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227 lines
8.7 KiB
HTML
227 lines
8.7 KiB
HTML
<!doctype html>
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<title>Hexadecimals</title>
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<div id="hdr"></div>
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<div id="cookOK"></div>
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Hexadecimals</h1>
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<p class="center larger">A Hexadecimal Number is based on the number
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<b>16</b></p>
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<h2>16 Different Values</h2>
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<p>There are <b>16</b> Hexadecimal digits. They are the same as the decimal digits up to 9, but then there are the letters A, B, C, D, E and F in place of the decimal numbers 10 to 15:</p>
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<table align="center" width="90%" border="0">
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<tbody>
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<tr style="text-align:center;">
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<th>Hexadecimal:</th>
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<td>0</td>
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<td>1</td>
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<td>2</td>
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<td>3</td>
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<td>4</td>
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<td>5</td>
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<td>6</td>
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<td>7</td>
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<td>8</td>
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<td>9</td>
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<td>A</td>
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<td>B</td>
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<td>C</td>
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<td>D</td>
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<td>E</td>
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<td>F</td>
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</tr>
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<tr style="text-align:center;">
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<th width="120">Decimal:</th>
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<td style="width:21px;">0</td>
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<td style="width:21px;">1</td>
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<td style="width:21px;">2</td>
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<td style="width:21px;">3</td>
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<td style="width:21px;">4</td>
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<td style="width:21px;">5</td>
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<td style="width:21px;">6</td>
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<td style="width:21px;">7</td>
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<td style="width:21px;">8</td>
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<td style="width:21px;">9</td>
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<td style="width:21px;">10</td>
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<td style="width:21px;">11</td>
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<td style="width:21px;">12</td>
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<td style="width:21px;">13</td>
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<td style="width:21px;">14</td>
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<td style="width:21px;">15</td>
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</tr>
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</tbody></table>
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<p>So a single Hexadecimal digit can show 16 different values instead of the normal 10.</p>
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<h2>Counting</h2>
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<p>Choose "Hexadecimal" below and watch it count:</p>
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<script>numberodometerMain(16);</script>
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<p>After the "Ones" position is filled up (after <b>F</b>) the ones start back at <b>0</b>, and we add <b>1</b> to the next position on the left (to show 1 lot of 16).</p>
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<p>And after <i>that</i> position reaches <b>F</b>, we do the same thing, and so on.</p>
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<p class="center larger">As we move left, every number place is <b>16
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times bigger</b>.</p><br>
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<div class="example">
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<h3>Example: What is the decimal value of the hexadecimal number "D1CE"</h3>
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<p class="center"><img src="numbers/images/hex-example.svg" alt="hexadecimal example D1CE" height="187" width="310" ></p>
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</div>
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<p class="center"><i>(Test it in the <a href="binary-decimal-hexadecimal-converter.html">Binary to Decimal to Hexadecimal Converter</a>.)</i></p>
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<h2>The Point !</h2>
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<div class="example">
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<h3>Example: 2E6.A3</h3>
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<p class="center"><img src="numbers/images/hexadecimal.svg" alt="hexadecimal example 2E6.A3" height="179" width="434" ></p>
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<p class="center">This is <b>2×16×16 + 14×16 + 6 + 10/16 + 3/(16×16)</b><br>
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=742.63671875 in Decimal<br>
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Read below to find out why</p>
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</div>
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<p>Numbers can be placed to the left
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or right of the point, to show values greater than one
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or less than one:</p>
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<table style="width: 100%" border="0">
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<tbody>
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<tr>
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<td class="larger"><img src="images/style/left-arrow.gif" alt="left arrow" height="46" width="46" > •</td>
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<td> </td>
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<td><br>
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<span class="larger">The number just to the left of the point is a whole number.
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</span><br>
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<span class="large">Moving <b>left</b> every number place is 16 times bigger.</span>
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</td></tr>
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<tr>
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<td><br>
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</td>
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<td><br>
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</td>
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<td><br>
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</td></tr>
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<tr>
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<td class="larger"> •<img src="images/style/right-arrow.gif" alt="right arrow" height="46" width="46" ></td>
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<td> </td>
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<td><br>
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<span class="larger">The first digit on the right of the point means sixteenths (1/16).</span><br>
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<span class="large">Moving <b>right</b> every number place is 16 times smaller (one sixteenth as big).</span></td></tr></tbody></table>
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<h2>More Examples</h2>
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<h3><b>Example 1:</b> What is 4B5 (Hexadecimal)?</h3>
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<ul>
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<li>The "4" is in the "16×16" position, so that means 4 ×16×16</li>
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<li>The "B" (11) is in the "16" position, so that means 11 ×16</li>
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<li>The "5" is in the "1" position so that means 5.</li>
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<li>Answer: 4B5 = 4×16×16 + 11×16 + 5 (=1205) in Decimal</li>
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</ul>
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<h3><b>Example</b> 2: What is 2.3 (Hexadecimal)?</h3>
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<ul>
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<li>On the left side is "2", that is the whole number
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part.</li>
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<li>The 3 is in the "sixteenths" position, meaning "3
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sixteenths", or 3/16</li>
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<li>So, 2.3 is "2 and 3 sixteenths" (=2.1875 in Decimal)</li>
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</ul>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="numbers/images/paws-16.svg" alt="Dogs have 16 toes" height="181" width="173" ></p>
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<h2>Dogs</h2>
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<p>Dogs would find hexadecimal easy to understand: just count on their toes!</p>
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<h2>The Word "Hexadecimal"</h2>
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<div class="words">The word "Hexadecimal" means "based on 16"
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(From Greek <i>hexa: "six"</i> and Latin <i>decima</i>: <i>"a tenth part"</i>).</div>
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<div class="questions">2016, 2017, 2018, 2019, 2020, 2021, 3595, 3596, 3597, 3598</div>
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<div class="related">
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<a href="binary-decimal-hexadecimal-converter.html">Binary to Decimal to Hexadecimal Converter</a>
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<a href="hexadecimal-multiplication-table.html">Hexadecimal Multiplication Table</a>
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<a href="games/hex-drums.html">Hexadecimal Drum Machine</a>
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<a href="hexadecimal-decimal-colors.html">Hexadecimal / Decimal Colors</a>
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<a href="base-conversion-method.html">Base Conversion Method</a>
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<a href="decimals.html">Decimal Numbers</a>
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<a href="binary-decimal-hexadecimal.html">Binary, Decimal and Hexadecimal Numbers</a>
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</div>
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<!-- #EndEditable -->
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<div id="copyrt">Copyright © 2022 Rod Pierce</div>
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