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<html>    <head>        <meta content="en-us" http-equiv="Content-Language">        <meta content="text/html; charset=UTF-8" http-equiv="Content-Type">        <link type="text/css" rel="stylesheet" href="../../../../../css/ccna.css">        <script src="../../../../../js/framesetHelper.js" language="JavaScript"></script><script language="JavaScript">        window.scrollTo(0,0);        function newPage(pageID) {            alert("COMMING SOON!!\nThis feature is currently in development.");        }        function launchMoreInfo(oid) {            dash = oid.indexOf('-');            sub1 = oid.substring(0,dash);            sub2 = oid.substring(dash+1);                                            // this is an URL base on the                                        // system that generated the static                                        // download of the curriculum.            httpref = 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(navigator.appVersion.indexOf('MSIE 5.5')>0)  	if (this.ie5) this.v = 5  	this.min = (this.ns||this.ie)  }  // automatically create the "is" object  is = new BrowserCheck()</script>    </head>    <body onLoad="window.focus();" alink="#000000" vlink="#000000" link="#000000" bgcolor="#E7E7E7" background="../../../../../images/ccna/common/bg.gif">        <table width="100%" cellspacing="0" cellpadding="2" border="0"><tr>                <td bgcolor="#000000"><img height="1" width="2" border="0" src="../../../../../images/ccna/common/transdot.gif"></td><td class="rlohdr"><img height="1" width="2" border="0" src="../../../../../images/ccna/common/transdot.gif"></td><td valign="top" class="rlohdr">1.3</td><td width="100%" class="rlohdr">                    <table width="90%" cellpadding="0" cellspacing="0" border="0">                        <tr>                            <td class="rlohdr">Binary Numbers</td>                        </tr>                    </table>                </td>            </tr>            <tr>                <td bgcolor="#000000"><img height="1" width="2" border="0" src="../../../../../images/ccna/common/transdot.gif"></td><td class="riohdr"><img height="1" width="2" border="0" src="../../../../../images/ccna/common/transdot.gif"></td><td valign="top" class="riohdr">1.3.4</td><td width="100%" class="riohdr">                    <table width="90%" cellpadding="0" cellspacing="0" border="0">                        <tr>                            <td class="riohdr">The Base 2 (binary) number system</td>                        </tr>                    </table>                </td>            </tr>            <tr>                <td colspan="4">                    <table width="90%" cellspacing="0" cellpadding="0" border="0">                        <tr>                            <td class="smtext">                                <p>                                </p><table cellpadding="0" cellspacing="0" width="100%" border="0" xmlns:java="http://xml.apache.org/xslt/java">                                    <tr>                                        <td width="100%"><img height="10" width="1" border="0" src="../../../../../images/ccna/common/transdot.gif"></td>                                    </tr>                                    <tr>                                        <td width="100%">                                            <table bgcolor="#000000" bordercolor="#000000" cellspacing="0" bordercolorlight="#000000" width="100%" border="0">                                                <tr>                                                    <td width="100%">                                                        <table bgcolor="#FFFFFF" cellspacing="0" cellpadding="2" width="100%" border="0">                                                            <tr>                                                                <td valign="middle"><img height="22" width="22" border="0" src="../../../../../images/ccna/common/inotes.gif"></td><td valign="middle"><span class="cstitle">Instructor Note</span></td>                                                            </tr>                                                            <tr>                                                                <td valign="top">&nbsp;</td><td valign="top"><span class="cstext">                                                                        <p>The purpose of this target indicator is to teach students the binary arithmetic they will need later in the course, especially in IP addressing. We have separated the learning of binary from IP addressing for two reasons: first, binary plus IP addressing can be a long, dry stretch for students; secondly, by introducing binary early in the semester there is ample time to make sure that before IP addressing is started binary arithmetic has been mastered. Unless binary arithmetic is mastered, there is no way the student can succeed at IP addressing.</p>                                                                        <p>The same formalism used for Base 10 number system in the prior target indicator is used in this target indicator to make binary look and feel similar -- it is "just" a Base 2 instead of a "Base 10" number system. Make this similarity clear. As you work through the binary exponents, you may want to call attention to the fact that many common sizes of computer technologies are actually powers of 2 -- 32 and 64-bit games, 256 colors, 32 Megabytes of RAM, and so on.</p>                                                                        <p>This TI relates to CCNA Certification Exam Objective #30.</p>                                                                    </span></td>                                                            </tr>                                                        </table>                                                    </td>                                                </tr>                                            </table>                                        </td>                                    </tr>                                </table><p>Computers recognize and process data using the binary (Base 2) numbering system. The binary number system uses only two symbols -- 0 and 1-- instead of the ten symbols used in the decimal numbering system. The position, or place, of each digit represents the number 2 -- the base number -- raised to a power (exponent), based on its position (2<sup>0</sup>, 2<sup>1</sup>, 2<sup>2</sup>, 2<sup>3</sup>, 2<sup>4</sup>, and so on).</p><p>                                    <b>Example:</b>                                </p><p>10110 = (1 x 2<sup>4</sup> = <b>16</b>) + (0 x 2<sup>3</sup> =<b> 0</b>) + (1 x 2<sup>2</sup> = <b>4</b>) + (1 x 2<sup>1</sup> =<b> 2</b>) + (0 x 2<sup>0</sup> = <b>0</b>) = 22 (<b>16</b> + <b>0</b> + <b>4</b> + <b>2</b> + <b>0</b>)</p><p>If you read the binary number (10110) from left to right, you see that there is a 1 in the 16s position, a 0 in the 8s position, a 1 in the 4s position, a 1 in the 2s position, and a 0 in the 1s position, which adds up to decimal number 22.</p><table cellpadding="0" cellspacing="4" width="63%" border="0" xmlns:java="http://xml.apache.org/xslt/java">                                    <tr>                                        <td valign="middle" width="8%"><img height="23" width="23" src="../../../../../images/ccna/common/icon2.gif"></td><td valign="middle" width="92%"><span class="cstitle">Web Links</span></td>                                    </tr>                                    <tr>                                        <td valign="middle" width="8%">&nbsp;</td><td valign="middle" width="92%"><span class="smtext"><a target="_blank" href="http://www.howstuffworks.com/bytes.htm">How Bits and Bytes Work</a></span></td>                                    </tr>                                </table></td>                        </tr>                    </table>                </td>            </tr></table>        <p>        </p>        <table width="100%" cellspacing="0" cellpadding="2" border="0" valign="bottom">            <tr>                <td></td>            </tr>        </table>    </body></html>

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