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                            <td class="riohdr">Converting decimal numbers to binary numbers</td>
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                                                                <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>
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                                                                <td valign="top">&nbsp;</td><td valign="top"><span class="cstext">
                                                                        <p>The purpose of this target indicator is that the student be able to convert decimal numbers to binary without the use of a calculator. It is important to learn the logic and basic algorithms of Base 2 number systems, and while calculator use can be permitted and encouraged after the basics are mastered, students must be agile with binary numbers. Also, calculators are not permitted on the certification exam.</p>
                                                                        <p>Two algorithms are presented for converting decimal to binary. Present whatever method you feel best works for your students. The algorithm in the graphic uses a flowchart to convey the steps to be followed; the algorithm described in the text is successive division. Actually they are the same algorithm, presented two different ways.</p>
                                                                        <p>An entertaining class activity is to have 8 students come to the front of the class. Give one of them a ONE sign, the next a TWO sign, the next a FOUR sign, the next an EIGHT sign, the next a SIXTEEN sign, the next a THIRTY-TWO sign, the next a SIXTY-FOUR sign, and the last student a ONE TWENTY-EIGHT sign. Arrange them in order, facing the class, Least significant bit to most significant bit. Have a student from the class call out a DECIMAL number between 0 and 255 (the largest decimal equivalent of an eight-bit binary number). The job of the students in front is to stand up if their bit is a ONE in the representation of the called-out decimal number; they should stay seated if their bit is a ZERO. This requires every student up front to do the conversion; require the students in the rest of the class do the conversion as well.</p>
                                                                        <p>This TI relates to CCNA Certification Exam Objective #30.</p>
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<p>There are two basic ways to convert decimal numbers to binary numbers. The flowchart in the main graphic describes one process with an example. Another approach is called the remainder method. This method uses repeated divisions using the base number of the system. In this case it is Base 2. <img border="0" src="../../../../../CHAPID=knet-v214aCH47501/RLOID=knet-v214aRLO47520/RIOID=knet-v214aRIO120864/knet/v214adataimage1/1.gif" width="12" height="12"></p>
<p>Conversion exercise. <img border="0" src="../../../../../CHAPID=knet-v214aCH47501/RLOID=knet-v214aRLO47520/RIOID=knet-v214aRIO120864/knet/v214adataimage2/2.gif" width="12" height="12"></p>
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                                    <b>Example:</b>
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<p>Convert the decimal number 192 to a binary number.</p>
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<td colspan="1" rowspan="1"><span class="smtext">192/2</span></td>
<td colspan="1" rowspan="1"><span class="smtext"> =</span></td>
<td colspan="1" rowspan="1"><span class="smtext">96</span></td>
<td colspan="1" rowspan="1"><span class="smtext"> with a remainder of</span></td>
<td colspan="1" rowspan="1"><span class="smtext"><b>0</b></span></td>
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<td colspan="1" rowspan="1"><span class="smtext">96/2</span></td>
<td colspan="1" rowspan="1"><span class="smtext"> =</span></td>
<td colspan="1" rowspan="1"><span class="smtext"> 48</span></td>
<td colspan="1" rowspan="1"><span class="smtext"> with a remainder of</span></td>
<td colspan="1" rowspan="1"><span class="smtext"><b>0</b></span></td>
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<td colspan="1" rowspan="1"><span class="smtext">48/2</span></td>
<td colspan="1" rowspan="1"><span class="smtext"> =</span></td>
<td colspan="1" rowspan="1"><span class="smtext">24</span></td>
<td colspan="1" rowspan="1"><span class="smtext"> with a remainder of</span></td>
<td colspan="1" rowspan="1"><span class="smtext"><b>0</b></span></td>
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<td colspan="1" rowspan="1"><span class="smtext">24/2</span></td>
<td colspan="1" rowspan="1"><span class="smtext"> =</span></td>
<td colspan="1" rowspan="1"><span class="smtext">12</span></td>
<td colspan="1" rowspan="1"><span class="smtext"> with a remainder of</span></td>
<td colspan="1" rowspan="1"><span class="smtext"><b>0</b></span></td>
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<td colspan="1" rowspan="1"><span class="smtext">12/2</span></td>
<td colspan="1" rowspan="1"><span class="smtext"> =</span></td>
<td colspan="1" rowspan="1"><span class="smtext">6</span></td>
<td colspan="1" rowspan="1"><span class="smtext"> with a remainder of</span></td>
<td colspan="1" rowspan="1"><span class="smtext"><b>0</b></span></td>
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<td colspan="1" rowspan="1"><span class="smtext">6/2</span></td>
<td colspan="1" rowspan="1"><span class="smtext"> =</span></td>
<td colspan="1" rowspan="1"><span class="smtext">3</span></td>
<td colspan="1" rowspan="1"><span class="smtext"> with a remainder of</span></td>
<td colspan="1" rowspan="1"><span class="smtext"><b>0</b></span></td>
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<td colspan="1" rowspan="1"><span class="smtext">3/2</span></td>
<td colspan="1" rowspan="1"><span class="smtext"> =</span></td>
<td colspan="1" rowspan="1"><span class="smtext">1</span></td>
<td colspan="1" rowspan="1"><span class="smtext"> with a remainder of</span></td>
<td colspan="1" rowspan="1"><span class="smtext"><b>1</b></span></td>
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<td colspan="1" rowspan="1"><span class="smtext">1/2</span></td>
<td colspan="1" rowspan="1"><span class="smtext"> =</span></td>
<td colspan="1" rowspan="1"><span class="smtext">0</span></td>
<td colspan="1" rowspan="1"><span class="smtext"> with a remainder of</span></td>
<td colspan="1" rowspan="1"><span class="smtext"><b>1</b></span></td>
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<p>Write down all the remainders, backwards, and you have the binary number <b>11000000</b>.</p>
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                                        <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>
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                                        <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>
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