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<header class="post-header">
<h1 class="post-title"><span class=".zh">数电期中总结</span><span class=".en" hidden>Mid-term Summary of Digital Circuits</span>
</h1>
<div class="post-meta">
<span class="post-time">
2019-02-28
</span><span class="post-category">
<a href="/categories/notes/">notes</a>
</span>
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<style>.toc-level-2 > .toc-child {display: none !important; }</style>
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<h2 class="post-toc-title">Contents</h2>
<div class="post-toc-content">
<ol class="toc"><li class="toc-item toc-level-1"><a class="toc-link" href="#1-数制与码制"><span class="toc-text">1. 数制与码制</span></a><ol class="toc-child"><li class="toc-item toc-level-2"><a class="toc-link" href="#二进制运算"><span class="toc-text">二进制运算</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#补码"><span class="toc-text">补码</span></a></li></ol></li><li class="toc-item toc-level-2"><a class="toc-link" href="#常用编码"><span class="toc-text">常用编码</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#DCB"><span class="toc-text">DCB</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#Signed-Numbers"><span class="toc-text">Signed Numbers</span></a></li></ol></li><li class="toc-item toc-level-2"><a class="toc-link" href="#期中总结"><span class="toc-text">期中总结</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#第一周-初识数电"><span class="toc-text">第一周 - 初识数电</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#第二周-数制"><span class="toc-text">第二周 - 数制</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#第三周-逻辑门与电路封装类型"><span class="toc-text">第三周 - 逻辑门与电路封装类型</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#第四周-布尔运算"><span class="toc-text">第四周 - 布尔运算</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#第五周-Karnaugh-Map"><span class="toc-text">第五周 - Karnaugh Map</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#第六周-逻辑门组合"><span class="toc-text">第六周 - 逻辑门组合</span></a></li></ol></li></ol></li><li class="toc-item toc-level-1"><a class="toc-link" href="#1-Number-system-and-code-system"><span class="toc-text">1. Number system and code system</span></a><ol class="toc-child"><li class="toc-item toc-level-2"><a class="toc-link" href="#Binary-operation"><span class="toc-text">Binary operation</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#Complement"><span class="toc-text">Complement</span></a></li></ol></li><li class="toc-item toc-level-2"><a class="toc-link" href="#Common-coding"><span class="toc-text">Common coding</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#DCB-1"><span class="toc-text">DCB</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#Signed-Numbers-1"><span class="toc-text">Signed Numbers</span></a></li></ol></li><li class="toc-item toc-level-2"><a class="toc-link" href="#Mid-term-summary"><span class="toc-text">Mid-term summary</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#First-week-first-acquaintance-with-digital-telephony"><span class="toc-text">First week-first acquaintance with digital telephony</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#Second-week-Number-system"><span class="toc-text">Second week-Number system</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#Week-3-Logic-Gate-and-Circuit-Package-Type"><span class="toc-text">Week 3-Logic Gate and Circuit Package Type</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#Week-4-Boolean-operations"><span class="toc-text">Week 4-Boolean operations</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#Week-5-Karnaugh-Map"><span class="toc-text">Week 5-Karnaugh Map</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#Week-6-Logic-Gate-Combination"><span class="toc-text">Week 6-Logic Gate Combination</span></a></li></ol></li></ol></li></ol>
</div>
</div>
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<p>上学期掉了魔电的坑，这学期来搞点数电小攻略掩饰一下(☆ω☆)</p>
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<p>I lost the pit of magic electricity last semester. This semester, let’s make a small strategy to hide it (☆ω☆)</p>
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<h1 id="1-数制与码制"><a href="#1-数制与码制" class="headerlink" title="1. 数制与码制"></a>1. 数制与码制</h1><h2 id="二进制运算"><a href="#二进制运算" class="headerlink" title="二进制运算"></a>二进制运算</h2><h3 id="补码"><a href="#补码" class="headerlink" title="补码"></a>补码</h3><p>常用补码来表示负数，以便于计算。<br>正数和零补码是其自身，负数的补码方法如下：<br>二进制减法可以通过被减数加要减数的补码来实现。<br><strong>&lt;法一&gt;直接法</strong><br>$$(N)_{COMP}=\begin{cases}N&amp;\text{N为正数}\2^{n}-N&amp; \text{N为负数} \end{cases}$$</p>
<p>符号位为零（正数）时，补码与源码相同，符号位为1（负数）时，补码为$2^{n}-N$.<br><strong>&lt;法二&gt;观察法</strong><br>欲求补码，可以先找其反码。<br>$$(N)_{INV}=\begin{cases}N&amp;\text{N为正数}\(2^{n}-1)-N&amp; \text{N为负数} \end{cases}$$</p>
<p>即，除符号位外其他值0变1，1变0。<br>随后反码整体加1即可得到补码~</p>
<h2 id="常用编码"><a href="#常用编码" class="headerlink" title="常用编码"></a>常用编码</h2><h3 id="DCB"><a href="#DCB" class="headerlink" title="DCB"></a>DCB</h3><p>即8421恒权码。DCB作为10进制显示时，须在每一个Invalid位(&gt;9)上加6。</p>
<h3 id="Signed-Numbers"><a href="#Signed-Numbers" class="headerlink" title="Signed Numbers"></a>Signed Numbers</h3><p>使用8位，最左边一位表示符号，其余7位表示数值。</p>
<h2 id="期中总结"><a href="#期中总结" class="headerlink" title="期中总结"></a>期中总结</h2><h3 id="第一周-初识数电"><a href="#第一周-初识数电" class="headerlink" title="第一周 - 初识数电"></a>第一周 - 初识数电</h3><ul>
<li>模拟量太复杂，不符合人类思维</li>
<li>三极管MOS管等非线性器件为魔转数提供了器件基础</li>
<li>因为模电太难，所以我们要学数电<br><strong>一些要点</strong></li>
<li>TTL意思是指晶体管逻辑电路，由各种三极管和电阻组成，特点是速度快</li>
<li>TTL中0-0.8V为低电平，2-5V为高电平</li>
<li>二进制与十进制相互转换(整数/小数)</li>
<li>LSB(Least Significant Bit)/MSB(Most S B)</li>
</ul>
<h3 id="第二周-数制"><a href="#第二周-数制" class="headerlink" title="第二周 - 数制"></a>第二周 - 数制</h3><ul>
<li>反码 1’s Complement</li>
<li>补码 2’s Complement</li>
<li>有时候二进制太长不好用，这使16进制很方便</li>
<li>16进制类似2进制的助记符，如观察<code>1100 0101</code>可直接写出<code>C5</code></li>
<li>BCD是用一个16进制表示一个10进制数</li>
<li>BCD很符合人类的思维习惯，但造成极大的资源浪费</li>
<li>BCD四则运算，我觉得最好转成10进制算完再转回去，反正很方便</li>
<li>计算机BCD加法采取+6进位法</li>
<li>数字储存时最左一位是符号位</li>
<li>负数使用补码来存储(<a href="https://zhidao.baidu.com/question/1692306348989800588.html" target="_blank" rel="noopener">栗子</a>)</li>
<li>1字节signed数字范围<code>-128-127</code></li>
<li>合理设计存储位数，小心溢出</li>
<li><a href="https://zhidao.baidu.com/question/293829485.html" target="_blank" rel="noopener">二进制乘法</a></li>
<li><a href="https://zhidao.baidu.com/question/304091753926723564.html" target="_blank" rel="noopener">二进制除法</a> 与十进制类似</li>
</ul>
<h3 id="第三周-逻辑门与电路封装类型"><a href="#第三周-逻辑门与电路封装类型" class="headerlink" title="第三周 - 逻辑门与电路封装类型"></a>第三周 - 逻辑门与电路封装类型</h3><ul>
<li>非门 NOT</li>
<li>与门 AND</li>
<li>或门 OR</li>
<li>非与门 NAND</li>
<li>非或门 NOR</li>
<li>异或门 XOR</li>
<li>常见有TTL和CMOS两类</li>
<li>CMOS按照供压可分为3.3V和5V两类</li>
<li>fan-out是指有效input个数</li>
<li>propagation delay time指响应时间</li>
<li>集成电路命名，如<code>74LS04</code>中74指商品级，LS指种类，04为型号</li>
<li>按复杂程度分类：SSI(1-12门)，MSI(13-99门)，LSI(100-9999门)，VLSI(10000-99999)，ULSI(100000+)</li>
</ul>
<h3 id="第四周-布尔运算"><a href="#第四周-布尔运算" class="headerlink" title="第四周 - 布尔运算"></a>第四周 - 布尔运算</h3><ul>
<li>遵循交换，结合，分配律</li>
<li>结论<code>A+AB=A</code>与<code>A+~AB=A+B</code></li>
<li>DeMorgan’s Theorems <code>~(AB)=(~A+~B)</code> 与 <code>~(A+B)=~A~B</code></li>
<li><code>~A~B</code>为Negative AND, <code>~(AB)</code>为NAND, OR同理</li>
<li>SOP格式为<code>··+··+··</code></li>
<li>POS格式为<code>()*()*()</code></li>
<li>Truth Table即为将全部可能的Input和output列表</li>
</ul>
<h3 id="第五周-Karnaugh-Map"><a href="#第五周-Karnaugh-Map" class="headerlink" title="第五周 - Karnaugh Map"></a>第五周 - Karnaugh Map</h3><ul>
<li>Karnaugh Map来可视化逻辑门化简</li>
</ul>
<h3 id="第六周-逻辑门组合"><a href="#第六周-逻辑门组合" class="headerlink" title="第六周 - 逻辑门组合"></a>第六周 - 逻辑门组合</h3><ul>
<li>NAND和NOR可以组合出其它任意门</li>
<li>加法器 左位放<code>A AND B</code>右位放<code>A XOR B</code></li>
<li>比较器 1bit<code>A XOR B</code> 2bit<code>(A0 XOR B0) NOR (A1 XOR B0)</code></li>
<li>译码器 逻辑二进制转控制电平输出</li>
</ul>
<hr>
<p>课件：<br><a href="https://www.eee.dog/usr/uploads/2019/02/1948813444.pdf">Lecture03.pdf</a><br><a href="https://www.eee.dog/usr/uploads/2019/02/20970449.pdf">Lecture04.pdf</a></p>
</span>
<span class=".en">
<h1 id="1-Number-system-and-code-system"><a href="#1-Number-system-and-code-system" class="headerlink" title="1. Number system and code system"></a>1. Number system and code system</h1><h2 id="Binary-operation"><a href="#Binary-operation" class="headerlink" title="Binary operation"></a>Binary operation</h2><h3 id="Complement"><a href="#Complement" class="headerlink" title="Complement"></a>Complement</h3><p>The complement is often used to represent negative numbers for easy calculation.<br>Positive numbers and zero complement are themselves, and the complement method of negative numbers is as follows:<br>Binary subtraction can be implemented by adding the complement of the subtracted number to the subtracted number.<br><strong><Method One> Direct Method</strong><br>$$(N)_{COMP}=\begin{cases}N&amp;\text{N is a positive number}\2^{n}-N&amp; \text{N is a negative number} \end{cases}$$</p>
<p>When the sign bit is zero (positive number), the complement is the same as the source code. When the sign bit is 1 (negative number), the complement is $2^{n}-N$.<br><strong><Method Two> Observation Method</strong><br>If you want the complement, you can find the inverse first.<br>$$(N)_{INV}=\begin{cases}N&amp;\text{N is a positive number}\(2^{n}-1)-N&amp; \text{N is a negative number} \end{cases}$$</p>
<p>That is, except for the sign bit, 0 changes to 1, and 1 changes to 0.<br>Then add 1 to the whole complement to get the complement~</p>
<h2 id="Common-coding"><a href="#Common-coding" class="headerlink" title="Common coding"></a>Common coding</h2><h3 id="DCB-1"><a href="#DCB-1" class="headerlink" title="DCB"></a>DCB</h3><p>That is, the 8421 constant weight code. When DCB is displayed as a decimal number, 6 must be added to each Invalid bit (&gt;9).</p>
<h3 id="Signed-Numbers-1"><a href="#Signed-Numbers-1" class="headerlink" title="Signed Numbers"></a>Signed Numbers</h3><p>8 bits are used, the leftmost bit represents the sign, and the remaining 7 bits represent the value.</p>
<h2 id="Mid-term-summary"><a href="#Mid-term-summary" class="headerlink" title="Mid-term summary"></a>Mid-term summary</h2><h3 id="First-week-first-acquaintance-with-digital-telephony"><a href="#First-week-first-acquaintance-with-digital-telephony" class="headerlink" title="First week-first acquaintance with digital telephony"></a>First week-first acquaintance with digital telephony</h3><ul>
<li>The analog quantity is too complicated to conform to human thinking</li>
<li>Non-linear devices such as triode and MOS tube provide the device basis for the magic speed</li>
<li>Because analog electricity is too difficult, we have to learn math electricity<br><strong>Some points</strong></li>
<li>TTL means transistor logic circuit, composed of various transistors and resistors, and is characterized by fast speed</li>
<li>0-0.8V in TTL is low level, 2-5V is high level</li>
<li>Conversion between binary and decimal (integer/decimal)</li>
<li>LSB(Least Significant Bit)/MSB(Most S B)</li>
</ul>
<h3 id="Second-week-Number-system"><a href="#Second-week-Number-system" class="headerlink" title="Second week-Number system"></a>Second week-Number system</h3><ul>
<li>1’s Complement</li>
<li>2’s Complement</li>
<li>Sometimes the binary is too long to use, which makes hexadecimal very convenient</li>
<li>Hexadecimal is similar to binary mnemonic, if you observe <code>1100 0101</code>, you can write <code>C5</code> directly</li>
<li>BCD uses a hexadecimal number to represent a decimal number</li>
<li>BCD is in line with human thinking habits, but it causes a great waste of resources</li>
<li>BCD four arithmetic, I think it’s best to convert to decimal and then convert it back. Anyway, it’s very convenient</li>
<li>Computer BCD addition adopts +6 carry method</li>
<li>When storing numbers, the leftmost digit is the sign bit</li>
<li>Negative numbers are stored using one’s complement (<a href="https://zhidao.baidu.com/question/1692306348989800588.html" target="_blank" rel="noopener">chestnut</a>)</li>
<li>1 byte signed number range <code>-128-127</code></li>
<li>Reasonably design the number of storage bits and be careful of overflow</li>
<li><a href="https://zhidao.baidu.com/question/293829485.html" target="_blank" rel="noopener">Binary Multiplication</a></li>
<li><a href="https://zhidao.baidu.com/question/304091753926723564.html" target="_blank" rel="noopener">Binary Division</a> Similar to decimal</li>
</ul>
<h3 id="Week-3-Logic-Gate-and-Circuit-Package-Type"><a href="#Week-3-Logic-Gate-and-Circuit-Package-Type" class="headerlink" title="Week 3-Logic Gate and Circuit Package Type"></a>Week 3-Logic Gate and Circuit Package Type</h3><ul>
<li>NOT</li>
<li>AND gate</li>
<li>OR gate OR</li>
<li>NOT AND gate NAND</li>
<li>NOR gate</li>
<li>Exclusive OR gate XOR</li>
<li>Commonly there are TTL and CMOS two types</li>
<li>CMOS can be divided into 3.3V and 5V according to the supply voltage</li>
<li>Fan-out refers to the number of valid inputs</li>
<li>propagation delay time refers to response time</li>
<li>IC naming, for example, 74 in <code>74LS04</code> means commodity grade, LS means type, 04 is model</li>
<li>Classification by complexity: SSI (1-12 doors), MSI (13-99 doors), LSI (100-9999 doors), VLSI (10000-99999), ULSI (100000+)</li>
</ul>
<h3 id="Week-4-Boolean-operations"><a href="#Week-4-Boolean-operations" class="headerlink" title="Week 4-Boolean operations"></a>Week 4-Boolean operations</h3><ul>
<li>Follow the exchange, combination, and distribution laws</li>
<li>Conclusion <code>A+AB=A</code> and <code>A+~AB=A+B</code></li>
<li>DeMorgan’s Theorems <code>~(AB)=(~A+~B)</code> and <code>~(A+B)=~A~B</code></li>
<li><code>~A~B</code> is Negative AND, <code>~(AB)</code> is NAND, OR is the same</li>
<li>SOP format is <code>··+··+··</code></li>
<li>POS format is <code>()*()*()</code></li>
<li>Truth Table is a list of all possible Input and Output</li>
</ul>
<h3 id="Week-5-Karnaugh-Map"><a href="#Week-5-Karnaugh-Map" class="headerlink" title="Week 5-Karnaugh Map"></a>Week 5-Karnaugh Map</h3><ul>
<li>Karnaugh Map to visualize logic gate simplification</li>
</ul>
<h3 id="Week-6-Logic-Gate-Combination"><a href="#Week-6-Logic-Gate-Combination" class="headerlink" title="Week 6-Logic Gate Combination"></a>Week 6-Logic Gate Combination</h3><ul>
<li>NAND and NOR can be combined into any other gate</li>
<li>Adder put <code>A AND B</code> on the left bit and <code>A XOR B</code> on the right bit</li>
<li>Comparator 1bit<code>A XOR B</code> 2bit<code>(A0 XOR B0) NOR (A1 XOR B0)</code></li>
<li>Decoder logic binary to control level output</li>
</ul>
<hr>
<p>Courseware:<br><a href="https://www.eee.dog/usr/uploads/2019/02/1948813444.pdf">Lecture03.pdf</a><br><a href="https://www.eee.dog/usr/uploads/2019/02/20970449.pdf">Lecture04.pdf</a></p>
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