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<div id="content">
<h1 class="title">Digital design fundamentals</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#sec-1">1. Basic logic components</a>
<ul>
<li><a href="#sec-1-1">1.1. SPDT switches</a>
<ul>
<li><a href="#sec-1-1-1">1.1.1. Odd Parity</a></li>
<li><a href="#sec-1-1-2">1.1.2. Even Parity</a></li>
</ul>
</li>
<li><a href="#sec-1-2">1.2. Relays</a>
<ul>
<li><a href="#sec-1-2-1">1.2.1. Relay 2-to-4</a></li>
</ul>
</li>
<li><a href="#sec-1-3">1.3. Truth tables of logic gates</a>
<ul>
<li><a href="#sec-1-3-1">1.3.1. NOT</a></li>
<li><a href="#sec-1-3-2">1.3.2. AND</a></li>
<li><a href="#sec-1-3-3">1.3.3. OR</a></li>
<li><a href="#sec-1-3-4">1.3.4. XOR</a></li>
<li><a href="#sec-1-3-5">1.3.5. NOR</a></li>
<li><a href="#sec-1-3-6">1.3.6. XNOR</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="#sec-2">2. Combinational circuits</a>
<ul>
<li><a href="#sec-2-1">2.1. Decoder 2to4</a></li>
<li><a href="#sec-2-2">2.2. Multiplexer 4to1</a></li>
<li><a href="#sec-2-3">2.3. Encoding</a>
<ul>
<li><a href="#sec-2-3-1">2.3.1. Seven segment display</a></li>
</ul>
</li>
<li><a href="#sec-2-4">2.4. Adders</a></li>
</ul>
</li>
<li><a href="#sec-3">3. 2s complement</a></li>
<li><a href="#sec-4">4. Memory components</a>
<ul>
<li><a href="#sec-4-1">4.1. Latch</a></li>
<li><a href="#sec-4-2">4.2. Register</a>
<ul>
<li><a href="#sec-4-2-1">4.2.1. Shift register</a></li>
<li><a href="#sec-4-2-2">4.2.2. Master-slave register</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="#sec-5">5. Sequential circuits</a>
<ul>
<li><a href="#sec-5-1">5.1. Counter</a></li>
<li><a href="#sec-5-2">5.2. Finite state machine (FSM)</a></li>
<li><a href="#sec-5-3">5.3. Arithmetic Logic Unit (ALU)</a></li>
</ul>
</li>
</ul>
</div>
</div>
<dl class="org-dl">
<dt> Copyright notice </dt><dd>The notes below are modified copies of the academic module CS-120 "Digital Design": <a href="http://www.csd.uoc.gr/~hy120/">http://www.csd.uoc.gr/~hy120/</a> copies or posting are not made or distributed for profit or commercial advantage.
</dd>
</dl>
© University of Crete.
<p>
<a href="http://www.csd.uoc.gr/~hy120/16f/copyright.html">http://www.csd.uoc.gr/~hy120/16f/copyright.html</a>
</p>
<div id="outline-container-sec-1" class="outline-2">
<h2 id="sec-1"><span class="section-number-2">1</span> Basic logic components</h2>
<div class="outline-text-2" id="text-1">
</div><div id="outline-container-sec-1-1" class="outline-3">
<h3 id="sec-1-1"><span class="section-number-3">1.1</span> SPDT switches</h3>
<div class="outline-text-3" id="text-1-1">
<p>
Switches which have 3 pins (1 input, 2 output).
</p>
<div class="figure">
<p><img src="./img/SPDT.png" alt="SPDT.png" />
</p>
<p><span class="figure-number">Figure 1:</span> SPDT switch</p>
</div>
</div>
<div id="outline-container-sec-1-1-1" class="outline-4">
<h4 id="sec-1-1-1"><span class="section-number-4">1.1.1</span> Odd Parity</h4>
<div class="outline-text-4" id="text-1-1-1">
<p>
Odd parity is the exclusive OR (XOR).
</p>
<div class="figure">
<p><img src="./img/ODD-PARITY.png" alt="ODD-PARITY.png" />
</p>
<p><span class="figure-number">Figure 2:</span> Odd parity</p>
</div>
</div>
</div>
<div id="outline-container-sec-1-1-2" class="outline-4">
<h4 id="sec-1-1-2"><span class="section-number-4">1.1.2</span> Even Parity</h4>
<div class="outline-text-4" id="text-1-1-2">
<p>
Even parity is the equality check.
</p>
<div class="figure">
<p><img src="./img/EVEN-PARITY.png" alt="EVEN-PARITY.png" />
</p>
<p><span class="figure-number">Figure 3:</span> Even parity</p>
</div>
</div>
</div>
</div>
<div id="outline-container-sec-1-2" class="outline-3">
<h3 id="sec-1-2"><span class="section-number-3">1.2</span> Relays</h3>
<div class="outline-text-3" id="text-1-2">
<p>
Switches which can be used as memory. The relay below has a DPDT switch (double SPDT) and a coil. If the coil is activated (pins: 1, 8) the DPDT switch moves from its default state (input pins: 3, 6 to output pins: 2, 7) to the active state (input pins: 3, 6 to output pins: 4, 5). Relay have been used as basic memory components or mechanical clocks.
</p>
<div class="figure">
<p><img src="./img/RELAY.png" alt="RELAY.png" />
</p>
<p><span class="figure-number">Figure 4:</span> Relay</p>
</div>
</div>
<div id="outline-container-sec-1-2-1" class="outline-4">
<h4 id="sec-1-2-1"><span class="section-number-4">1.2.1</span> Relay 2-to-4</h4>
<div class="outline-text-4" id="text-1-2-1">
<div class="figure">
<p><img src="./img/RELAY-2-4.png" alt="RELAY-2-4.png" />
</p>
</div>
</div>
</div>
</div>
<div id="outline-container-sec-1-3" class="outline-3">
<h3 id="sec-1-3"><span class="section-number-3">1.3</span> Truth tables of logic gates</h3>
<div class="outline-text-3" id="text-1-3">
<p>
In principle we need three basic gates to compose every other gate: logical NOT, logical AND, logical OR.
</p>
</div>
<div id="outline-container-sec-1-3-1" class="outline-4">
<h4 id="sec-1-3-1"><span class="section-number-4">1.3.1</span> NOT</h4>
<div class="outline-text-4" id="text-1-3-1">
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<col class="right" />
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<td class="right">NOT A</td>
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<td class="right">0</td>
<td class="right">1</td>
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<td class="right">1</td>
<td class="right">0</td>
</tr>
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<p><a href="https://commons.wikimedia.org/wiki/File:Not-gate-en.svg#/media/File:Not-gate-en.svg"><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Not-gate-en.svg/1200px-Not-gate-en.svg.png" alt="Not-gate-en.svg"></a><br><a href="http://creativecommons.org/licenses/by-sa/3.0/" title="Creative Commons Attribution-Share Alike 3.0">CC BY-SA 3.0</a>, <a href="https://commons.wikimedia.org/w/index.php?curid=829068">Link</a></p>
</div>
</div>
<div id="outline-container-sec-1-3-2" class="outline-4">
<h4 id="sec-1-3-2"><span class="section-number-4">1.3.2</span> AND</h4>
<div class="outline-text-4" id="text-1-3-2">
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="right" />
<col class="right" />
<col class="right" />
</colgroup>
<thead>
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<th scope="col" class="right">INPUT</th>
<th scope="col" class="right">OUTPUT</th>
</tr>
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<tbody>
<tr>
<td class="right">A</td>
<td class="right">B</td>
<td class="right">A AND B</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="right">0</td>
<td class="right">0</td>
<td class="right">0</td>
</tr>
<tr>
<td class="right">0</td>
<td class="right">1</td>
<td class="right">0</td>
</tr>
<tr>
<td class="right">1</td>
<td class="right">0</td>
<td class="right">0</td>
</tr>
<tr>
<td class="right">1</td>
<td class="right">1</td>
<td class="right">1</td>
</tr>
</tbody>
</table>
<p><a href="https://commons.wikimedia.org/wiki/File:AND_ANSI_Labelled.svg#/media/File:AND_ANSI_Labelled.svg"><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b9/AND_ANSI_Labelled.svg/1200px-AND_ANSI_Labelled.svg.png" alt="AND ANSI Labelled.svg"></a><br>By <a href="//commons.wikimedia.org/wiki/User:Inductiveload" title="User:Inductiveload">Inductiveload</a> - <span class="int-own-work" lang="en">Own work</span>, Public Domain, <a href="https://commons.wikimedia.org/w/index.php?curid=5729013">Link</a></p>
</div>
</div>
<div id="outline-container-sec-1-3-3" class="outline-4">
<h4 id="sec-1-3-3"><span class="section-number-4">1.3.3</span> OR</h4>
<div class="outline-text-4" id="text-1-3-3">
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="right" />
<col class="right" />
<col class="right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="right">INPUT</th>
<th scope="col" class="right">INPUT</th>
<th scope="col" class="right">OUTPUT</th>
</tr>
</thead>
<tbody>
<tr>
<td class="right">A</td>
<td class="right">B</td>
<td class="right">A OR B</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="right">0</td>
<td class="right">0</td>
<td class="right">0</td>
</tr>
<tr>
<td class="right">0</td>
<td class="right">1</td>
<td class="right">1</td>
</tr>
<tr>
<td class="right">1</td>
<td class="right">0</td>
<td class="right">1</td>
</tr>
<tr>
<td class="right">1</td>
<td class="right">1</td>
<td class="right">1</td>
</tr>
</tbody>
</table>
<p><a href="https://commons.wikimedia.org/wiki/File:OR_ANSI_Labelled.svg#/media/File:OR_ANSI_Labelled.svg"><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/1/16/OR_ANSI_Labelled.svg/1200px-OR_ANSI_Labelled.svg.png" alt="OR ANSI Labelled.svg"></a><br>By <a href="//commons.wikimedia.org/wiki/User:Inductiveload" title="User:Inductiveload">Inductiveload</a> - <span class="int-own-work" lang="en">Own work</span>, Public Domain, <a href="https://commons.wikimedia.org/w/index.php?curid=5729019">Link</a></p>
</div>
</div>
<div id="outline-container-sec-1-3-4" class="outline-4">
<h4 id="sec-1-3-4"><span class="section-number-4">1.3.4</span> XOR</h4>
<div class="outline-text-4" id="text-1-3-4">
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="right" />
<col class="right" />
<col class="right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="right">INPUT</th>
<th scope="col" class="right">INPUT</th>
<th scope="col" class="right">OUTPUT</th>
</tr>
</thead>
<tbody>
<tr>
<td class="right">A</td>
<td class="right">B</td>
<td class="right">A XOR B</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="right">0</td>
<td class="right">0</td>
<td class="right">0</td>
</tr>
<tr>
<td class="right">0</td>
<td class="right">1</td>
<td class="right">1</td>
</tr>
<tr>
<td class="right">1</td>
<td class="right">0</td>
<td class="right">1</td>
</tr>
<tr>
<td class="right">1</td>
<td class="right">1</td>
<td class="right">0</td>
</tr>
</tbody>
</table>
<p><a href="https://commons.wikimedia.org/wiki/File:XOR_ANSI.svg#/media/File:XOR_ANSI.svg"><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/01/XOR_ANSI.svg/1200px-XOR_ANSI.svg.png" alt="XOR ANSI.svg"></a><br>By jjbeard - Own Drawing, made in Inkscape 0.43, Public Domain, <a href="https://commons.wikimedia.org/w/index.php?curid=830757">Link</a></p>
</div>
</div>
<div id="outline-container-sec-1-3-5" class="outline-4">
<h4 id="sec-1-3-5"><span class="section-number-4">1.3.5</span> NOR</h4>
<div class="outline-text-4" id="text-1-3-5">
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="right" />
<col class="right" />
<col class="right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="right">INPUT</th>
<th scope="col" class="right">INPUT</th>
<th scope="col" class="right">OUTPUT</th>
</tr>
</thead>
<tbody>
<tr>
<td class="right">A</td>
<td class="right">B</td>
<td class="right">A NOR B</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="right">0</td>
<td class="right">0</td>
<td class="right">1</td>
</tr>
<tr>
<td class="right">0</td>
<td class="right">1</td>
<td class="right">0</td>
</tr>
<tr>
<td class="right">1</td>
<td class="right">0</td>
<td class="right">0</td>
</tr>
<tr>
<td class="right">1</td>
<td class="right">1</td>
<td class="right">0</td>
</tr>
</tbody>
</table>
<p><a href="https://commons.wikimedia.org/wiki/File:NOR_ANSI_Labelled.svg#/media/File:NOR_ANSI_Labelled.svg"><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c6/NOR_ANSI_Labelled.svg/1200px-NOR_ANSI_Labelled.svg.png" alt="NOR ANSI Labelled.svg"></a><br>By <a href="//commons.wikimedia.org/wiki/User:Inductiveload" title="User:Inductiveload">Inductiveload</a> - <span class="int-own-work" lang="en">Own work</span>, Public Domain, <a href="https://commons.wikimedia.org/w/index.php?curid=5729017">Link</a></p>
</div>
</div>
<div id="outline-container-sec-1-3-6" class="outline-4">
<h4 id="sec-1-3-6"><span class="section-number-4">1.3.6</span> XNOR</h4>
<div class="outline-text-4" id="text-1-3-6">
<p>
XNOR is the logical equality.
</p>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="right" />
<col class="right" />
<col class="right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="right">INPUT</th>
<th scope="col" class="right">INPUT</th>
<th scope="col" class="right">OUTPUT</th>
</tr>
</thead>
<tbody>
<tr>
<td class="right">A</td>
<td class="right">B</td>
<td class="right">A NOR B</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="right">0</td>
<td class="right">0</td>
<td class="right">1</td>
</tr>
<tr>
<td class="right">0</td>
<td class="right">1</td>
<td class="right">0</td>
</tr>
<tr>
<td class="right">1</td>
<td class="right">0</td>
<td class="right">0</td>
</tr>
<tr>
<td class="right">1</td>
<td class="right">1</td>
<td class="right">1</td>
</tr>
</tbody>
</table>
<p><a href="https://commons.wikimedia.org/wiki/File:Xnor-gate-en.svg#/media/File:Xnor-gate-en.svg"><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/3/35/Xnor-gate-en.svg/1200px-Xnor-gate-en.svg.png" alt="Xnor-gate-en.svg"></a><br><a href="http://creativecommons.org/licenses/by-sa/3.0/" title="Creative Commons Attribution-Share Alike 3.0">CC BY-SA 3.0</a>, <a href="https://commons.wikimedia.org/w/index.php?curid=829201">Link</a></p>
</div>
</div>
</div>
</div>
<div id="outline-container-sec-2" class="outline-2">
<h2 id="sec-2"><span class="section-number-2">2</span> Combinational circuits</h2>
<div class="outline-text-2" id="text-2">
<p>
High level description of combinational circuits.
</p>
<div class="figure">
<p><img src="./img/combinational-cirsuits.png" alt="combinational-cirsuits.png" />
</p>
</div>
</div>
<div id="outline-container-sec-2-1" class="outline-3">
<h3 id="sec-2-1"><span class="section-number-3">2.1</span> Decoder 2to4</h3>
<div class="outline-text-3" id="text-2-1">
<dl class="org-dl">
<dt> <a href="http://www.cburch.com/logisim/">logisim</a> file </dt><dd><a href="./src/logisim/decoder_2_to_4.circ">./src/logisim/decoder_2_to_4.circ</a>
</dd>
</dl>
<div class="figure">
<p><img src="./img/DECODER-2-4-7408.png" alt="DECODER-2-4-7408.png" />
</p>
</div>
</div>
</div>
<div id="outline-container-sec-2-2" class="outline-3">
<h3 id="sec-2-2"><span class="section-number-3">2.2</span> Multiplexer 4to1</h3>
<div class="outline-text-3" id="text-2-2">
<p>
Multiplexer 4-to-1 using a decoder 2-to-4.
</p>
<dl class="org-dl">
<dt> <a href="http://www.cburch.com/logisim/">logisim</a> file </dt><dd><a href="./src/logisim/multiplexer_4_to_1.circ">./src/logisim/multiplexer_4_to_1.circ</a>
</dd>
</dl>
<div class="figure">
<p><img src="./img/MUX-4-1.png" alt="MUX-4-1.png" />
</p>
</div>
<p>
A multiplexer's module below.
</p>
<p><a href="https://commons.wikimedia.org/wiki/File:Multiplexer_4-to-1.svg#/media/File:Multiplexer_4-to-1.svg"><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/75/Multiplexer_4-to-1.svg/1200px-Multiplexer_4-to-1.svg.png" alt="Multiplexer 4-to-1.svg"></a><br>By <a href="https://en.wikipedia.org/wiki/User:Cburnett" class="extiw" title="en:User:Cburnett">en:User:Cburnett</a> - <span class="int-own-work" lang="en">Own work</span>
<a href="//commons.wikimedia.org/wiki/File:Inkscape_Logo.svg" title="File:Inkscape Logo.svg"></a>
This <a href="https://en.wikipedia.org/wiki/Vector_images" class="extiw" title="w:Vector images">vector image</a> was created with <a href="//commons.wikimedia.org/wiki/Help:Inkscape" title="Help:Inkscape">Inkscape</a>., <a href="http://creativecommons.org/licenses/by-sa/3.0/" title="Creative Commons Attribution-Share Alike 3.0">CC BY-SA 3.0</a>, <a href="https://commons.wikimedia.org/w/index.php?curid=1505578">Link</a></p>
</div>
</div>
<div id="outline-container-sec-2-3" class="outline-3">
<h3 id="sec-2-3"><span class="section-number-3">2.3</span> Encoding</h3>
<div class="outline-text-3" id="text-2-3">
</div><div id="outline-container-sec-2-3-1" class="outline-4">
<h4 id="sec-2-3-1"><span class="section-number-4">2.3.1</span> Seven segment display</h4>
<div class="outline-text-4" id="text-2-3-1">
<p><a href="https://commons.wikimedia.org/wiki/File:7_segment_display_labeled.svg#/media/File:7_segment_display_labeled.svg"><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/02/7_segment_display_labeled.svg/1200px-7_segment_display_labeled.svg.png" alt="7 segment display labeled.svg"></a><br>By <a href="//commons.wikimedia.org/wiki/User:H2g2bob" title="User:H2g2bob">user:h2g2bob</a> - Own work using Inkscape, <a href="http://creativecommons.org/licenses/by-sa/3.0/" title="Creative Commons Attribution-Share Alike 3.0">CC BY-SA 3.0</a>, <a href="https://commons.wikimedia.org/w/index.php?curid=1451959">Link</a></p>
</div>
<ol class="org-ol"><li><a id="sec-2-3-1-1" name="sec-2-3-1-1"></a>Combinational circuit and truth table<br /><div class="outline-text-5" id="text-2-3-1-1">
<p>
How to print numbers 0-3 to 7-segment alphanumeric display.
</p>
<ul class="org-ul">
<li>You need only 2 bits to display numbers 0-3 using binary numbers
</li>
<li>Check which LEDs should be switched on (value = 1, ie. logical TRUE) to display number 0
<ul class="org-ul">
<li>Repeat for all numbers
</li>
</ul>
</li>
</ul>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="right" />
<col class="right" />
<col class="left" />
<col class="right" />
<col class="right" />
<col class="right" />
<col class="right" />
<col class="right" />
<col class="right" />
<col class="right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="right">In0</th>
<th scope="col" class="right">In1</th>
<th scope="col" class="left">-</th>
<th scope="col" class="right">A</th>
<th scope="col" class="right">B</th>
<th scope="col" class="right">C</th>
<th scope="col" class="right">D</th>
<th scope="col" class="right">E</th>
<th scope="col" class="right">F</th>
<th scope="col" class="right">G</th>
</tr>
</thead>
<tbody>
<tr>
<td class="right">0</td>
<td class="right">0</td>
<td class="left"> </td>
<td class="right">1</td>
<td class="right">1</td>
<td class="right">1</td>
<td class="right">1</td>
<td class="right">1</td>
<td class="right">1</td>
<td class="right">0</td>
</tr>
<tr>
<td class="right">0</td>
<td class="right">1</td>
<td class="left"> </td>
<td class="right">0</td>
<td class="right">1</td>
<td class="right">1</td>
<td class="right">0</td>
<td class="right">0</td>
<td class="right">0</td>
<td class="right">0</td>
</tr>
<tr>
<td class="right">1</td>
<td class="right">0</td>
<td class="left"> </td>
<td class="right">1</td>
<td class="right">1</td>
<td class="right">0</td>
<td class="right">1</td>
<td class="right">1</td>
<td class="right">0</td>
<td class="right">1</td>
</tr>
<tr>
<td class="right">1</td>
<td class="right">1</td>
<td class="left"> </td>
<td class="right">1</td>
<td class="right">1</td>
<td class="right">1</td>
<td class="right">1</td>
<td class="right">0</td>
<td class="right">0</td>
<td class="right">1</td>
</tr>
</tbody>
</table>
<dl class="org-dl">
<dt> How to make the logical functions </dt><dd>Express using basic logic operations (AND, NOT, OR) the output (7-segments) based on the input (2-bits)
</dd>
</dl>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="left" />
</colgroup>
<tbody>
<tr>
<td class="left">A = NOT( In0' ⋅ In1 )</td>
</tr>
<tr>
<td class="left">B = 1</td>
</tr>
<tr>
<td class="left">C = NOT( In0 ⋅ In1' )</td>
</tr>
<tr>
<td class="left">D = A</td>
</tr>
<tr>
<td class="left">E = In1'</td>
</tr>
<tr>
<td class="left">F = In0' ⋅ In1'</td>
</tr>
<tr>
<td class="left">G = In0</td>
</tr>
</tbody>
</table>
</div>
</li></ol>
</div>
</div>
<div id="outline-container-sec-2-4" class="outline-3">
<h3 id="sec-2-4"><span class="section-number-3">2.4</span> Adders</h3>
<div class="outline-text-3" id="text-2-4">
<p>
Half-adder and full-adder implementation.
</p>
<dl class="org-dl">
<dt> <a href="http://www.cburch.com/logisim/">logisim</a> file </dt><dd><a href="./src/logisim/half_full_adder.circ">./src/logisim/half_full_adder.circ</a>
</dd>
</dl>
<div class="figure">
<p><img src="./img/ADDER.png" alt="ADDER.png" />
</p>
</div>
</div>
</div>
</div>
<div id="outline-container-sec-3" class="outline-2">
<h2 id="sec-3"><span class="section-number-2">3</span> 2s complement</h2>
<div class="outline-text-2" id="text-3">
<p>
The inner circle shows the unsigned numbers (1s complement), the outer (helix) shows the signed numbers (2s complement).
</p>
<div class="figure">
<p><img src="./img/2scomplement.png" alt="2scomplement.png" />
</p>
</div>
</div>
</div>
<div id="outline-container-sec-4" class="outline-2">
<h2 id="sec-4"><span class="section-number-2">4</span> Memory components</h2>
<div class="outline-text-2" id="text-4">
</div><div id="outline-container-sec-4-1" class="outline-3">
<h3 id="sec-4-1"><span class="section-number-3">4.1</span> Latch</h3>
<div class="outline-text-3" id="text-4-1">
<p>
Latches are basic module for implementing memory.
</p>
<dl class="org-dl">
<dt> <a href="http://www.cburch.com/logisim/">logisim</a> file </dt><dd><a href="./src/logisim/latches_RS_D.circ">./src/logisim/latches_RS_D.circ</a>
</dd>
</dl>
<div class="figure">
<p><img src="./img/latches.png" alt="latches.png" />
</p>
</div>
</div>
</div>
<div id="outline-container-sec-4-2" class="outline-3">
<h3 id="sec-4-2"><span class="section-number-3">4.2</span> Register</h3>
<div class="outline-text-3" id="text-4-2">
</div><div id="outline-container-sec-4-2-1" class="outline-4">
<h4 id="sec-4-2-1"><span class="section-number-4">4.2.1</span> Shift register</h4>
<div class="outline-text-4" id="text-4-2-1">
<dl class="org-dl">
<dt> <a href="http://www.cburch.com/logisim/">logisim</a> file </dt><dd><a href="./src/logisim/shift_register.circ">./src/logisim/shift_register.circ</a>
</dd>
</dl>
<div class="figure">
<p><img src="./img/shift-register.png" alt="shift-register.png" />
</p>
</div>
</div>
</div>
<div id="outline-container-sec-4-2-2" class="outline-4">
<h4 id="sec-4-2-2"><span class="section-number-4">4.2.2</span> Master-slave register</h4>
<div class="outline-text-4" id="text-4-2-2">
<p>
The basic memory component. Below master-slave register using two latches RS, activated by positive edge clock.
</p>
<dl class="org-dl">
<dt> <a href="http://www.cburch.com/logisim/">logisim</a> file </dt><dd><a href="./src/logisim/master_slave_register.circ">./src/logisim/master_slave_register.circ</a>
</dd>
</dl>
<div class="figure">
<p><img src="./img/master-slave.png" alt="master-slave.png" />
</p>
</div>
</div>
</div>
</div>
</div>
<div id="outline-container-sec-5" class="outline-2">
<h2 id="sec-5"><span class="section-number-2">5</span> Sequential circuits</h2>
<div class="outline-text-2" id="text-5">
<p>
High level description of sequential circuits.
</p>
<div class="figure">
<p><img src="./img/sequential-cirsuits.png" alt="sequential-cirsuits.png" />
</p>
</div>
</div>
<div id="outline-container-sec-5-1" class="outline-3">
<h3 id="sec-5-1"><span class="section-number-3">5.1</span> Counter</h3>
<div class="outline-text-3" id="text-5-1">
<p>
A 3 bit counter.
</p>
<dl class="org-dl">
<dt> <a href="http://www.cburch.com/logisim/">logisim</a> file </dt><dd><a href="./src/logisim/3_bit_counter.circ">./src/logisim/3_bit_counter.circ</a>
</dd>
</dl>
<div class="figure">