white;width:79.5pt;border:black 1pt inset;padding:1.5pt;" width="106">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;"> </span></span></p>
</td>
<td style="background:white;width:84pt;border:black 1pt inset;padding:1.5pt;" width="112">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;"> </span></span></p>
</td>
<td style="background:white;width:165.75pt;border:black 1pt inset;padding:1.5pt;" width="221">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;"> </span></span></p>
</td>
</tr>
<tr>
<td style="background:#ccffff;width:79.5pt;border:black 1pt inset;padding:1.5pt;" width="106">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">ANSWER</span></span></p>
</td>
<td style="background:#ccffff;width:84pt;border:black 1pt inset;padding:1.5pt;" width="112">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;"> </span></span></p>
</td>
<td style="background:#ccffff;width:165.75pt;border:black 1pt inset;padding:1.5pt;" width="221">
<p class="MsoNormal" style="margin:0;"><span style="color:#003333;font-family:Arial;"><span style="font-size:small;">24E</span></span></p>
</td>
</tr>
</tbody>
</table>
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		<title>Binary Number Tutorial</title>
		<link>http://hockeyplaya55.wordpress.com/2008/12/12/binary-number-tutorial/</link>
		<comments>http://hockeyplaya55.wordpress.com/2008/12/12/binary-number-tutorial/#comments</comments>
		<pubDate>Fri, 12 Dec 2008 17:34:12 +0000</pubDate>
		<dc:creator>hockeyplaya55</dc:creator>
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		<description><![CDATA[The simplest arithmetic operation in binary is addition. Adding two single-digit binary numbers is relatively simple: 0 + 0 → 0 0 + 1 → 1 1 + 0 → 1 1 + 1 → 0, carry 1 (since 1 + 1 = 0 + 1 × 10 in binary) Adding two &#8220;1&#8243; digits produces [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=hockeyplaya55.wordpress.com&amp;blog=4734180&amp;post=18&amp;subd=hockeyplaya55&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>The simplest arithmetic operation in binary is <a title="Addition" href="http://hockeyplaya55.wordpress.com/wiki/Addition"><span style="color:#002bb8;">addition</span></a>. Adding two single-digit binary numbers is relatively simple:</p>
<dl>
<dd>0 + 0 → 0 </dd>
<dd>0 + 1 → 1 </dd>
<dd>1 + 0 → 1 </dd>
<dd>1 + 1 → 0, carry 1 (since 1 + 1 = 0 + 1 × 10 in binary) </dd>
</dl>
<p>Adding two &#8220;1&#8243; digits produces a digit &#8220;0&#8243;, while 1 will have to be added to the next column. This is similar to what happens in decimal when certain single-digit numbers are added together; if the result equals or exceeds the value of the radix (10), the digit to the left is incremented:</p>
<dl>
<dd>5 + 5 → 0, carry 1 (since 5 + 5 = 0 + 1 × 10) </dd>
<dd>7 + 9 → 6, carry 1 (since 7 + 9 = 6 + 1 × 10) </dd>
</dl>
<p>This is known as <em>carrying</em>. When the result of an addition exceeds the value of a digit, the procedure is to &#8220;carry&#8221; the excess amount divided by the radix (that is, 10/10) to the left, adding it to the next positional value. This is correct since the next position has a weight that is higher by a factor equal to the radix. Carrying works the same way in binary:</p>
<pre>  1 1 1 1 1  (carried digits)
    0 1 1 0 1
+   1 0 1 1 1
-------------
= 1 0 0 1 0 0</pre>
<p>In this example, two numerals are being added together: 01101<sub>2</sub> (13 decimal) and 10111<sub>2</sub> (23 decimal). The top row shows the carry bits used. Starting in the rightmost column, 1 + 1 = 10<sub>2</sub>. The 1 is carried to the left, and the 0 is written at the bottom of the rightmost column. The second column from the right is added: 1 + 0 + 1 = 10<sub>2</sub> again; the 1 is carried, and 0 is written at the bottom. The third column: 1 + 1 + 1 = 11<sub>2</sub>. This time, a 1 is carried, and a 1 is written in the bottom row. Proceeding like this gives the final answer 100100<sub>2</sub> (36 decimal).</p>
<p>When computers must add two numbers, the rule that: x xor y = (x + y) mod 2 for any two bits x and y allows for very fast calculation, as well.</p>
<p><a id="Subtraction" name="Subtraction"></a></p>
<h3><span class="editsection">[<a title="Subtraction" href="http://hockeyplaya55.wordpress.com/w/index.php?title=Binary_numeral_system&amp;action=edit&amp;section=6"><span style="color:#002bb8;">edit</span></a>]</span> <span class="mw-headline">Subtraction</span></h3>
<p><a title="Subtraction" href="http://hockeyplaya55.wordpress.com/wiki/Subtraction"><span style="color:#002bb8;">Subtraction</span></a> works in much the same way:</p>
<dl>
<dd>0 − 0 → 0 </dd>
<dd>0 − 1 → 1, borrow 1 </dd>
<dd>1 − 0 → 1 </dd>
<dd>1 − 1 → 0 </dd>
</dl>
<p>Subtracting a &#8220;1&#8243; digit from a &#8220;0&#8243; digit produces the digit &#8220;1&#8243;, while 1 will have to be subtracted from the next column. This is known as <em>borrowing</em>. The principle is the same as for carrying. When the result of a subtraction is less than 0, the least possible value of a digit, the procedure is to &#8220;borrow&#8221; the deficit divided by the radix (that is, 10/10) from the left, subtracting it from the next positional value.</p>
<pre>    *   * * *   (starred columns are borrowed from)
  1 1 0 1 1 1 0
−     1 0 1 1 1
----------------
= 1 0 1 0 1 1 1</pre>
<p>Subtracting a positive number is equivalent to <em>adding</em> a <a title="Negative and non-negative numbers" href="http://hockeyplaya55.wordpress.com/wiki/Negative_and_non-negative_numbers"><span style="color:#002bb8;">negative</span></a> number of equal <a title="Absolute value" href="http://hockeyplaya55.wordpress.com/wiki/Absolute_value"><span style="color:#002bb8;">absolute value</span></a>; computers typically use <a title="Two's complement" href="http://hockeyplaya55.wordpress.com/wiki/Two%27s_complement"><span style="color:#002bb8;">two&#8217;s complement</span></a> notation to represent negative values. This notation eliminates the need for a separate &#8220;subtract&#8221; operation. The subtraction can be summarized with this formula:</p>
<p><strong>A &#8211; B = A + not B + 1</strong></p>
<p>For further details, see <a title="Two's complement" href="http://hockeyplaya55.wordpress.com/wiki/Two%27s_complement"><span style="color:#002bb8;">two&#8217;s complement</span></a>.</p>
<p><a id="Multiplication" name="Multiplication"></a></p>
<h3><span class="editsection">[<a title="Multiplication" href="http://hockeyplaya55.wordpress.com/w/index.php?title=Binary_numeral_system&amp;action=edit&amp;section=7"><span style="color:#002bb8;">edit</span></a>]</span> <span class="mw-headline">Multiplication</span></h3>
<p><a title="Multiplication" href="http://hockeyplaya55.wordpress.com/wiki/Multiplication"><span style="color:#002bb8;">Multiplication</span></a> in binary is similar to its decimal counterpart. Two numbers <em>A</em> and <em>B</em> can be multiplied by partial products: for each digit in <em>B</em>, the product of that digit in <em>A</em> is calculated and written on a new line, shifted leftward so that its rightmost digit lines up with the digit in <em>B</em> that was used. The sum of all these partial products gives the final result.</p>
<p>Since there are only two digits in binary, there are only two possible outcomes of each partial multiplication:</p>
<ul>
<li>If the digit in <em>B</em> is 0, the partial product is also 0</li>
<li>If the digit in <em>B</em> is 1, the partial product is equal to <em>A</em></li>
</ul>
<p>For example, the binary numbers 1011 and 1010 are multiplied as follows:</p>
<pre>           1 0 1 1   (A)
         × 1 0 1 0   (B)
         ---------
           0 0 0 0   ← Corresponds to a zero in B
   +     1 0 1 1     ← Corresponds to a one in B
   +   0 0 0 0
   + 1 0 1 1
   ---------------
   = 1 1 0 1 1 1 0</pre>
<p>Binary numbers can also be multiplied with bits after a <a class="mw-redirect" title="Binary point" href="http://hockeyplaya55.wordpress.com/wiki/Binary_point"><span style="color:#002bb8;">binary point</span></a>:</p>
<pre>               1 0 1.1 0 1   (A) (5.625 in decimal)
             ×   1 1 0.0 1   (B) (6.25  in decimal)
             -------------
               1 0 1 1 0 1   ← Corresponds to a one in B
   +         0 0 0 0 0 0     ← Corresponds to a zero in B
   +       0 0 0 0 0 0
   +     1 0 1 1 0 1
   +   1 0 1 1 0 1
   -----------------------
   = 1 0 0 0 1 1.0 0 1 0 1   (35.15625 in decimal)</pre>
<p>See also <a title="Booth's multiplication algorithm" href="http://hockeyplaya55.wordpress.com/wiki/Booth%27s_multiplication_algorithm"><span style="color:#002bb8;">Booth&#8217;s multiplication algorithm</span></a>.</p>
<p><a id="Division" name="Division"></a></p>
<h3><span class="editsection">[<a title="Division" href="http://hockeyplaya55.wordpress.com/w/index.php?title=Binary_numeral_system&amp;action=edit&amp;section=8"><span style="color:#002bb8;">edit</span></a>]</span> <span class="mw-headline">Division</span></h3>
<p>Binary <a title="Division (mathematics)" href="http://hockeyplaya55.wordpress.com/wiki/Division_(mathematics)"><span style="color:#002bb8;">division</span></a> is again similar to its decimal counterpart:</p>
<pre>        __________
1 0 1  | 1 1 0 1 1</pre>
<p>Here, the divisor is 101<sub>2</sub>, or 5 decimal, while the dividend is 11011<sub>2</sub>, or 27 decimal. The procedure is the same as that of decimal <a title="Long division" href="http://hockeyplaya55.wordpress.com/wiki/Long_division"><span style="color:#002bb8;">long division</span></a>; here, the divisor 101<sub>2</sub> goes into the first three digits 110<sub>2</sub> of the dividend one time, so a &#8220;1&#8243; is written on the top line. This result is multiplied by the divisor, and subtracted from the first three digits of the dividend; the next digit (a &#8220;1&#8243;) is included to obtain a new three-digit sequence:</p>
<pre>             1
        __________
1 0 1  | 1 1 0 1 1
       − 1 0 1
         -----
           0 1 1</pre>
<p>The procedure is then repeated with the new sequence, continuing until the digits in the dividend have been exhausted:</p>
<pre>             1 0 1
        __________
1 0 1  | 1 1 0 1 1
       − 1 0 1
         -----
           0 1 1
         − 0 0 0
           -----
             1 1 1
           − 1 0 1
             -----
               1 0</pre>
<p>Thus, the quotient of 11011<sub>2</sub> divided by 101<sub>2</sub> is 101<sub>2</sub>, as shown on the top line, while the remainder, shown on the bottom line, is 10<sub>2</sub>. In decimal, 27 divided by 5 is 5, with a remainder of 2.</p>
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		<title>Movie Gadget</title>
		<link>http://hockeyplaya55.wordpress.com/2008/10/01/movie-gadget/</link>
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		<pubDate>Wed, 01 Oct 2008 21:27:07 +0000</pubDate>
		<dc:creator>hockeyplaya55</dc:creator>
				<category><![CDATA[Uncategorized]]></category>

		<guid isPermaLink="false">http://hockeyplaya55.wordpress.com/?p=16</guid>
		<description><![CDATA[The product from the movies is called the Mophie Juice Pack. What this gadget does is give your battery extra life, most ipods can run up to 3 hours so basically with the Mophie Juice pack you are giving your ipod or your iphone 2x the battery life. The Mophie Juice Pack is good for [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=hockeyplaya55.wordpress.com&amp;blog=4734180&amp;post=16&amp;subd=hockeyplaya55&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>The product from the movies is called the Mophie Juice Pack. What this gadget does is give your battery extra life, most ipods can run up to 3 hours so basically with the Mophie Juice pack you are giving your ipod or your iphone 2x the battery life. The Mophie Juice Pack is good for people who use their iphone or ipod a lot.</p>
<p>Some positive things for the Mophie Juice Pack is that it gives your ipod or iphone 2x the battery life so you would have to charge the ipod or iphone less and you would save money on your electric bill. The downfall of the Mophie Juice Pakc is that it costs $99.99 and it is only available for the ipod and iphone</p>
<p> <img src="http://www.cellphone9.com/wp-content/uploads/2008/05/mophie-juice-pack.jpg" alt="" /></p>
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		<title>Paragraph</title>
		<link>http://hockeyplaya55.wordpress.com/2008/09/15/paragraph/</link>
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		<pubDate>Mon, 15 Sep 2008 20:23:47 +0000</pubDate>
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		<description><![CDATA[This school year i would like to accomplish a lot. I want to know how to use different types of programs and how to hack. I also want to learn how to make my own computer game and how to build myself my own computer.<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=hockeyplaya55.wordpress.com&amp;blog=4734180&amp;post=10&amp;subd=hockeyplaya55&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>This school year i would like to accomplish a lot. I want to know how to use different types of programs and how to hack. I also want to learn how to make my own computer game and how to build myself my own computer.</p>
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		<title>Definitions</title>
		<link>http://hockeyplaya55.wordpress.com/2008/09/10/definitions/</link>
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		<pubDate>Wed, 10 Sep 2008 20:40:53 +0000</pubDate>
		<dc:creator>hockeyplaya55</dc:creator>
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		<description><![CDATA[Hard Drive- a disk drive containing a hard disk CPU- cental processing unit: the key component of a computer system, which contains the circuitry necassary to interpret and execute program instructions Motherboard- a rigid, slotted board upon which other boards that contain the basic circuitry of a computer or of a computer component can be mounted Power [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=hockeyplaya55.wordpress.com&amp;blog=4734180&amp;post=4&amp;subd=hockeyplaya55&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>Hard Drive- a disk drive containing a hard disk</p>
<p>CPU- cental processing unit: the key component of a computer system, which contains the circuitry necassary to interpret and execute program instructions</p>
<p>Motherboard- a rigid, slotted board upon which other boards that contain the basic circuitry of a computer or of a computer component can be mounted</p>
<p>Power Supply- a source of electricity for a device, which converts, regulates, and transmits the external power for the device</p>
<p>PCI- pounds per cubic inch</p>
<p>PCI Express- a <a title="Computer" href="http://hockeyplaya55.wordpress.com/wiki/Computer">computer</a> <a title="Expansion card" href="http://hockeyplaya55.wordpress.com/wiki/Expansion_card">expansion card</a> interface format</p>
<p>USB- Universal Serial Bus</p>
<p>Firewire- <a title="Institute of Electrical and Electronics Engineers" href="http://hockeyplaya55.wordpress.com/wiki/Institute_of_Electrical_and_Electronics_Engineers"><strong>IEEE</strong></a><strong> 1394</strong> interface is a <a class="mw-redirect" title="Serial communications" href="http://hockeyplaya55.wordpress.com/wiki/Serial_communications">serial bus</a> <a title="Interface standard" href="http://hockeyplaya55.wordpress.com/wiki/Interface_standard">interface standard</a> for high-speed communications and <a title="Isochronous" href="http://hockeyplaya55.wordpress.com/wiki/Isochronous">isochronous</a> real-time data transfer, frequently used in a <a title="Personal computer" href="http://hockeyplaya55.wordpress.com/wiki/Personal_computer">personal computer</a> (and <a title="Digital audio" href="http://hockeyplaya55.wordpress.com/wiki/Digital_audio">digital audio</a> and <a title="Digital video" href="http://hockeyplaya55.wordpress.com/wiki/Digital_video">digital video</a>).</p>
<p>IEEE-1394- Institute of Electrical and Electronics Engineers</p>
<p>LCD- liquid-crystal display: a method of displaying readings continuously, as on digital watches, portable computers, and calculators, using a liquid-crystal film, sealed between glass plates, that changes its optical properties when a voltage is applied</p>
<p>Plasma- a thin, high-definition television or computer display created with pixel-sized gas-filled cells that emit different colors when electric current is connected; also called <a href="http://hockeyplaya55.wordpress.com/browse/plasma%20display">plasma display</a></p>
<p>HDMI- is a compact audio/video connector interface for transmitting uncompressed digital streams</p>
<p>Ram- computer memory available to the user for creating, loading, or running programs and for the temporary storage and manipulation of data, in which time of access to each item is independent of the storage sequence</p>
<p>Flash Memory- a type of reprogrammable memory that retains information even with the power turned off</p>
<p>AGP- is a high-speed point-to-point channel for attaching a <a title="Graphics cards" href="http://hockeyplaya55.wordpress.com/wiki/Category:Graphics_cards">graphics card</a> to a <a title="Computer" href="http://hockeyplaya55.wordpress.com/wiki/Computer">computer</a>&#8216;s <a title="Motherboard" href="http://hockeyplaya55.wordpress.com/wiki/Motherboard">motherboard</a>, primarily to assist in the acceleration of <a title="3D computer graphics" href="http://hockeyplaya55.wordpress.com/wiki/3D_computer_graphics">3D computer graphics</a><br />
<!--EOF_DEF--><br />
DVD- an optical disk that can store a very large amount of digital data, as text, music, or images</p>
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		<title>Hello world!</title>
		<link>http://hockeyplaya55.wordpress.com/2008/09/04/hello-world/</link>
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		<pubDate>Thu, 04 Sep 2008 21:24:11 +0000</pubDate>
		<dc:creator>hockeyplaya55</dc:creator>
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		<description><![CDATA[Welcome to WordPress.com. This is your first post. Edit or delete it and start blogging!<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=hockeyplaya55.wordpress.com&amp;blog=4734180&amp;post=1&amp;subd=hockeyplaya55&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>Welcome to <a href="http://wordpress.com/">WordPress.com</a>. This is your first post. Edit or delete it and start blogging!</p>
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