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| <html> | ||
| <head> | ||
| <link rel="stylesheet" href="../../main.css"> | ||
| <link rel="stylesheet" href="../main.css"> | ||
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| <title>Computer Science Revision</title> | ||
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| <link rel="icon" type="image/png" href="../icons/logo.svg"/> | ||
| <meta property="og:image" content="../icons/logo.png" /> | ||
| <meta property="og:image:width" content="640" /> | ||
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| <meta name="viewport" content="width=device-width, initial-scale=1.0"> | ||
| <meta name="description" content="3.02 - Binary and Hexadecimal | Computer Science Revision"> | ||
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| <body> | ||
| <h1>3.02 – Binary and Hexadecimal</h1> | ||
| <h3 class="home-link"><a href="../">Computer Science Revision</a></h3> | ||
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| <a class="prev-link" href="../3-01-Storage-Units/">Previous: 3.01 - Storage Units</a> | ||
| <br /> <br /> | ||
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| <p>Counting in binary (also called base-2) is similar to counting in decimal (our normal number system, also called base-10).</p> | ||
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| <p>The only difference is that instead of the digits representing powers of 10 (..., 1000, 100, 10, 1) <b>they represent powers of 2 (..., 8, 4, 2, 1)</b>.</p> | ||
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| <p class="definition"> | ||
| <img src="../icons/book.svg" class="icon" /> | ||
| The <strong>hexadecimal number system</strong> (also called base-16) is a way of writing numbers using 16 different digits. | ||
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| <p>The digits are: <code>0123456789ABCDEF</code>. <b><code>A = 10</code>, <code>B = 11</code>, ..., <code>F = 15</code></b>.</p> | ||
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| <p>In hexadecimal, the digits represent powers of 16 (..., 4096, 256, 16, 1).</p> | ||
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| <p> | ||
| <b> | ||
| Each digit in hexadecimal exactly corresponds to one nibble (four bits). | ||
| </b> <br /> | ||
| This means that it is very easy to convert between binary and hexadecimal, | ||
| as each group of four binary digits con be converted to one hexadecimal digit. | ||
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| <p><br/>Diagram 1 shows the number 206 in decimal, binary, and hexadecimal.</p> | ||
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| <p class="diagram"> | ||
| <img src="../icons/image.svg" class="icon" /> | ||
| Diagram 1 <br /> <br /> | ||
| <img src="./diagram.png" width="400px" /> | ||
| </p> | ||
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| <p> | ||
| A computer can only understand binary machine code, but programmers often write machine code in hexadecimal because: <br /> | ||
| - Hexadecimal is four times shorter than binary <br /> | ||
| - It's easy to convert from hexadecimal into binary | ||
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| <p class="definition"> | ||
| <img src="../icons/book.svg" class="icon" /> | ||
| <strong>Subscript notation</strong> is a way of writing the base a number has been represented in so that we don't get confused. | ||
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| <p> | ||
| <b>The base is written next to the number in a small font:</b> <br /> | ||
| - <code>206</code><sub>10</sub> means <i>"206 in base-10 (decimal)"</i> <br /> | ||
| - <code>11001110</code><sub>2</sub> means <i>"11001110 in base-2 (binary)"</i> <br /> | ||
| - <code>CE</code><sub>16</sub> means <i>"CE in base-16 (hexadecimal)"</i> | ||
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| <p class="question"> | ||
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| Convert <code>9D</code><sub>16</sub> to binary. | ||
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| <p class="spoiler noselect"> | ||
| <el class="default">Tap/click to reveal</el> | ||
| <el class="answer"> | ||
| Because each hexadecimal digit is equivalent to a nibble, we can convert each digit to four binary digits: <br /> | ||
| <code>9<sub>16</sub></code> = <code>9<sub>10</sub></code> = 8 + 1 = <code>1001<sub>2</sub></code> <br /> | ||
| <code>D<sub>16</sub></code> = <code>13<sub>10</sub></code> = 8 + 4 + 1 = <code>1101<sub>2</sub></code> <br /> | ||
| So, <code>9D<sub>16</sub></code> = <code>10011101<sub>2</sub></code> | ||
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| <br /> <br /> | ||
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| <div id="sub">© Rujul Nayak <el id="year">2024-</el></div> | ||
| <script src="../../year.js"></script> | ||
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| <script src="../spoilers.js"></script> | ||
| </body> | ||
| </html> |
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