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import{_ as s,c as i,o as a,a6 as n}from"./chunks/framework.CZRoMP2i.js";const l="/c/assets/1.CXNJqOOc.png",e="/c/assets/2.E0LS08Y5.png",t="/c/assets/3.6recRAvz.jpeg",p="/c/assets/4.DcyDw4rB.jpg",h="/c/assets/5.q20QOAIA.png",d="/c/assets/6.CmrWpBzQ.png",k="/c/assets/7.CocAjZjO.png",c="/c/assets/8.CHZSlb-7.png",r="/c/assets/9.RD2M_pYn.png",o="/c/assets/10.CmNKK_Ug.png",u="/c/assets/11.CbGZ55Dj.png",E="/c/assets/12.DpTBR420.png",g="/c/assets/13.XcPl7d9s.png",b="/c/assets/14.DL02VQMp.png",y="/c/assets/15.Dr67r_Ws.png",F="/c/assets/16.C5XiXNVN.png",m="/c/assets/17.DO8XxSV6.jpg",C="/c/assets/18.CUXrdefp.jpeg",v="/c/assets/19.uqLiL_yu.png",B="/c/assets/20.CVy9jq-k.svg",A="/c/assets/21.D0s35-Np.svg",D="/c/assets/22.CGctd5l_.svg",_="/c/assets/23.DQIGB6FY.svg",q="/c/assets/24.DBiJDp82.svg",f="/c/assets/25.r0a7UWIb.svg",x="/c/assets/26.-KoNS5D_.svg",P="/c/assets/27.9LAsi3gH.svg",T="/c/assets/28.CbxjdJlI.svg",N="/c/assets/29.DouEaZ2q.svg",O="/c/assets/30.BAASpiz6.svg",z="/c/assets/31.CSLcq3FJ.svg",M="/c/assets/32.8wVUSUxs.svg",w="/c/assets/33.B8T792CZ.svg",I="/c/assets/34.D7XSVA_S.svg",U="/c/assets/35.BeI_-jpB.svg",$=JSON.parse('{"title":"第一章:变量(⭐)","description":"","frontmatter":{},"headers":[],"relativePath":"notes/01_c-basic/02_xdx/index.md","filePath":"notes/01_c-basic/02_xdx/index.md","lastUpdated":1723946050000}'),R={name:"notes/01_c-basic/02_xdx/index.md"},L=n('<h1 id="第一章-变量-⭐" tabindex="-1">第一章:变量(⭐) <a class="header-anchor" href="#第一章-变量-⭐" aria-label="Permalink to "第一章:变量(⭐)""></a></h1><h2 id="_1-1-程序中变化的数据" tabindex="-1">1.1 程序中变化的数据 <a class="header-anchor" href="#_1-1-程序中变化的数据" aria-label="Permalink to "1.1 程序中变化的数据""></a></h2><ul><li>在生活中,我们使用最多的不是固定的数据,而是会变化的数据: <ul><li>① 购物车商品的<code>数量</code>、<code>价格</code>等。</li><li>② 一首歌<code>播放的时间</code>、<code>进度条</code>、<code>歌词的展示</code>等。</li><li>③ 微信聊天中<code>消息条数</code>、<code>时间</code>、<code>语音的长度</code>、<code>头像</code>、<code>名称</code>等。</li><li>④ 游戏中技能的<code>冷却时间</code>、<code>血量</code>、<code>蓝量</code>、<code>buff 时间</code>、<code>金币的数量</code>等。</li><li>……</li></ul></li></ul><ul><li>下图是一个<code>购物车</code>中<code>变化</code>的<code>数据</code>,即:</li></ul><p><img src="'+l+'" alt="" loading="lazy"></p><ul><li>那么,在实际开发中,我们就会使用<code>变量</code>来<code>保存</code>和<code>操作</code>这些<code>变化</code>的<code>数据</code>。</li></ul><h2 id="_1-2-变量" tabindex="-1">1.2 变量 <a class="header-anchor" href="#_1-2-变量" aria-label="Permalink to "1.2 变量""></a></h2><ul><li>变量的定义:变量是程序中不可或缺的组成单位,最基本的存储单元。其实,变量就是一个存储数据的临时空间,可以向其中存储不同类型的数据,如:整数、小数、字符、字符串等,并且变量中的数据在程序运行的时候可以动态改变。</li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><ul><li><code>变量</code>:用来<code>存储数据</code>的<code>容器</code>。</li><li><code>数据</code>:可以是一个用来计算的<code>数字</code>,如:上文购物车中的<code>价格</code>等;也可以是一句话中的<code>关键词</code>或<code>其它任意格式的数据</code>。</li><li>变量的<code>特别</code>之处就在于<code>它存放的数据是可以改变</code>的。</li></ul></div><ul><li>我们可以将<code>变量</code>想象为一个<code>容器</code>,盒子中<code>装的</code>就是我们想要的<code>数据</code>,并且我们需要<code>给</code>盒子<code>取</code>一个<code>特别的名称</code>;通过这个<code>特别的名称</code>,我们可以<code>给</code>盒子<code>添加数据</code>或<code>移除数据</code>,这个<code>特别的名称</code>就是<code>变量名</code>。</li></ul><p><img src="'+e+`" alt="" loading="lazy"></p><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><ul><li>① <code>变量</code>是内存中的一个<code>存储区域</code>,该区域的数据可以在<code>同一类型</code>范围内<code>不断变化</code>。</li><li>② 通过<code>变量名</code>,可以<code>操作</code>这块内存区域,向其中<code>存储数据</code>或<code>获取数据</code>以及<code>移除数据</code>。</li><li>③ 变量的构成包含三个要素:<code>数据类型</code>、<code>变量名</code>、<code>需要存储的数据</code>。</li><li>④ 在生活中,我们会经常说:这件衣服的价格是 <code>100(整型)</code> 元,这双鞋子的价格是 <code>250.5(小数,浮点类型)</code> 元,<code>今天天气真好(字符串类型)</code>之类的话;在计算机科学中,这些都是数据,并且它们是有类型,即:数据类型。(数据类型用于定义变量所能存储的数据的种类以及可以对这些数据进行的操作的一种分类,每种数据类型都有特定的属性和用途,它们决定了变量在内存中如何表示和存储,以及变量可以执行哪些操作)</li></ul></div><h2 id="_1-3-变量的声明和使用" tabindex="-1">1.3 变量的声明和使用 <a class="header-anchor" href="#_1-3-变量的声明和使用" aria-label="Permalink to "1.3 变量的声明和使用""></a></h2><ul><li>① 变量必须先声明,后使用。</li><li>② 可以先声明变量再赋值,也可以在声明变量的同时进行赋值。</li><li>③ 变量的值可以在同一类型范围内不断变化。</li></ul><div class="important custom-block github-alert"><p class="custom-block-title">IMPORTANT</p><p></p><ul><li>① 在实际开发中,我们通常都会在声明变量的同时,给其赋值,这被称为初始化。</li><li>② 如果不在声明变量的同时,进行初始化,默认情况下,系统会赋予的随机值,我们也称为垃圾值。</li></ul></div><ul><li>示例:先声明,再使用</li></ul><div class="language-c vp-adaptive-theme line-numbers-mode"><button title="Copy Code" class="copy"></button><span class="lang">c</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">#include</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> <stdio.h></span></span>
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<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">int</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;"> main</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">() {</span></span>
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@ -237,4 +237,4 @@ import{_ as s,c as i,o as a,a6 as n}from"./chunks/framework.CZRoMP2i.js";const l
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<span class="line"><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;"> printf</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">"</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">%d</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> 的十六进制(前缀)整数: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">%#X\\n</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">"</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">, num, num);</span><span style="--shiki-light:#6A737D;--shiki-dark:#6A737D;"> // 100 的十六进制(前缀)整数: 0X64</span></span>
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<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> 0</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">;</span></span>
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<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">}</span></span></code></pre><div class="line-numbers-wrapper" aria-hidden="true"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br><span class="line-number">12</span><br><span class="line-number">13</span><br><span class="line-number">14</span><br><span class="line-number">15</span><br></div></div><h2 id="_3-3-进制的运算规则" tabindex="-1">3.3 进制的运算规则 <a class="header-anchor" href="#_3-3-进制的运算规则" aria-label="Permalink to "3.3 进制的运算规则""></a></h2><ul><li><code>十进制</code>的运算规则,如下所示: <ul><li>逢<code>十</code>进<code>一</code>(针对加法而言)。</li><li>借<code>一</code>当<code>十</code>(针对减法而言)。</li></ul></li><li><code>二进制</code>的运算规则,如下所示: <ul><li>逢<code>二</code>进<code>一</code>(针对加法而言)。</li><li>借<code>一</code>当<code>二</code>(针对减法而言)。</li></ul></li><li><code>八进制</code>的运算规则,如下所示: <ul><li>逢<code>八</code>进<code>一</code>(针对加法而言)。</li><li>借<code>一</code>当<code>八</code>(针对减法而言)。</li></ul></li><li><code>十六进制</code>的运算规则,如下所示: <ul><li>逢<code>十六</code>进<code>一</code>(针对加法而言)。</li><li>借<code>一</code>当<code>十六</code>(针对减法而言)。</li></ul></li></ul><h2 id="_3-4-进制的转换" tabindex="-1">3.4 进制的转换 <a class="header-anchor" href="#_3-4-进制的转换" aria-label="Permalink to "3.4 进制的转换""></a></h2><h3 id="_3-4-1-概述" tabindex="-1">3.4.1 概述 <a class="header-anchor" href="#_3-4-1-概述" aria-label="Permalink to "3.4.1 概述""></a></h3><ul><li>不同进制的转换,如下所示:</li></ul><p><img src="`+B+'" alt="" loading="lazy"></p><ul><li>在计算机中,数据是从右往左的方式排列的;其中,最右边的是低位,最左边的是高位,即:</li></ul><p><img src="'+v+'" alt="" loading="lazy"></p><h3 id="_3-4-2-二进制和十进制的转换" tabindex="-1">3.4.2 二进制和十进制的转换 <a class="header-anchor" href="#_3-4-2-二进制和十进制的转换" aria-label="Permalink to "3.4.2 二进制和十进制的转换""></a></h3><h4 id="_3-4-2-1-二进制转换为十进制" tabindex="-1">3.4.2.1 二进制转换为十进制 <a class="header-anchor" href="#_3-4-2-1-二进制转换为十进制" aria-label="Permalink to "3.4.2.1 二进制转换为十进制""></a></h4><ul><li>规则:从最低位开始,将每个位上的数提取出来,乘以 2 的 (位数 - 1 )次方,然后求和。</li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><ul><li>① 在学术界,将这种计算规则,称为<code>位权相加法</code>。</li><li>② <code>八进制转换为十进制</code>、<code>十六进制转换为十进制</code>和<code>二进制转换为十进制</code>的算法相同!!!</li></ul></div><ul><li>示例:十进制转十进制</li></ul><p><img src="'+A+'" alt="" loading="lazy"></p><ul><li>示例:二进制转十进制</li></ul><p><img src="'+D+'" alt="" loading="lazy"></p><h4 id="_3-4-2-2-十进制转换二进制" tabindex="-1">3.4.2.2 十进制转换二进制 <a class="header-anchor" href="#_3-4-2-2-十进制转换二进制" aria-label="Permalink to "3.4.2.2 十进制转换二进制""></a></h4><ul><li>规则:将该数不断除以 2 ,直到商为 0 为止,然后将每步得到的余数倒过来,就是对应的二进制。</li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><ul><li>① 在学术界,将这种计算规则,称为<code>短除法</code>或<code>连续除2取余法</code>。</li><li>② 很好理解,只有不断地除以 2 ,就能保证最大的数字不超过 2 ,这不就是二进制(只能有 0 或 1)吗?</li><li>③ <code>八进制转换为二进制</code>、<code>十六进制转换为二进制</code>和<code>十进制转换为二进制</code>的算法相同!!!</li></ul></div><ul><li>示例:十进制转十进制</li></ul><p><img src="'+_+'" alt="" loading="lazy"></p><ul><li>示例:十进制转二进制</li></ul><p><img src="'+q+'" alt="" loading="lazy"></p><h3 id="_3-4-3-二进制转八进制" tabindex="-1">3.4.3 二进制转八进制 <a class="header-anchor" href="#_3-4-3-二进制转八进制" aria-label="Permalink to "3.4.3 二进制转八进制""></a></h3><ul><li><p>规则:每 3 位二进制就是一个八进制。</p></li><li><p>示例:011 101 001 -> 351</p></li></ul><p><img src="'+f+'" alt="" loading="lazy"></p><h3 id="_3-4-4-二进制转十六进制" tabindex="-1">3.4.4 二进制转十六进制 <a class="header-anchor" href="#_3-4-4-二进制转十六进制" aria-label="Permalink to "3.4.4 二进制转十六进制""></a></h3><ul><li><p>规则:每 4 位二进制就是一个十六进制。</p></li><li><p>示例:1110 1001 -> 0xE9</p></li></ul><p><img src="'+x+'" alt="" loading="lazy"></p><h2 id="_3-5-原码、反码和补码" tabindex="-1">3.5 原码、反码和补码 <a class="header-anchor" href="#_3-5-原码、反码和补码" aria-label="Permalink to "3.5 原码、反码和补码""></a></h2><h3 id="_3-5-1-概述" tabindex="-1">3.5.1 概述 <a class="header-anchor" href="#_3-5-1-概述" aria-label="Permalink to "3.5.1 概述""></a></h3><ul><li>机器数:一个数在计算机的存储形式是二进制,我们称这些二进制数为机器数。机器数可以是有符号的,用机器数的最高位来存放符号位,0 表示正数,1 表示负数。</li></ul><p><img src="'+P+'" alt="" loading="lazy"></p><ul><li>真值:因为机器数带有符号位,所以机器数的形式值不等于其真实表示的值(真值),以机器数 1000 0001 为例,其真正表示的值(首位是符号位)为 -1,而形式值却是 129 ,因此将带有符号位的机器数的真正表示的值称为机器数的真值。</li></ul><p><img src="'+T+'" alt="" loading="lazy"></p><h3 id="_3-5-2-原码" tabindex="-1">3.5.2 原码 <a class="header-anchor" href="#_3-5-2-原码" aria-label="Permalink to "3.5.2 原码""></a></h3><ul><li>原码的表示与机器数真值表示的一样,即用第一位表示符号,其余位表示数值。</li><li>规则: <ul><li>正数的<code>原码</code>是它本身对应的二进制数,符号位是 0 。</li><li>负数的<code>原码</code>是它本身绝对值对应的二进制数,但是符号位是 1 。</li></ul></li><li>+1 的原码,使用 8 位二进数来表示,就是:</li></ul><table tabindex="0"><thead><tr><th>十进制数</th><th>原码(8位二进制数)</th></tr></thead><tbody><tr><td>+1</td><td><code>0</code>000 0001</td></tr></tbody></table><ul><li>-1 的原码,使用 8 位二进数来表示,就是:</li></ul><table tabindex="0"><thead><tr><th>十进制数</th><th>原码(8位二进制数)</th></tr></thead><tbody><tr><td>-1</td><td><code>1</code>000 0001</td></tr></tbody></table><div class="important custom-block github-alert"><p class="custom-block-title">IMPORTANT</p><p></p><p>按照原码的规则,会出现 <code>+0</code> 和 <code>-0</code> 的情况,即:<code>0</code>000 0000(+0)、<code>1</code>000 0000(-0),显然不符合实际情况;所以,计算机底层虽然存储和计算的都是二进数,但显然不是原码。</p></div><h3 id="_3-5-3-反码" tabindex="-1">3.5.3 反码 <a class="header-anchor" href="#_3-5-3-反码" aria-label="Permalink to "3.5.3 反码""></a></h3><ul><li><p>规则:</p><ul><li>正数的反码和它的原码相同。</li><li>负数的反码是在其原码的基础上,符号位不变,其余各位取反。</li></ul></li><li><p>+1 的反码,使用 8 位二进数来表示,就是:</p></li></ul><table tabindex="0"><thead><tr><th>十进制数</th><th>原码(8位二进制数)</th><th>反码(8位二进制数)</th></tr></thead><tbody><tr><td>+1</td><td><code>0</code>000 0001</td><td><code>0</code>000 0001</td></tr></tbody></table><ul><li>-1 的反码,使用 8 位二进数来表示,就是:</li></ul><table tabindex="0"><thead><tr><th>十进制数</th><th>原码(8位二进制数)</th><th>反码(8位二进制数)</th></tr></thead><tbody><tr><td>-1</td><td><code>1</code>000 0001</td><td><code>1</code>111 1110</td></tr></tbody></table><div class="important custom-block github-alert"><p class="custom-block-title">IMPORTANT</p><p></p><p>按照反码的规则,如果是 <code>+0</code>,对应的原码是 <code>0</code>000 0000;那么,其反码还是 <code>0</code>000 0000 ;如果是 <code>-0</code>,对应的原码是 <code>1</code>000 0000,其反码是 <code>1</code>111 1111,显然不符合实际情况;所以,计算机底层虽然存储和计算的都是二进数,但显然不是反码。</p></div><h3 id="_3-5-4-补码" tabindex="-1">3.5.4 补码 <a class="header-anchor" href="#_3-5-4-补码" aria-label="Permalink to "3.5.4 补码""></a></h3><ul><li><p>规则:</p><ul><li>正数的补码和它的原码相同。</li><li>负数的补码是在其反码的基础上 + 1 。</li></ul></li><li><p>+1 的补码,使用 8 位二进数来表示,就是:</p></li></ul><table tabindex="0"><thead><tr><th>十进制数</th><th>原码(8位二进制数)</th><th>反码(8位二进制数)</th><th>补码(8位二进制数)</th></tr></thead><tbody><tr><td>+1</td><td><code>0</code>000 0001</td><td><code>0</code>000 0001</td><td><code>0</code>000 0001</td></tr></tbody></table><ul><li>-1 的补码,使用 8 位二进数来表示,就是:</li></ul><table tabindex="0"><thead><tr><th>十进制数</th><th>原码(8位二进制数)</th><th>反码(8位二进制数)</th><th>补码(8位二进制数)</th></tr></thead><tbody><tr><td>-1</td><td><code>1</code>000 0001</td><td><code>1</code>111 1110</td><td><code>1</code>111 1111</td></tr></tbody></table><ul><li>如果 0 ,按照 <code>+0</code> 的情况进行处理,即:</li></ul><p><img src="'+O+'" alt="" loading="lazy"></p><ul><li>如果 0 ,按照 <code>-0</code> 的情况进行处理,即:</li></ul><p><img src="'+N+'" alt="" loading="lazy"></p><div class="important custom-block github-alert"><p class="custom-block-title">IMPORTANT</p><p></p><ul><li>① 补码表示法解决了<code>原码</code>和<code>反码</code>存在的<code>两种</code>零(<code>+0</code> 和 <code>-0</code>)的问题,即:在补码表示法中,只有<code>一个</code>零,即 <code>0000 0000</code>。</li><li>②补码使得<code>加法运算</code>和<code>减法运算</code>可以统一处理,通过将减法运算<code>转换</code>为加法运算,可以简化硬件设计,提高了运算效率。</li><li>③ 计算机底层<code>存储</code>和<code>计算</code>的都是<code>二进数的补码</code>。换言之,当读取整数的时候,需要采用逆向的转换,即:将补码转换为原码。正数的原码、反码、补码都是一样的,三码合一。负数的补码转换为原码的方法就是先减去 <code>1</code> ,得到反码,再按位取反,得到原码。</li></ul></div><h3 id="_3-5-5-总结" tabindex="-1">3.5.5 总结 <a class="header-anchor" href="#_3-5-5-总结" aria-label="Permalink to "3.5.5 总结""></a></h3><ul><li>① 正数的原码、反码和补码都是一样的,三码合一。</li><li>② 负数的反码是在其原码的基础上,按位取反(0 变 1 ,1 变 0 ),符号位不变;负数的补码是其反码 + 1 。</li><li>③ 0 的补码是 0 。</li></ul><h2 id="_3-6-计算机底层为什么使用补码" tabindex="-1">3.6 计算机底层为什么使用补码? <a class="header-anchor" href="#_3-6-计算机底层为什么使用补码" aria-label="Permalink to "3.6 计算机底层为什么使用补码?""></a></h2><ul><li>如果计算是 <code>2 - 2</code> ,那么可以转换为 <code>2 + (-2)</code>,这样计算机内部在处理<code>减法计算</code>的时候,就会将其转换为<code>加法计算</code>的形式,以简化硬件设计和提高计算效率。</li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><ul><li>① 加法和减法是计算机中最基本的运算,计算机时时刻刻都离不开它们,所以它们由硬件直接支持。为了提高加法和减法的运行效率,硬件电路必须设计得尽量简单。</li><li>② 对于有符号位的数字来说,内存需要区分符号位和数值位:对于人类来说,很容易识别(最高位是 0 还是 1);但是,对于计算机来说,需要设计专门的电路,这无疑增加了硬件的复杂性,增加了计算时间。如果能将符号位和数值位等同起来,让它们一起参与运算,不再加以区分,这样硬件电路就可以变得非常简单。</li><li>③ 此外,加法和减法也可以合并为一种运算,即:加法运算。换言之,减去一个数就相当于加上这个数的相反数,如:5 - 3 相当于 5 +(-3),10 -(-9)相当于 10 + 9 。</li><li>④ 如果能够实现上述的两个目标,那么只需要设计一种简单的、不用区分符号位和数值位的加法电路,就能同时实现加法运算和减法运算,而且非常高效。其实,这两个目标已经实现了,真正的计算机的硬件电路就是这样设计的。</li><li>⑤ 但是,简化硬件电路是有代价的,这个代价就是有符号数在存储和读取的时候都要继续转换。这也是对于有符号数的运算来说,计算机底层为什么使用<code>补码</code>的原因所在。</li></ul></div><ul><li><code>最高位</code>表示<code>符号位</code>,由于符号位的存在,如果使用<code>原码</code>来计算,就会导致<code>计算结果不正确</code>,即:</li></ul><p><img src="'+z+'" alt="" loading="lazy"></p><ul><li><code>补码</code>的设计可以巧妙的让<code>符号位</code>也参与计算,并且可以得到<code>正确的计算结果</code>,即:</li></ul><p><img src="'+M+'" alt="" loading="lazy"></p><h2 id="_3-7-补码到底是如何简化硬件电路的" tabindex="-1">3.7 补码到底是如何简化硬件电路的? <a class="header-anchor" href="#_3-7-补码到底是如何简化硬件电路的" aria-label="Permalink to "3.7 补码到底是如何简化硬件电路的?""></a></h2><ul><li>假设 6 和 18 都是 short 类型,现在我们要计算 <code>6 - 18</code> 的结果,根据运算规则,它等价于 <code>6 +(-18)</code>。如果按照采用<code>原码</code>来计算,那么运算过程是这样的,如下所示:</li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><p>直接使用原码表示整数,让符号位也参与运算,那么对于减法来说,结果显然是不正确的。</p></div><p><img src="'+w+'" alt="" loading="lazy"></p><ul><li>于是,人们开始继续探索,不断试错,终于设计出了<code>反码</code>,如下所示:</li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><p>直接使用反码表示整数,让符号位也参与运算,对于 6 +(-18)来说,结果貌似正确。</p></div><p><img src="'+I+'" alt="" loading="lazy"></p><ul><li>如果我们将<code>被减数</code>和<code>减数</code>对调一下,即:计算 <code>18 - 6</code> 的结果,也就是 <code>18 +(-6)</code>的结果,继续采用<code>反码</code>来进行运算,如下所示:</li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><ul><li>① 6 - 18,即:6+(-18),如果采用<code>反码</code>计算,结果是正确的;但是,18 - 6,即:18 +(-6),如果采用<code>反码</code>计算,结果相差 1 。</li><li>② 可以推断:如果按照<code>反码</code>来计算,小数 - 大数,结果正确;而大数 - 小数,结果相差 1 。</li></ul></div><p><img src="'+U+'" alt="" loading="lazy"></p><ul><li>对于这个相差的 <code>1</code> 必须进行纠正,但是又不能影响<code>小数-大数</code>的结果。于是,人们又绞尽脑汁设计出了<code>补码</code>,给<code>反码</code>打了一个<code>“补丁”</code>,终于把相差的 <code>1</code> 给纠正过来了。那么,<code>6 - 18</code> 按照<code>补码</code>的运算过程,如下所示:</li></ul><p><img src="'+L+'" alt="" loading="lazy"></p><ul><li>那么,<code>18 - 6</code> 按照<code>补码</code>的运算过程,如下所示:</li></ul><p><img src="'+S+'" alt="" loading="lazy"></p><div class="important custom-block github-alert"><p class="custom-block-title">IMPORTANT</p><p></p><p>总结:采用<code>补码</code>的形式正好将相差的 <code>1</code>纠正过来,也没有影响到小数减大数,这个“补丁”非常巧妙。</p><ul><li>① 小数减去大数,结果为负,之前(负数从反码转换为补码需要 +1)加上的 1 ,后来(负数从补码转换为反码要 -1)还需要减去,正好抵消掉,所以不会受到影响。</li><li>② 大数减去小数,结果为正,之前(负数从反码转换为补码需要 +1)加上的 1 ,后来(正数的补码和反码相同,从补码转换为反码不用 -1)就没有再减去,不能抵消掉,这就相当于给计算结果多加了一个 1。</li></ul><p><code>补码</code>这种天才般的设计,一举达成了之前加法运算和减法运算提到的两个目标,简化了硬件电路。</p></div>',263),j=[X];function V(J,Z,H,K,Q,$){return a(),i("div",null,j)}const 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<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">}</span></span></code></pre><div class="line-numbers-wrapper" aria-hidden="true"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br><span class="line-number">12</span><br><span class="line-number">13</span><br><span class="line-number">14</span><br><span class="line-number">15</span><br></div></div><h2 id="_3-3-进制的运算规则" tabindex="-1">3.3 进制的运算规则 <a class="header-anchor" href="#_3-3-进制的运算规则" aria-label="Permalink to "3.3 进制的运算规则""></a></h2><ul><li><code>十进制</code>的运算规则,如下所示: <ul><li>逢<code>十</code>进<code>一</code>(针对加法而言)。</li><li>借<code>一</code>当<code>十</code>(针对减法而言)。</li></ul></li><li><code>二进制</code>的运算规则,如下所示: <ul><li>逢<code>二</code>进<code>一</code>(针对加法而言)。</li><li>借<code>一</code>当<code>二</code>(针对减法而言)。</li></ul></li><li><code>八进制</code>的运算规则,如下所示: <ul><li>逢<code>八</code>进<code>一</code>(针对加法而言)。</li><li>借<code>一</code>当<code>八</code>(针对减法而言)。</li></ul></li><li><code>十六进制</code>的运算规则,如下所示: <ul><li>逢<code>十六</code>进<code>一</code>(针对加法而言)。</li><li>借<code>一</code>当<code>十六</code>(针对减法而言)。</li></ul></li></ul><h2 id="_3-4-进制的转换" tabindex="-1">3.4 进制的转换 <a class="header-anchor" href="#_3-4-进制的转换" aria-label="Permalink to "3.4 进制的转换""></a></h2><h3 id="_3-4-1-概述" tabindex="-1">3.4.1 概述 <a class="header-anchor" href="#_3-4-1-概述" aria-label="Permalink to "3.4.1 概述""></a></h3><ul><li>不同进制的转换,如下所示:</li></ul><p><img src="`+v+'" alt="" loading="lazy"></p><ul><li>在计算机中,数据是从右往左的方式排列的;其中,最右边的是低位,最左边的是高位,即:</li></ul><p><img src="'+B+'" alt="" loading="lazy"></p><h3 id="_3-4-2-二进制和十进制的转换" tabindex="-1">3.4.2 二进制和十进制的转换 <a class="header-anchor" href="#_3-4-2-二进制和十进制的转换" aria-label="Permalink to "3.4.2 二进制和十进制的转换""></a></h3><h4 id="_3-4-2-1-二进制转换为十进制" tabindex="-1">3.4.2.1 二进制转换为十进制 <a class="header-anchor" href="#_3-4-2-1-二进制转换为十进制" aria-label="Permalink to "3.4.2.1 二进制转换为十进制""></a></h4><ul><li>规则:从最低位开始,将每个位上的数提取出来,乘以 2 的 (位数 - 1 )次方,然后求和。</li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><ul><li>① 在学术界,将这种计算规则,称为<code>位权相加法</code>。</li><li>② <code>八进制转换为十进制</code>、<code>十六进制转换为十进制</code>和<code>二进制转换为十进制</code>的算法相同!!!</li></ul></div><ul><li>示例:十进制转十进制</li></ul><p><img src="'+A+'" alt="" loading="lazy"></p><ul><li>示例:二进制转十进制</li></ul><p><img src="'+D+'" alt="" loading="lazy"></p><h4 id="_3-4-2-2-十进制转换二进制" tabindex="-1">3.4.2.2 十进制转换二进制 <a class="header-anchor" href="#_3-4-2-2-十进制转换二进制" aria-label="Permalink to "3.4.2.2 十进制转换二进制""></a></h4><ul><li>规则:将该数不断除以 2 ,直到商为 0 为止,然后将每步得到的余数倒过来,就是对应的二进制。</li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><ul><li>① 在学术界,将这种计算规则,称为<code>短除法</code>或<code>连续除2取余法</code>。</li><li>② 很好理解,只有不断地除以 2 ,就能保证最大的数字不超过 2 ,这不就是二进制(只能有 0 或 1)吗?</li><li>③ <code>八进制转换为二进制</code>、<code>十六进制转换为二进制</code>和<code>十进制转换为二进制</code>的算法相同!!!</li></ul></div><ul><li>示例:十进制转十进制</li></ul><p><img src="'+_+'" alt="" loading="lazy"></p><ul><li>示例:十进制转二进制</li></ul><p><img src="'+q+'" alt="" loading="lazy"></p><h3 id="_3-4-3-二进制转八进制" tabindex="-1">3.4.3 二进制转八进制 <a class="header-anchor" href="#_3-4-3-二进制转八进制" aria-label="Permalink to "3.4.3 二进制转八进制""></a></h3><ul><li><p>规则:从右向左,每 3 位二进制就是一个八进制,不足补 0(分组转换法)。</p></li><li><p>示例:011 101 001 -> 351</p></li></ul><p><img src="'+f+'" alt="" loading="lazy"></p><h3 id="_3-4-4-二进制转十六进制" tabindex="-1">3.4.4 二进制转十六进制 <a class="header-anchor" href="#_3-4-4-二进制转十六进制" aria-label="Permalink to "3.4.4 二进制转十六进制""></a></h3><ul><li><p>规则:从右向左,每 4 位二进制就是一个十六进制,不足补 0(分组转换法)。</p></li><li><p>示例:1110 1001 -> 0xE9</p></li></ul><p><img src="'+x+'" alt="" loading="lazy"></p><h2 id="_3-5-原码、反码和补码" tabindex="-1">3.5 原码、反码和补码 <a class="header-anchor" href="#_3-5-原码、反码和补码" aria-label="Permalink to "3.5 原码、反码和补码""></a></h2><h3 id="_3-5-1-概述" tabindex="-1">3.5.1 概述 <a class="header-anchor" href="#_3-5-1-概述" aria-label="Permalink to "3.5.1 概述""></a></h3><ul><li>机器数:一个数在计算机的存储形式是二进制,我们称这些二进制数为机器数。机器数可以是有符号的,用机器数的最高位来存放符号位,0 表示正数,1 表示负数。</li></ul><div class="important custom-block github-alert"><p class="custom-block-title">IMPORTANT</p><p></p><p>这里讨论的适用于<code>符号位</code>的整数,如:int 等;而不适用于<code>无符号位</code>的整数,即:unsinged int 等。</p></div><p><img src="'+P+'" alt="" loading="lazy"></p><ul><li>真值(数据位):因为机器数带有符号位,所以机器数的形式值不等于其真实表示的值(真值),以机器数 1000 0001 为例,其真正表示的值(首位是符号位)为 -1,而形式值却是 129 ,因此将带有符号位的机器数的真正表示的值称为机器数的真值。</li></ul><div class="important custom-block github-alert"><p class="custom-block-title">IMPORTANT</p><p></p><p>这里讨论的适用于<code>符号位</code>的整数,如:int 等;而不适用于<code>无符号位</code>的整数,即:unsinged int 等。</p></div><p><img src="'+T+'" alt="" loading="lazy"></p><h3 id="_3-5-2-原码" tabindex="-1">3.5.2 原码 <a class="header-anchor" href="#_3-5-2-原码" aria-label="Permalink to "3.5.2 原码""></a></h3><ul><li>原码的表示与机器数真值表示的一样,即用第一位表示符号,其余位表示数值。</li><li>规则: <ul><li>正数的<code>原码</code>是它本身对应的二进制数,符号位是 0 。</li><li>负数的<code>原码</code>是它本身绝对值对应的二进制数,但是符号位是 1 。</li></ul></li><li>+1 的原码,使用 8 位二进数来表示,就是:</li></ul><table tabindex="0"><thead><tr><th>十进制数</th><th>原码(8位二进制数)</th></tr></thead><tbody><tr><td>+1</td><td><code>0</code>000 0001</td></tr></tbody></table><ul><li>-1 的原码,使用 8 位二进数来表示,就是:</li></ul><table tabindex="0"><thead><tr><th>十进制数</th><th>原码(8位二进制数)</th></tr></thead><tbody><tr><td>-1</td><td><code>1</code>000 0001</td></tr></tbody></table><div class="important custom-block github-alert"><p class="custom-block-title">IMPORTANT</p><p></p><p>总结:</p><ul><li>① 按照原码的规则,会出现 <code>+0</code> 和 <code>-0</code> 的情况,即:<code>0</code>000 0000(+0)、<code>1</code>000 0000(-0),显然不符合实际情况。</li><li>② 所以,计算机底层虽然存储和计算的都是二进数,但显然不是原码。</li></ul></div><h3 id="_3-5-3-反码" tabindex="-1">3.5.3 反码 <a class="header-anchor" href="#_3-5-3-反码" aria-label="Permalink to "3.5.3 反码""></a></h3><ul><li><p>规则:</p><ul><li>正数的反码和它的原码相同。</li><li>负数的反码是在其原码的基础上,符号位不变,其余各位取反。</li></ul></li><li><p>+1 的反码,使用 8 位二进数来表示,就是:</p></li></ul><table tabindex="0"><thead><tr><th>十进制数</th><th>原码(8位二进制数)</th><th>反码(8位二进制数)</th></tr></thead><tbody><tr><td>+1</td><td><code>0</code>000 0001</td><td><code>0</code>000 0001</td></tr></tbody></table><ul><li>-1 的反码,使用 8 位二进数来表示,就是:</li></ul><table tabindex="0"><thead><tr><th>十进制数</th><th>原码(8位二进制数)</th><th>反码(8位二进制数)</th></tr></thead><tbody><tr><td>-1</td><td><code>1</code>000 0001</td><td><code>1</code>111 1110</td></tr></tbody></table><div class="important custom-block github-alert"><p class="custom-block-title">IMPORTANT</p><p></p><p>总结:</p><ul><li>① 按照反码的规则,如果是 <code>+0</code>,对应的原码是 <code>0</code>000 0000;那么,其反码还是 <code>0</code>000 0000 ;如果是 <code>-0</code>,对应的原码是 <code>1</code>000 0000,其反码是 <code>1</code>111 1111,显然不符合实际情况。</li><li>② 所以,计算机底层虽然存储和计算的都是二进数,但显然不是反码。</li></ul></div><h3 id="_3-5-4-补码" tabindex="-1">3.5.4 补码 <a class="header-anchor" href="#_3-5-4-补码" aria-label="Permalink to "3.5.4 补码""></a></h3><ul><li><p>规则:</p><ul><li>正数的补码和它的原码相同。</li><li>负数的补码是在其反码的基础上 + 1 。</li></ul></li><li><p>+1 的补码,使用 8 位二进数来表示,就是:</p></li></ul><table tabindex="0"><thead><tr><th>十进制数</th><th>原码(8位二进制数)</th><th>反码(8位二进制数)</th><th>补码(8位二进制数)</th></tr></thead><tbody><tr><td>+1</td><td><code>0</code>000 0001</td><td><code>0</code>000 0001</td><td><code>0</code>000 0001</td></tr></tbody></table><ul><li>-1 的补码,使用 8 位二进数来表示,就是:</li></ul><table tabindex="0"><thead><tr><th>十进制数</th><th>原码(8位二进制数)</th><th>反码(8位二进制数)</th><th>补码(8位二进制数)</th></tr></thead><tbody><tr><td>-1</td><td><code>1</code>000 0001</td><td><code>1</code>111 1110</td><td><code>1</code>111 1111</td></tr></tbody></table><ul><li>如果 <code>0</code> ,按照 <code>+0</code> 的情况进行处理,如下所示:</li></ul><p><img src="'+N+'" alt="" loading="lazy"></p><ul><li>如果 <code>0</code> ,按照 <code>-0</code> 的情况进行处理,如下所示:</li></ul><p><img src="'+O+'" alt="" loading="lazy"></p><div class="important custom-block github-alert"><p class="custom-block-title">IMPORTANT</p><p></p><p>总结:</p><ul><li>① 补码表示法解决了<code>原码</code>和<code>反码</code>存在的<code>两种</code>零(<code>+0</code> 和 <code>-0</code>)的问题,即:在补码表示法中,只有<code>一个</code>零,即 <code>0000 0000</code>。</li><li>②补码使得<code>加法运算</code>和<code>减法运算</code>可以统一处理,通过将减法运算<code>转换</code>为加法运算,可以简化硬件设计,提高了运算效率。</li><li>③ 计算机底层<code>存储</code>和<code>计算</code>的都是<code>二进数的补码</code>。换言之,当读取整数的时候,需要采用逆向的转换,即:将补码转换为原码。正数的原码、反码、补码都是一样的,三码合一。负数的补码转换为原码的方法就是先减去 <code>1</code> ,得到反码,再按位取反,得到原码。</li></ul></div><h3 id="_3-5-5-总结" tabindex="-1">3.5.5 总结 <a class="header-anchor" href="#_3-5-5-总结" aria-label="Permalink to "3.5.5 总结""></a></h3><ul><li>① 正数的原码、反码和补码都是一样的,三码合一。</li><li>② 负数的反码是在其原码的基础上,按位取反(0 变 1 ,1 变 0 ),符号位不变;负数的补码是其反码 + 1 。</li><li>③ 0 的补码是 0 。</li></ul><h2 id="_3-6-计算机底层为什么使用补码" tabindex="-1">3.6 计算机底层为什么使用补码? <a class="header-anchor" href="#_3-6-计算机底层为什么使用补码" aria-label="Permalink to "3.6 计算机底层为什么使用补码?""></a></h2><ul><li><p><code>加法</code>和<code>减法</code>是计算机中最基本的运算,计算机时时刻刻都离不开它们,所以它们由硬件直接支持。为了提高加法和减法的运行效率,硬件电路必须设计得尽量简单。</p></li><li><p>对于有符号位的数字来说,内存需要区分符号位和数值位:对于人类来说,很容易识别(最高位是 0 还是 1);但是,对于计算机来说,需要设计专门的电路,这无疑增加了硬件的复杂性,增加了计算时间。如果能将符号位和数值位等同起来,让它们一起参与运算,不再加以区分,这样硬件电路就可以变得非常简单。</p></li><li><p>此外,加法和减法也可以合并为一种运算,即:加法运算。换言之,减去一个数就相当于加上这个数的相反数,如:<code>5 - 3</code> 相当于 <code>5 +(-3)</code>,<code>10 -(-9)</code>相当于 <code>10 + 9</code> 。</p></li><li><p>如果能够实现上述的两个目标,那么只需要设计一种简单的、不用区分符号位和数值位的加法电路,就能同时实现加法运算和减法运算,而且非常高效。其实,这两个目标已经实现了,真正的计算机的硬件电路就是这样设计的。</p></li><li><p>但是,简化硬件电路是有代价的,这个代价就是有符号数在存储和读取的时候都要继续转换。这也是对于有符号数的运算来说,计算机底层为什么使用<code>补码</code>的原因所在。</p></li></ul><h2 id="_3-7-补码到底是如何简化硬件电路的" tabindex="-1">3.7 补码到底是如何简化硬件电路的? <a class="header-anchor" href="#_3-7-补码到底是如何简化硬件电路的" aria-label="Permalink to "3.7 补码到底是如何简化硬件电路的?""></a></h2><ul><li>假设 6 和 18 都是 short 类型,现在我们要计算 <code>6 - 18</code> 的结果,根据运算规则,它等价于 <code>6 +(-18)</code>。如果按照采用<code>原码</code>来计算,那么运算过程是这样的,如下所示:</li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><p>直接使用原码表示整数,让符号位也参与运算,那么对于减法来说,结果显然是不正确的。</p></div><p><img src="'+z+'" alt="" loading="lazy"></p><ul><li>于是,人们开始继续探索,不断试错,终于设计出了<code>反码</code>,如下所示:</li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><p>直接使用反码表示整数,让符号位也参与运算,对于 6 +(-18)来说,结果貌似正确。</p></div><p><img src="'+M+'" alt="" loading="lazy"></p><ul><li>如果我们将<code>被减数</code>和<code>减数</code>对调一下,即:计算 <code>18 - 6</code> 的结果,也就是 <code>18 +(-6)</code>的结果,继续采用<code>反码</code>来进行运算,如下所示:</li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><ul><li>① 6 - 18,即:6+(-18),如果采用<code>反码</code>计算,结果是正确的;但是,18 - 6,即:18 +(-6),如果采用<code>反码</code>计算,结果相差 1 。</li><li>② 可以推断:如果按照<code>反码</code>来计算,小数 - 大数,结果正确;而大数 - 小数,结果相差 1 。</li></ul></div><p><img src="'+w+'" alt="" loading="lazy"></p><ul><li>对于这个相差的 <code>1</code> 必须进行纠正,但是又不能影响<code>小数-大数</code>的结果。于是,人们又绞尽脑汁设计出了<code>补码</code>,给<code>反码</code>打了一个<code>“补丁”</code>,终于把相差的 <code>1</code> 给纠正过来了。那么,<code>6 - 18</code> 按照<code>补码</code>的运算过程,如下所示:</li></ul><p><img src="'+I+'" alt="" loading="lazy"></p><ul><li>那么,<code>18 - 6</code> 按照<code>补码</code>的运算过程,如下所示:</li></ul><p><img src="'+U+'" alt="" loading="lazy"></p><div class="important custom-block github-alert"><p class="custom-block-title">IMPORTANT</p><p></p><p>总结:采用<code>补码</code>的形式正好将相差的 <code>1</code>纠正过来,也没有影响到小数减大数,这个“补丁”非常巧妙。</p><ul><li>① 小数减去大数,结果为负,之前(负数从反码转换为补码需要 +1)加上的 1 ,后来(负数从补码转换为反码要 -1)还需要减去,正好抵消掉,所以不会受到影响。</li><li>② 大数减去小数,结果为正,之前(负数从反码转换为补码需要 +1)加上的 1 ,后来(正数的补码和反码相同,从补码转换为反码不用 -1)就没有再减去,不能抵消掉,这就相当于给计算结果多加了一个 1。</li></ul><p><code>补码</code>这种天才般的设计,一举达成了之前加法运算和减法运算提到的两个目标,简化了硬件电路。</p></div>',260),S=[L];function X(j,V,Z,J,G,K){return a(),i("div",null,S)}const 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<span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> --depth</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> 1</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> \</span></span>
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<span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> --single-branch</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> --branch=linux-msft-wsl-${</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">KERNEL_VERSION</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">}</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> \</span></span>
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<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> https://github.com/microsoft/WSL2-Linux-Kernel.git</span></span></code></pre><div class="line-numbers-wrapper" aria-hidden="true"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br></div></div><p><img src="/c/assets/161.B1eB55rC.gif" alt="" loading="lazy"></p><ul><li>编译内核代码:</li></ul><div class="language-shell vp-adaptive-theme line-numbers-mode"><button title="Copy Code" class="copy"></button><span class="lang">shell</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">cd</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> WSL2-Linux-Kernel</span></span></code></pre><div class="line-numbers-wrapper" aria-hidden="true"><span class="line-number">1</span><br></div></div><div class="language-shell vp-adaptive-theme line-numbers-mode"><button title="Copy Code" class="copy"></button><span class="lang">shell</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;">make</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> -j</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> $(</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;">nproc</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">KCONFIG_CONFIG=Microsoft/config-wsl</span></span></code></pre><div class="line-numbers-wrapper" aria-hidden="true"><span class="line-number">1</span><br></div></div><p><img src="/c/assets/162.VIcU-hkN.gif" alt="" loading="lazy"></p><ul><li>编译 perf 工具:</li></ul><div class="language-shell vp-adaptive-theme line-numbers-mode"><button title="Copy Code" class="copy"></button><span class="lang">shell</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">cd</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> tools/perf</span></span></code></pre><div class="line-numbers-wrapper" aria-hidden="true"><span class="line-number">1</span><br></div></div><div class="language-shell vp-adaptive-theme line-numbers-mode"><button title="Copy Code" class="copy"></button><span class="lang">shell</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;">make</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> clean</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> && </span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;">make</span></span></code></pre><div class="line-numbers-wrapper" aria-hidden="true"><span class="line-number">1</span><br></div></div><p><img src="/c/assets/163.BM9viRZJ.gif" alt="" loading="lazy"></p><ul><li>复制到 PATH 变量所指向的路径中:</li></ul><div class="language-shell vp-adaptive-theme line-numbers-mode"><button title="Copy Code" class="copy"></button><span class="lang">shell</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;">cp</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> perf</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> /usr/bin/</span></span></code></pre><div class="line-numbers-wrapper" aria-hidden="true"><span class="line-number">1</span><br></div></div><p><img src="/c/assets/164.DpMBA1SK.gif" alt="" loading="lazy"></p><h3 id="_8-4-3-整合" tabindex="-1">8.4.3 整合 <a class="header-anchor" href="#_8-4-3-整合" aria-label="Permalink to "8.4.3 整合""></a></h3><ul><li>CLion 中配置 perf 的路径:</li></ul><p><img src="/c/assets/165.DgXuU6LF.png" alt="" loading="lazy"></p><ul><li>在 CLion 中通过 perf 运行代码:</li></ul><p><img src="/c/assets/166.Dnw73s2h.gif" alt="" loading="lazy"></p><h2 id="_8-5-win-中文乱码问题" tabindex="-1">8.5 Win 中文乱码问题 <a class="header-anchor" href="#_8-5-win-中文乱码问题" aria-label="Permalink to "8.5 Win 中文乱码问题""></a></h2><ul><li>前文,我们提及到,在 Win 中,如果出现<code>中文乱码</code>问题,就需要去<code>语言和区别</code>设置<code>系统区域</code>的编码为 UTF-8 ;但是,这样可能会造成其它的软件出现中文乱码问题,如:Xshell 等。</li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><ul><li>① 之所以,修改系统的编码为 UTF-8 会出现问题,是因为早期的 Win 系统的中文默认编码是 GBK(目前也是,Win 并没有强制第三方软件使用 UTF-8 编码) ,而 Xshell 等也使用的这些编码,一旦我们修改为 UTF-8 之后,可能会造成这些第三方软件出现中文乱码问题(第三方软件适配问题,相信将来应该都会切换为 UTF-8 编码),体验较差!!!</li><li>② 在 Linux 或 MacOS 之所以不会出现中文乱码的问题,是因为这些系统默认的编码就是 UTF-8 。</li></ul></div><ul><li>其实,还有一种解决方案,如下所示:</li></ul><p><img src="/c/assets/167.SnFXRSaL.png" alt="" loading="lazy"></p><p><img src="/c/assets/168.DnoEqOjV.png" alt="" loading="lazy"></p><p><img src="/c/assets/169.BJBdn7pw.png" alt="" loading="lazy"></p><ul><li>测试一下,是否配置成功:</li></ul><p><img src="/c/assets/170.DXtQWYsM.gif" alt="" loading="lazy"></p><h2 id="_8-6-clion-中自动导入头文件" tabindex="-1">8.6 CLion 中自动导入头文件 <a class="header-anchor" href="#_8-6-clion-中自动导入头文件" aria-label="Permalink to "8.6 CLion 中自动导入头文件""></a></h2><ul><li>在 CLion 中,最为强大的功能就是直接输入函数,然后让 IDE 帮我们自动导入头文件,包括自定义的头文件,相当实用。</li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><ul><li>① CLion 中的<code>自动导入头文件</code>的<code>快捷键</code>是 <code>Alt + Enter</code> 。</li><li>② CLion 中的<code>自动提取变量的类型</code>的<code>快捷键</code>是 <code>Ctrl + Alt + V</code> 。</li></ul></div><p><img src="/c/assets/171.hcERTQkN.gif" alt="" loading="lazy"></p><ul><li>开启自动导入头文件的步骤,如下所示:</li></ul><p><img src="/c/assets/172.CioraEUv.png" alt="" loading="lazy"></p><p><img src="/c/assets/173.kWHWwnc_.png" alt="" loading="lazy"></p></div></div></main><footer class="VPDocFooter" 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<span class="line"><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;"> printf</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">"</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">%d</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> 的十六进制(前缀)整数: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">%#X\n</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">"</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">, num, num);</span><span style="--shiki-light:#6A737D;--shiki-dark:#6A737D;"> // 100 的十六进制(前缀)整数: 0X64</span></span>
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<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> 0</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">;</span></span>
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<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">}</span></span></code></pre><div class="line-numbers-wrapper" aria-hidden="true"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br><span class="line-number">12</span><br><span class="line-number">13</span><br><span class="line-number">14</span><br><span class="line-number">15</span><br></div></div><h2 id="_3-3-进制的运算规则" tabindex="-1">3.3 进制的运算规则 <a class="header-anchor" href="#_3-3-进制的运算规则" aria-label="Permalink to "3.3 进制的运算规则""></a></h2><ul><li><code>十进制</code>的运算规则,如下所示: <ul><li>逢<code>十</code>进<code>一</code>(针对加法而言)。</li><li>借<code>一</code>当<code>十</code>(针对减法而言)。</li></ul></li><li><code>二进制</code>的运算规则,如下所示: <ul><li>逢<code>二</code>进<code>一</code>(针对加法而言)。</li><li>借<code>一</code>当<code>二</code>(针对减法而言)。</li></ul></li><li><code>八进制</code>的运算规则,如下所示: <ul><li>逢<code>八</code>进<code>一</code>(针对加法而言)。</li><li>借<code>一</code>当<code>八</code>(针对减法而言)。</li></ul></li><li><code>十六进制</code>的运算规则,如下所示: <ul><li>逢<code>十六</code>进<code>一</code>(针对加法而言)。</li><li>借<code>一</code>当<code>十六</code>(针对减法而言)。</li></ul></li></ul><h2 id="_3-4-进制的转换" tabindex="-1">3.4 进制的转换 <a class="header-anchor" href="#_3-4-进制的转换" aria-label="Permalink to "3.4 进制的转换""></a></h2><h3 id="_3-4-1-概述" tabindex="-1">3.4.1 概述 <a class="header-anchor" href="#_3-4-1-概述" aria-label="Permalink to "3.4.1 概述""></a></h3><ul><li>不同进制的转换,如下所示:</li></ul><p><img src="/c/assets/19.uqLiL_yu.png" alt="" loading="lazy"></p><ul><li>在计算机中,数据是从右往左的方式排列的;其中,最右边的是低位,最左边的是高位,即:</li></ul><p><img src="/c/assets/20.CkykpHY2.png" alt="" loading="lazy"></p><h3 id="_3-4-2-二进制和十进制的转换" tabindex="-1">3.4.2 二进制和十进制的转换 <a class="header-anchor" href="#_3-4-2-二进制和十进制的转换" aria-label="Permalink to "3.4.2 二进制和十进制的转换""></a></h3><h4 id="_3-4-2-1-二进制转换为十进制" tabindex="-1">3.4.2.1 二进制转换为十进制 <a class="header-anchor" href="#_3-4-2-1-二进制转换为十进制" aria-label="Permalink to "3.4.2.1 二进制转换为十进制""></a></h4><ul><li>规则:从最低位开始,将每个位上的数提取出来,乘以 2 的 (位数 - 1 )次方,然后求和。</li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><ul><li>① 在学术界,将这种计算规则,称为<code>位权相加法</code>。</li><li>② <code>八进制转换为十进制</code>、<code>十六进制转换为十进制</code>和<code>二进制转换为十进制</code>的算法相同!!!</li></ul></div><ul><li>示例:十进制转十进制</li></ul><p><img src="/c/assets/21.DV1YbrOP.png" alt="" loading="lazy"></p><ul><li>示例:二进制转十进制</li></ul><p><img src="/c/assets/22.AHNJT9TV.png" alt="" loading="lazy"></p><h4 id="_3-4-2-2-十进制转换二进制" tabindex="-1">3.4.2.2 十进制转换二进制 <a class="header-anchor" href="#_3-4-2-2-十进制转换二进制" aria-label="Permalink to "3.4.2.2 十进制转换二进制""></a></h4><ul><li>规则:将该数不断除以 2 ,直到商为 0 为止,然后将每步得到的余数倒过来,就是对应的二进制。</li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><ul><li>① 在学术界,将这种计算规则,称为<code>短除法</code>或<code>连续除2取余法</code>。</li><li>② 很好理解,只有不断地除以 2 ,就能保证最大的数字不超过 2 ,这不就是二进制(只能有 0 或 1)吗?</li><li>③ <code>八进制转换为二进制</code>、<code>十六进制转换为二进制</code>和<code>十进制转换为二进制</code>的算法相同!!!</li></ul></div><ul><li>示例:十进制转十进制</li></ul><p><img src="/c/assets/23.Bs-MOwx2.png" alt="" loading="lazy"></p><ul><li>示例:十进制转二进制</li></ul><p><img src="/c/assets/24.StzjmBz-.png" alt="" loading="lazy"></p><h3 id="_3-4-3-二进制转八进制" tabindex="-1">3.4.3 二进制转八进制 <a class="header-anchor" href="#_3-4-3-二进制转八进制" aria-label="Permalink to "3.4.3 二进制转八进制""></a></h3><ul><li><p>规则:每 3 位二进制就是一个八进制。</p></li><li><p>示例:011 101 001 -> 351</p></li></ul><p><img src="/c/assets/25.C0wVWaxD.png" alt="" loading="lazy"></p><h3 id="_3-4-4-二进制转十六进制" tabindex="-1">3.4.4 二进制转十六进制 <a class="header-anchor" href="#_3-4-4-二进制转十六进制" aria-label="Permalink to "3.4.4 二进制转十六进制""></a></h3><ul><li><p>规则:每 4 位二进制就是一个十六进制。</p></li><li><p>示例:1110 1001 -> 0xE9</p></li></ul><p><img src="/c/assets/26.LXJMAihe.png" alt="" loading="lazy"></p><h2 id="_3-5-原码、反码和补码" tabindex="-1">3.5 原码、反码和补码 <a class="header-anchor" href="#_3-5-原码、反码和补码" aria-label="Permalink to "3.5 原码、反码和补码""></a></h2><h3 id="_3-5-1-概述" tabindex="-1">3.5.1 概述 <a class="header-anchor" href="#_3-5-1-概述" aria-label="Permalink to "3.5.1 概述""></a></h3><ul><li>机器数:一个数在计算机的存储形式是二进制,我们称这些二进制数为机器数。机器数可以是有符号的,用机器数的最高位来存放符号位,0 表示正数,1 表示负数。</li></ul><p><img src="/c/assets/27._UTCq3PD.png" alt="" loading="lazy"></p><ul><li>真值:因为机器数带有符号位,所以机器数的形式值不等于其真实表示的值(真值),以机器数 1000 0001 为例,其真正表示的值(首位是符号位)为 -1,而形式值却是 129 ,因此将带有符号位的机器数的真正表示的值称为机器数的真值。</li></ul><p><img src="/c/assets/28.BjQ5kBL-.png" alt="" loading="lazy"></p><h3 id="_3-5-2-原码" tabindex="-1">3.5.2 原码 <a class="header-anchor" href="#_3-5-2-原码" aria-label="Permalink to "3.5.2 原码""></a></h3><ul><li>原码的表示与机器数真值表示的一样,即用第一位表示符号,其余位表示数值。</li><li>规则: <ul><li>正数的<code>原码</code>是它本身对应的二进制数,符号位是 0 。</li><li>负数的<code>原码</code>是它本身绝对值对应的二进制数,但是符号位是 1 。</li></ul></li><li>+1 的原码,使用 8 位二进数来表示,就是:</li></ul><table tabindex="0"><thead><tr><th>十进制数</th><th>原码(8位二进制数)</th></tr></thead><tbody><tr><td>+1</td><td><code>0</code>000 0001</td></tr></tbody></table><ul><li>-1 的原码,使用 8 位二进数来表示,就是:</li></ul><table tabindex="0"><thead><tr><th>十进制数</th><th>原码(8位二进制数)</th></tr></thead><tbody><tr><td>-1</td><td><code>1</code>000 0001</td></tr></tbody></table><div class="important custom-block github-alert"><p class="custom-block-title">IMPORTANT</p><p></p><p>按照原码的规则,会出现 <code>+0</code> 和 <code>-0</code> 的情况,即:<code>0</code>000 0000(+0)、<code>1</code>000 0000(-0),显然不符合实际情况;所以,计算机底层虽然存储和计算的都是二进数,但显然不是原码。</p></div><h3 id="_3-5-3-反码" tabindex="-1">3.5.3 反码 <a class="header-anchor" href="#_3-5-3-反码" aria-label="Permalink to "3.5.3 反码""></a></h3><ul><li><p>规则:</p><ul><li>正数的反码和它的原码相同。</li><li>负数的反码是在其原码的基础上,符号位不变,其余各位取反。</li></ul></li><li><p>+1 的反码,使用 8 位二进数来表示,就是:</p></li></ul><table tabindex="0"><thead><tr><th>十进制数</th><th>原码(8位二进制数)</th><th>反码(8位二进制数)</th></tr></thead><tbody><tr><td>+1</td><td><code>0</code>000 0001</td><td><code>0</code>000 0001</td></tr></tbody></table><ul><li>-1 的反码,使用 8 位二进数来表示,就是:</li></ul><table tabindex="0"><thead><tr><th>十进制数</th><th>原码(8位二进制数)</th><th>反码(8位二进制数)</th></tr></thead><tbody><tr><td>-1</td><td><code>1</code>000 0001</td><td><code>1</code>111 1110</td></tr></tbody></table><div class="important custom-block github-alert"><p class="custom-block-title">IMPORTANT</p><p></p><p>按照反码的规则,如果是 <code>+0</code>,对应的原码是 <code>0</code>000 0000;那么,其反码还是 <code>0</code>000 0000 ;如果是 <code>-0</code>,对应的原码是 <code>1</code>000 0000,其反码是 <code>1</code>111 1111,显然不符合实际情况;所以,计算机底层虽然存储和计算的都是二进数,但显然不是反码。</p></div><h3 id="_3-5-4-补码" tabindex="-1">3.5.4 补码 <a class="header-anchor" href="#_3-5-4-补码" aria-label="Permalink to "3.5.4 补码""></a></h3><ul><li><p>规则:</p><ul><li>正数的补码和它的原码相同。</li><li>负数的补码是在其反码的基础上 + 1 。</li></ul></li><li><p>+1 的补码,使用 8 位二进数来表示,就是:</p></li></ul><table tabindex="0"><thead><tr><th>十进制数</th><th>原码(8位二进制数)</th><th>反码(8位二进制数)</th><th>补码(8位二进制数)</th></tr></thead><tbody><tr><td>+1</td><td><code>0</code>000 0001</td><td><code>0</code>000 0001</td><td><code>0</code>000 0001</td></tr></tbody></table><ul><li>-1 的补码,使用 8 位二进数来表示,就是:</li></ul><table tabindex="0"><thead><tr><th>十进制数</th><th>原码(8位二进制数)</th><th>反码(8位二进制数)</th><th>补码(8位二进制数)</th></tr></thead><tbody><tr><td>-1</td><td><code>1</code>000 0001</td><td><code>1</code>111 1110</td><td><code>1</code>111 1111</td></tr></tbody></table><ul><li>如果 0 ,按照 <code>+0</code> 的情况进行处理,即:</li></ul><p><img src="/c/assets/29.COIOzcmT.png" alt="" loading="lazy"></p><ul><li>如果 0 ,按照 <code>-0</code> 的情况进行处理,即:</li></ul><p><img src="/c/assets/30.Cu__mjav.png" alt="" loading="lazy"></p><div class="important custom-block github-alert"><p class="custom-block-title">IMPORTANT</p><p></p><ul><li>① 补码表示法解决了<code>原码</code>和<code>反码</code>存在的<code>两种</code>零(<code>+0</code> 和 <code>-0</code>)的问题,即:在补码表示法中,只有<code>一个</code>零,即 <code>0000 0000</code>。</li><li>②补码使得<code>加法运算</code>和<code>减法运算</code>可以统一处理,通过将减法运算<code>转换</code>为加法运算,可以简化硬件设计,提高了运算效率。</li><li>③ 计算机底层<code>存储</code>和<code>计算</code>的都是<code>二进数的补码</code>。换言之,当读取整数的时候,需要采用逆向的转换,即:将补码转换为原码。正数的原码、反码、补码都是一样的,三码合一。负数的补码转换为原码的方法就是先减去 <code>1</code> ,得到反码,再按位取反,得到原码。</li></ul></div><h3 id="_3-5-5-总结" tabindex="-1">3.5.5 总结 <a class="header-anchor" href="#_3-5-5-总结" aria-label="Permalink to "3.5.5 总结""></a></h3><ul><li>① 正数的原码、反码和补码都是一样的,三码合一。</li><li>② 负数的反码是在其原码的基础上,按位取反(0 变 1 ,1 变 0 ),符号位不变;负数的补码是其反码 + 1 。</li><li>③ 0 的补码是 0 。</li></ul><h2 id="_3-6-计算机底层为什么使用补码" tabindex="-1">3.6 计算机底层为什么使用补码? <a class="header-anchor" href="#_3-6-计算机底层为什么使用补码" aria-label="Permalink to "3.6 计算机底层为什么使用补码?""></a></h2><ul><li>如果计算是 <code>2 - 2</code> ,那么可以转换为 <code>2 + (-2)</code>,这样计算机内部在处理<code>减法计算</code>的时候,就会将其转换为<code>加法计算</code>的形式,以简化硬件设计和提高计算效率。</li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><ul><li>① 加法和减法是计算机中最基本的运算,计算机时时刻刻都离不开它们,所以它们由硬件直接支持。为了提高加法和减法的运行效率,硬件电路必须设计得尽量简单。</li><li>② 对于有符号位的数字来说,内存需要区分符号位和数值位:对于人类来说,很容易识别(最高位是 0 还是 1);但是,对于计算机来说,需要设计专门的电路,这无疑增加了硬件的复杂性,增加了计算时间。如果能将符号位和数值位等同起来,让它们一起参与运算,不再加以区分,这样硬件电路就可以变得非常简单。</li><li>③ 此外,加法和减法也可以合并为一种运算,即:加法运算。换言之,减去一个数就相当于加上这个数的相反数,如:5 - 3 相当于 5 +(-3),10 -(-9)相当于 10 + 9 。</li><li>④ 如果能够实现上述的两个目标,那么只需要设计一种简单的、不用区分符号位和数值位的加法电路,就能同时实现加法运算和减法运算,而且非常高效。其实,这两个目标已经实现了,真正的计算机的硬件电路就是这样设计的。</li><li>⑤ 但是,简化硬件电路是有代价的,这个代价就是有符号数在存储和读取的时候都要继续转换。这也是对于有符号数的运算来说,计算机底层为什么使用<code>补码</code>的原因所在。</li></ul></div><ul><li><code>最高位</code>表示<code>符号位</code>,由于符号位的存在,如果使用<code>原码</code>来计算,就会导致<code>计算结果不正确</code>,即:</li></ul><p><img src="/c/assets/31.BX_KzkHt.png" alt="" loading="lazy"></p><ul><li><code>补码</code>的设计可以巧妙的让<code>符号位</code>也参与计算,并且可以得到<code>正确的计算结果</code>,即:</li></ul><p><img src="/c/assets/32.COt_QxSP.png" alt="" loading="lazy"></p><h2 id="_3-7-补码到底是如何简化硬件电路的" tabindex="-1">3.7 补码到底是如何简化硬件电路的? <a class="header-anchor" href="#_3-7-补码到底是如何简化硬件电路的" aria-label="Permalink to "3.7 补码到底是如何简化硬件电路的?""></a></h2><ul><li>假设 6 和 18 都是 short 类型,现在我们要计算 <code>6 - 18</code> 的结果,根据运算规则,它等价于 <code>6 +(-18)</code>。如果按照采用<code>原码</code>来计算,那么运算过程是这样的,如下所示:</li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><p>直接使用原码表示整数,让符号位也参与运算,那么对于减法来说,结果显然是不正确的。</p></div><p><img src="/c/assets/33.CSLcq3FJ.svg" alt="" loading="lazy"></p><ul><li>于是,人们开始继续探索,不断试错,终于设计出了<code>反码</code>,如下所示:</li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><p>直接使用反码表示整数,让符号位也参与运算,对于 6 +(-18)来说,结果貌似正确。</p></div><p><img src="/c/assets/34.8wVUSUxs.svg" alt="" loading="lazy"></p><ul><li>如果我们将<code>被减数</code>和<code>减数</code>对调一下,即:计算 <code>18 - 6</code> 的结果,也就是 <code>18 +(-6)</code>的结果,继续采用<code>反码</code>来进行运算,如下所示:</li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><ul><li>① 6 - 18,即:6+(-18),如果采用<code>反码</code>计算,结果是正确的;但是,18 - 6,即:18 +(-6),如果采用<code>反码</code>计算,结果相差 1 。</li><li>② 可以推断:如果按照<code>反码</code>来计算,小数 - 大数,结果正确;而大数 - 小数,结果相差 1 。</li></ul></div><p><img src="/c/assets/35.B8T792CZ.svg" alt="" loading="lazy"></p><ul><li>对于这个相差的 <code>1</code> 必须进行纠正,但是又不能影响<code>小数-大数</code>的结果。于是,人们又绞尽脑汁设计出了<code>补码</code>,给<code>反码</code>打了一个<code>“补丁”</code>,终于把相差的 <code>1</code> 给纠正过来了。那么,<code>6 - 18</code> 按照<code>补码</code>的运算过程,如下所示:</li></ul><p><img src="/c/assets/36.D7XSVA_S.svg" alt="" loading="lazy"></p><ul><li>那么,<code>18 - 6</code> 按照<code>补码</code>的运算过程,如下所示:</li></ul><p><img src="/c/assets/37.BeI_-jpB.svg" alt="" loading="lazy"></p><div class="important custom-block github-alert"><p class="custom-block-title">IMPORTANT</p><p></p><p>总结:采用<code>补码</code>的形式正好将相差的 <code>1</code>纠正过来,也没有影响到小数减大数,这个“补丁”非常巧妙。</p><ul><li>① 小数减去大数,结果为负,之前(负数从反码转换为补码需要 +1)加上的 1 ,后来(负数从补码转换为反码要 -1)还需要减去,正好抵消掉,所以不会受到影响。</li><li>② 大数减去小数,结果为正,之前(负数从反码转换为补码需要 +1)加上的 1 ,后来(正数的补码和反码相同,从补码转换为反码不用 -1)就没有再减去,不能抵消掉,这就相当于给计算结果多加了一个 1。</li></ul><p><code>补码</code>这种天才般的设计,一举达成了之前加法运算和减法运算提到的两个目标,简化了硬件电路。</p></div></div></div></main><footer class="VPDocFooter" data-v-39a288b8 data-v-e257564d><!--[--><!--]--><div class="edit-info" data-v-e257564d><!----><div class="last-updated" data-v-e257564d><p class="VPLastUpdated" data-v-e257564d data-v-e98dd255>上次更新: <time datetime="2024-08-17T09:26:01.000Z" data-v-e98dd255></time></p></div></div><nav class="prev-next" aria-labelledby="doc-footer-aria-label" data-v-e257564d><span class="visually-hidden" id="doc-footer-aria-label" data-v-e257564d>Pager</span><div class="pager" data-v-e257564d><a class="VPLink link pager-link prev" href="/c/notes/01_c-basic/01_xdx/" 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<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">}</span></span></code></pre><div class="line-numbers-wrapper" aria-hidden="true"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br><span class="line-number">12</span><br><span class="line-number">13</span><br><span class="line-number">14</span><br><span class="line-number">15</span><br></div></div><h2 id="_3-3-进制的运算规则" tabindex="-1">3.3 进制的运算规则 <a class="header-anchor" href="#_3-3-进制的运算规则" aria-label="Permalink to "3.3 进制的运算规则""></a></h2><ul><li><code>十进制</code>的运算规则,如下所示: <ul><li>逢<code>十</code>进<code>一</code>(针对加法而言)。</li><li>借<code>一</code>当<code>十</code>(针对减法而言)。</li></ul></li><li><code>二进制</code>的运算规则,如下所示: <ul><li>逢<code>二</code>进<code>一</code>(针对加法而言)。</li><li>借<code>一</code>当<code>二</code>(针对减法而言)。</li></ul></li><li><code>八进制</code>的运算规则,如下所示: <ul><li>逢<code>八</code>进<code>一</code>(针对加法而言)。</li><li>借<code>一</code>当<code>八</code>(针对减法而言)。</li></ul></li><li><code>十六进制</code>的运算规则,如下所示: <ul><li>逢<code>十六</code>进<code>一</code>(针对加法而言)。</li><li>借<code>一</code>当<code>十六</code>(针对减法而言)。</li></ul></li></ul><h2 id="_3-4-进制的转换" tabindex="-1">3.4 进制的转换 <a class="header-anchor" href="#_3-4-进制的转换" aria-label="Permalink to "3.4 进制的转换""></a></h2><h3 id="_3-4-1-概述" tabindex="-1">3.4.1 概述 <a class="header-anchor" href="#_3-4-1-概述" aria-label="Permalink to "3.4.1 概述""></a></h3><ul><li>不同进制的转换,如下所示:</li></ul><p><img src="/c/assets/19.uqLiL_yu.png" alt="" loading="lazy"></p><ul><li>在计算机中,数据是从右往左的方式排列的;其中,最右边的是低位,最左边的是高位,即:</li></ul><p><img src="/c/assets/20.CVy9jq-k.svg" alt="" loading="lazy"></p><h3 id="_3-4-2-二进制和十进制的转换" tabindex="-1">3.4.2 二进制和十进制的转换 <a class="header-anchor" href="#_3-4-2-二进制和十进制的转换" aria-label="Permalink to "3.4.2 二进制和十进制的转换""></a></h3><h4 id="_3-4-2-1-二进制转换为十进制" tabindex="-1">3.4.2.1 二进制转换为十进制 <a class="header-anchor" href="#_3-4-2-1-二进制转换为十进制" aria-label="Permalink to "3.4.2.1 二进制转换为十进制""></a></h4><ul><li>规则:从最低位开始,将每个位上的数提取出来,乘以 2 的 (位数 - 1 )次方,然后求和。</li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><ul><li>① 在学术界,将这种计算规则,称为<code>位权相加法</code>。</li><li>② <code>八进制转换为十进制</code>、<code>十六进制转换为十进制</code>和<code>二进制转换为十进制</code>的算法相同!!!</li></ul></div><ul><li>示例:十进制转十进制</li></ul><p><img src="/c/assets/21.D0s35-Np.svg" alt="" loading="lazy"></p><ul><li>示例:二进制转十进制</li></ul><p><img src="/c/assets/22.CGctd5l_.svg" alt="" loading="lazy"></p><h4 id="_3-4-2-2-十进制转换二进制" tabindex="-1">3.4.2.2 十进制转换二进制 <a class="header-anchor" href="#_3-4-2-2-十进制转换二进制" aria-label="Permalink to "3.4.2.2 十进制转换二进制""></a></h4><ul><li>规则:将该数不断除以 2 ,直到商为 0 为止,然后将每步得到的余数倒过来,就是对应的二进制。</li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><ul><li>① 在学术界,将这种计算规则,称为<code>短除法</code>或<code>连续除2取余法</code>。</li><li>② 很好理解,只有不断地除以 2 ,就能保证最大的数字不超过 2 ,这不就是二进制(只能有 0 或 1)吗?</li><li>③ <code>八进制转换为二进制</code>、<code>十六进制转换为二进制</code>和<code>十进制转换为二进制</code>的算法相同!!!</li></ul></div><ul><li>示例:十进制转十进制</li></ul><p><img src="/c/assets/23.DQIGB6FY.svg" alt="" loading="lazy"></p><ul><li>示例:十进制转二进制</li></ul><p><img src="/c/assets/24.DBiJDp82.svg" alt="" loading="lazy"></p><h3 id="_3-4-3-二进制转八进制" tabindex="-1">3.4.3 二进制转八进制 <a class="header-anchor" href="#_3-4-3-二进制转八进制" aria-label="Permalink to "3.4.3 二进制转八进制""></a></h3><ul><li><p>规则:从右向左,每 3 位二进制就是一个八进制,不足补 0(分组转换法)。</p></li><li><p>示例:011 101 001 -> 351</p></li></ul><p><img src="/c/assets/25.r0a7UWIb.svg" alt="" loading="lazy"></p><h3 id="_3-4-4-二进制转十六进制" tabindex="-1">3.4.4 二进制转十六进制 <a class="header-anchor" href="#_3-4-4-二进制转十六进制" aria-label="Permalink to "3.4.4 二进制转十六进制""></a></h3><ul><li><p>规则:从右向左,每 4 位二进制就是一个十六进制,不足补 0(分组转换法)。</p></li><li><p>示例:1110 1001 -> 0xE9</p></li></ul><p><img src="/c/assets/26.-KoNS5D_.svg" alt="" loading="lazy"></p><h2 id="_3-5-原码、反码和补码" tabindex="-1">3.5 原码、反码和补码 <a class="header-anchor" href="#_3-5-原码、反码和补码" aria-label="Permalink to "3.5 原码、反码和补码""></a></h2><h3 id="_3-5-1-概述" tabindex="-1">3.5.1 概述 <a class="header-anchor" href="#_3-5-1-概述" aria-label="Permalink to "3.5.1 概述""></a></h3><ul><li>机器数:一个数在计算机的存储形式是二进制,我们称这些二进制数为机器数。机器数可以是有符号的,用机器数的最高位来存放符号位,0 表示正数,1 表示负数。</li></ul><div class="important custom-block github-alert"><p class="custom-block-title">IMPORTANT</p><p></p><p>这里讨论的适用于<code>符号位</code>的整数,如:int 等;而不适用于<code>无符号位</code>的整数,即:unsinged int 等。</p></div><p><img src="/c/assets/27.9LAsi3gH.svg" alt="" loading="lazy"></p><ul><li>真值(数据位):因为机器数带有符号位,所以机器数的形式值不等于其真实表示的值(真值),以机器数 1000 0001 为例,其真正表示的值(首位是符号位)为 -1,而形式值却是 129 ,因此将带有符号位的机器数的真正表示的值称为机器数的真值。</li></ul><div class="important custom-block github-alert"><p class="custom-block-title">IMPORTANT</p><p></p><p>这里讨论的适用于<code>符号位</code>的整数,如:int 等;而不适用于<code>无符号位</code>的整数,即:unsinged int 等。</p></div><p><img src="/c/assets/28.CbxjdJlI.svg" alt="" loading="lazy"></p><h3 id="_3-5-2-原码" tabindex="-1">3.5.2 原码 <a class="header-anchor" href="#_3-5-2-原码" aria-label="Permalink to "3.5.2 原码""></a></h3><ul><li>原码的表示与机器数真值表示的一样,即用第一位表示符号,其余位表示数值。</li><li>规则: <ul><li>正数的<code>原码</code>是它本身对应的二进制数,符号位是 0 。</li><li>负数的<code>原码</code>是它本身绝对值对应的二进制数,但是符号位是 1 。</li></ul></li><li>+1 的原码,使用 8 位二进数来表示,就是:</li></ul><table tabindex="0"><thead><tr><th>十进制数</th><th>原码(8位二进制数)</th></tr></thead><tbody><tr><td>+1</td><td><code>0</code>000 0001</td></tr></tbody></table><ul><li>-1 的原码,使用 8 位二进数来表示,就是:</li></ul><table tabindex="0"><thead><tr><th>十进制数</th><th>原码(8位二进制数)</th></tr></thead><tbody><tr><td>-1</td><td><code>1</code>000 0001</td></tr></tbody></table><div class="important custom-block github-alert"><p class="custom-block-title">IMPORTANT</p><p></p><p>总结:</p><ul><li>① 按照原码的规则,会出现 <code>+0</code> 和 <code>-0</code> 的情况,即:<code>0</code>000 0000(+0)、<code>1</code>000 0000(-0),显然不符合实际情况。</li><li>② 所以,计算机底层虽然存储和计算的都是二进数,但显然不是原码。</li></ul></div><h3 id="_3-5-3-反码" tabindex="-1">3.5.3 反码 <a class="header-anchor" href="#_3-5-3-反码" aria-label="Permalink to "3.5.3 反码""></a></h3><ul><li><p>规则:</p><ul><li>正数的反码和它的原码相同。</li><li>负数的反码是在其原码的基础上,符号位不变,其余各位取反。</li></ul></li><li><p>+1 的反码,使用 8 位二进数来表示,就是:</p></li></ul><table tabindex="0"><thead><tr><th>十进制数</th><th>原码(8位二进制数)</th><th>反码(8位二进制数)</th></tr></thead><tbody><tr><td>+1</td><td><code>0</code>000 0001</td><td><code>0</code>000 0001</td></tr></tbody></table><ul><li>-1 的反码,使用 8 位二进数来表示,就是:</li></ul><table tabindex="0"><thead><tr><th>十进制数</th><th>原码(8位二进制数)</th><th>反码(8位二进制数)</th></tr></thead><tbody><tr><td>-1</td><td><code>1</code>000 0001</td><td><code>1</code>111 1110</td></tr></tbody></table><div class="important custom-block github-alert"><p class="custom-block-title">IMPORTANT</p><p></p><p>总结:</p><ul><li>① 按照反码的规则,如果是 <code>+0</code>,对应的原码是 <code>0</code>000 0000;那么,其反码还是 <code>0</code>000 0000 ;如果是 <code>-0</code>,对应的原码是 <code>1</code>000 0000,其反码是 <code>1</code>111 1111,显然不符合实际情况。</li><li>② 所以,计算机底层虽然存储和计算的都是二进数,但显然不是反码。</li></ul></div><h3 id="_3-5-4-补码" tabindex="-1">3.5.4 补码 <a class="header-anchor" href="#_3-5-4-补码" aria-label="Permalink to "3.5.4 补码""></a></h3><ul><li><p>规则:</p><ul><li>正数的补码和它的原码相同。</li><li>负数的补码是在其反码的基础上 + 1 。</li></ul></li><li><p>+1 的补码,使用 8 位二进数来表示,就是:</p></li></ul><table tabindex="0"><thead><tr><th>十进制数</th><th>原码(8位二进制数)</th><th>反码(8位二进制数)</th><th>补码(8位二进制数)</th></tr></thead><tbody><tr><td>+1</td><td><code>0</code>000 0001</td><td><code>0</code>000 0001</td><td><code>0</code>000 0001</td></tr></tbody></table><ul><li>-1 的补码,使用 8 位二进数来表示,就是:</li></ul><table tabindex="0"><thead><tr><th>十进制数</th><th>原码(8位二进制数)</th><th>反码(8位二进制数)</th><th>补码(8位二进制数)</th></tr></thead><tbody><tr><td>-1</td><td><code>1</code>000 0001</td><td><code>1</code>111 1110</td><td><code>1</code>111 1111</td></tr></tbody></table><ul><li>如果 <code>0</code> ,按照 <code>+0</code> 的情况进行处理,如下所示:</li></ul><p><img src="/c/assets/29.DouEaZ2q.svg" alt="" loading="lazy"></p><ul><li>如果 <code>0</code> ,按照 <code>-0</code> 的情况进行处理,如下所示:</li></ul><p><img src="/c/assets/30.BAASpiz6.svg" alt="" loading="lazy"></p><div class="important custom-block github-alert"><p class="custom-block-title">IMPORTANT</p><p></p><p>总结:</p><ul><li>① 补码表示法解决了<code>原码</code>和<code>反码</code>存在的<code>两种</code>零(<code>+0</code> 和 <code>-0</code>)的问题,即:在补码表示法中,只有<code>一个</code>零,即 <code>0000 0000</code>。</li><li>②补码使得<code>加法运算</code>和<code>减法运算</code>可以统一处理,通过将减法运算<code>转换</code>为加法运算,可以简化硬件设计,提高了运算效率。</li><li>③ 计算机底层<code>存储</code>和<code>计算</code>的都是<code>二进数的补码</code>。换言之,当读取整数的时候,需要采用逆向的转换,即:将补码转换为原码。正数的原码、反码、补码都是一样的,三码合一。负数的补码转换为原码的方法就是先减去 <code>1</code> ,得到反码,再按位取反,得到原码。</li></ul></div><h3 id="_3-5-5-总结" tabindex="-1">3.5.5 总结 <a class="header-anchor" href="#_3-5-5-总结" aria-label="Permalink to "3.5.5 总结""></a></h3><ul><li>① 正数的原码、反码和补码都是一样的,三码合一。</li><li>② 负数的反码是在其原码的基础上,按位取反(0 变 1 ,1 变 0 ),符号位不变;负数的补码是其反码 + 1 。</li><li>③ 0 的补码是 0 。</li></ul><h2 id="_3-6-计算机底层为什么使用补码" tabindex="-1">3.6 计算机底层为什么使用补码? <a class="header-anchor" href="#_3-6-计算机底层为什么使用补码" aria-label="Permalink to "3.6 计算机底层为什么使用补码?""></a></h2><ul><li><p><code>加法</code>和<code>减法</code>是计算机中最基本的运算,计算机时时刻刻都离不开它们,所以它们由硬件直接支持。为了提高加法和减法的运行效率,硬件电路必须设计得尽量简单。</p></li><li><p>对于有符号位的数字来说,内存需要区分符号位和数值位:对于人类来说,很容易识别(最高位是 0 还是 1);但是,对于计算机来说,需要设计专门的电路,这无疑增加了硬件的复杂性,增加了计算时间。如果能将符号位和数值位等同起来,让它们一起参与运算,不再加以区分,这样硬件电路就可以变得非常简单。</p></li><li><p>此外,加法和减法也可以合并为一种运算,即:加法运算。换言之,减去一个数就相当于加上这个数的相反数,如:<code>5 - 3</code> 相当于 <code>5 +(-3)</code>,<code>10 -(-9)</code>相当于 <code>10 + 9</code> 。</p></li><li><p>如果能够实现上述的两个目标,那么只需要设计一种简单的、不用区分符号位和数值位的加法电路,就能同时实现加法运算和减法运算,而且非常高效。其实,这两个目标已经实现了,真正的计算机的硬件电路就是这样设计的。</p></li><li><p>但是,简化硬件电路是有代价的,这个代价就是有符号数在存储和读取的时候都要继续转换。这也是对于有符号数的运算来说,计算机底层为什么使用<code>补码</code>的原因所在。</p></li></ul><h2 id="_3-7-补码到底是如何简化硬件电路的" tabindex="-1">3.7 补码到底是如何简化硬件电路的? <a class="header-anchor" href="#_3-7-补码到底是如何简化硬件电路的" aria-label="Permalink to "3.7 补码到底是如何简化硬件电路的?""></a></h2><ul><li>假设 6 和 18 都是 short 类型,现在我们要计算 <code>6 - 18</code> 的结果,根据运算规则,它等价于 <code>6 +(-18)</code>。如果按照采用<code>原码</code>来计算,那么运算过程是这样的,如下所示:</li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><p>直接使用原码表示整数,让符号位也参与运算,那么对于减法来说,结果显然是不正确的。</p></div><p><img src="/c/assets/31.CSLcq3FJ.svg" alt="" loading="lazy"></p><ul><li>于是,人们开始继续探索,不断试错,终于设计出了<code>反码</code>,如下所示:</li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><p>直接使用反码表示整数,让符号位也参与运算,对于 6 +(-18)来说,结果貌似正确。</p></div><p><img src="/c/assets/32.8wVUSUxs.svg" alt="" loading="lazy"></p><ul><li>如果我们将<code>被减数</code>和<code>减数</code>对调一下,即:计算 <code>18 - 6</code> 的结果,也就是 <code>18 +(-6)</code>的结果,继续采用<code>反码</code>来进行运算,如下所示:</li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><ul><li>① 6 - 18,即:6+(-18),如果采用<code>反码</code>计算,结果是正确的;但是,18 - 6,即:18 +(-6),如果采用<code>反码</code>计算,结果相差 1 。</li><li>② 可以推断:如果按照<code>反码</code>来计算,小数 - 大数,结果正确;而大数 - 小数,结果相差 1 。</li></ul></div><p><img src="/c/assets/33.B8T792CZ.svg" alt="" loading="lazy"></p><ul><li>对于这个相差的 <code>1</code> 必须进行纠正,但是又不能影响<code>小数-大数</code>的结果。于是,人们又绞尽脑汁设计出了<code>补码</code>,给<code>反码</code>打了一个<code>“补丁”</code>,终于把相差的 <code>1</code> 给纠正过来了。那么,<code>6 - 18</code> 按照<code>补码</code>的运算过程,如下所示:</li></ul><p><img src="/c/assets/34.D7XSVA_S.svg" alt="" loading="lazy"></p><ul><li>那么,<code>18 - 6</code> 按照<code>补码</code>的运算过程,如下所示:</li></ul><p><img src="/c/assets/35.BeI_-jpB.svg" alt="" loading="lazy"></p><div class="important custom-block github-alert"><p class="custom-block-title">IMPORTANT</p><p></p><p>总结:采用<code>补码</code>的形式正好将相差的 <code>1</code>纠正过来,也没有影响到小数减大数,这个“补丁”非常巧妙。</p><ul><li>① 小数减去大数,结果为负,之前(负数从反码转换为补码需要 +1)加上的 1 ,后来(负数从补码转换为反码要 -1)还需要减去,正好抵消掉,所以不会受到影响。</li><li>② 大数减去小数,结果为正,之前(负数从反码转换为补码需要 +1)加上的 1 ,后来(正数的补码和反码相同,从补码转换为反码不用 -1)就没有再减去,不能抵消掉,这就相当于给计算结果多加了一个 1。</li></ul><p><code>补码</code>这种天才般的设计,一举达成了之前加法运算和减法运算提到的两个目标,简化了硬件电路。</p></div></div></div></main><footer class="VPDocFooter" data-v-39a288b8 data-v-e257564d><!--[--><!--]--><div class="edit-info" data-v-e257564d><!----><div class="last-updated" data-v-e257564d><p class="VPLastUpdated" data-v-e257564d data-v-e98dd255>上次更新: <time datetime="2024-08-18T01:54:10.000Z" data-v-e98dd255></time></p></div></div><nav class="prev-next" aria-labelledby="doc-footer-aria-label" data-v-e257564d><span class="visually-hidden" id="doc-footer-aria-label" data-v-e257564d>Pager</span><div class="pager" data-v-e257564d><a 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<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> 0</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">;</span></span>
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<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">}</span></span></code></pre><div class="line-numbers-wrapper" aria-hidden="true"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br></div></div><h2 id="_2-8-运算符优先级" tabindex="-1">2.8 运算符优先级 <a class="header-anchor" href="#_2-8-运算符优先级" aria-label="Permalink to "2.8 运算符优先级""></a></h2><ul><li>C 语言中运算符的优先级,如下所示:</li></ul><table tabindex="0"><thead><tr><th><strong>优先级</strong></th><th><strong>运算符</strong></th><th><strong>名称或含义</strong></th><th><strong>结合方向</strong></th></tr></thead><tbody><tr><td><strong>1</strong></td><td><code>[]</code></td><td>数组下标</td><td>➡️(从左到右)</td></tr><tr><td></td><td><code>()</code></td><td>圆括号</td><td></td></tr><tr><td></td><td><code>.</code></td><td>成员选择(对象)</td><td></td></tr><tr><td></td><td><code>-></code></td><td>成员选择(指针)</td><td></td></tr><tr><td><strong>2</strong></td><td><code>-</code></td><td>负号运算符</td><td>⬅️(从右到左)</td></tr><tr><td></td><td><code>(类型)</code></td><td>强制类型转换</td><td></td></tr><tr><td></td><td><code>++</code></td><td>自增运算符</td><td></td></tr><tr><td></td><td><code>--</code></td><td>自减运算符</td><td></td></tr><tr><td></td><td><code>*</code></td><td>取值运算符</td><td></td></tr><tr><td></td><td><code>&</code></td><td>取地址运算符</td><td></td></tr><tr><td></td><td><code>!</code></td><td>逻辑非运算符</td><td></td></tr><tr><td></td><td><code>~</code></td><td>按位取反运算符</td><td></td></tr><tr><td></td><td><code>sizeof</code></td><td>长度运算符</td><td></td></tr><tr><td><strong>3</strong></td><td><code>/</code></td><td>除</td><td>➡️(从左到右)</td></tr><tr><td></td><td><code>*</code></td><td>乘</td><td></td></tr><tr><td></td><td><code>%</code></td><td>余数(取模)</td><td></td></tr><tr><td><strong>4</strong></td><td><code>+</code></td><td>加</td><td>➡️(从左到右)</td></tr><tr><td></td><td><code>-</code></td><td>减</td><td></td></tr><tr><td><strong>5</strong></td><td><code><<</code></td><td>左移</td><td>➡️(从左到右)</td></tr><tr><td></td><td><code>>></code></td><td>右移</td><td></td></tr><tr><td><strong>6</strong></td><td><code>></code></td><td>大于</td><td>➡️(从左到右)</td></tr><tr><td></td><td><code>>=</code></td><td>大于等于</td><td></td></tr><tr><td></td><td><code><</code></td><td>小于</td><td></td></tr><tr><td></td><td><code><=</code></td><td>小于等于</td><td></td></tr><tr><td><strong>7</strong></td><td><code>==</code></td><td>等于</td><td>➡️(从左到右)</td></tr><tr><td></td><td><code>!=</code></td><td>不等于</td><td></td></tr><tr><td><strong>8</strong></td><td><code>&</code></td><td>按位与</td><td>➡️(从左到右)</td></tr><tr><td><strong>9</strong></td><td><code>^</code></td><td>按位异或</td><td>➡️(从左到右)</td></tr><tr><td><strong>10</strong></td><td><code>|</code></td><td>按位或</td><td>➡️(从左到右)</td></tr><tr><td><strong>11</strong></td><td><code>&&</code></td><td>逻辑与</td><td>➡️(从左到右)</td></tr><tr><td><strong>12</strong></td><td><code>||</code></td><td>逻辑或</td><td>➡️(从左到右)</td></tr><tr><td><strong>13</strong></td><td><code>?:</code></td><td>条件运算符</td><td>⬅️(从右到左)</td></tr><tr><td><strong>14</strong></td><td><code>=</code></td><td>赋值运算符</td><td>⬅️(从右到左)</td></tr><tr><td></td><td><code>/=</code></td><td>除后赋值</td><td></td></tr><tr><td></td><td><code>*=</code></td><td>乘后赋值</td><td></td></tr><tr><td></td><td><code>%=</code></td><td>取模后赋值</td><td></td></tr><tr><td></td><td><code>+=</code></td><td>加后赋值</td><td></td></tr><tr><td></td><td><code>-=</code></td><td>减后赋值</td><td></td></tr><tr><td></td><td><code><<=</code></td><td>左移后赋值</td><td></td></tr><tr><td></td><td><code>>>=</code></td><td>右移后赋值</td><td></td></tr><tr><td></td><td><code>&=</code></td><td>按位与后赋值</td><td></td></tr><tr><td></td><td><code>^=</code></td><td>按位异或后赋值</td><td></td></tr><tr><td></td><td><code>|=</code></td><td>按位或后赋值</td><td></td></tr><tr><td><strong>15</strong></td><td><code>,</code></td><td>逗号运算符</td><td>➡️(从左到右)</td></tr></tbody></table><div class="warning custom-block github-alert"><p class="custom-block-title">WARNING</p><p></p><ul><li>① 不要过多的依赖运算符的优先级来控制表达式的执行顺序,这样可读性太差,尽量<code>使用小括号来控制</code>表达式的执行顺序。</li><li>② 不要把一个表达式写得过于复杂,如果一个表达式过于复杂,则把它<code>分成几步</code>来完成。</li><li>③ 运算符优先级不用刻意地去记忆,总体上:一元运算符 > 算术运算符 > 关系运算符 > 逻辑运算符 > 三元运算符 > 赋值运算符。</li></ul></div><h1 id="第三章-附录" tabindex="-1">第三章:附录 <a class="header-anchor" href="#第三章-附录" aria-label="Permalink to "第三章:附录""></a></h1><h2 id="_3-1-字符集和字符集编码" tabindex="-1">3.1 字符集和字符集编码 <a class="header-anchor" href="#_3-1-字符集和字符集编码" aria-label="Permalink to "3.1 字符集和字符集编码""></a></h2><h3 id="_3-3-1-概述" tabindex="-1">3.3.1 概述 <a class="header-anchor" href="#_3-3-1-概述" aria-label="Permalink to "3.3.1 概述""></a></h3><ul><li>字符集和字符集编码(简称编码)计算机系统中处理文本数据的两个基本概念,它们密切相关但又有区别。</li><li>字符集(Character Set)是一组字符的集合,其中每个字符都被分配了一个<code>唯一的编号</code>(通常是数字)。字符可以是字母、数字、符号、控制代码(如换行符)等。<code>字符集定义了可以表示的字符的范围</code>,但它并不直接定义如何将这些字符存储在计算机中。</li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><p>ASCII(美国信息交换标准代码)是最早期和最简单的字符集之一,它只包括了英文字母、数字和一些特殊字符,共 128 个字符。每个字符都分配给了一个从 0 到 127 的数字。</p></div><ul><li>字符集编码(Character Encoding,简称编码)是一种方案或方法,<code>它定义了如何将字符集中的字符转换为计算机存储和传输的数据(通常是一串二进制数字)</code>。简而言之,编码是字符到二进制数据之间的映射规则。</li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><p>ASCII 编码方案定义了如何将 ASCII 字符集中的每个字符表示为 7 位的二进制数字。例如:大写字母<code>'A'</code>在 ASCII 编码中表示为二进制的<code>1000001</code>,十进制的 <code>65</code> 。</p></div><ul><li><code>字符集</code>和<code>字符集编码</code>之间的关系如下:</li></ul><p><img src="/c/assets/32.CGTVELeO.png" alt="" loading="lazy"></p><ul><li>Linux 中安装帮助手册:</li></ul><p><img src="/c/assets/33.Bz4_lEH0.gif" alt="" loading="lazy"></p><h3 id="_3-3-2-ascii-编码" tabindex="-1">3.3.2 ASCII 编码 <a class="header-anchor" href="#_3-3-2-ascii-编码" aria-label="Permalink to "3.3.2 ASCII 编码""></a></h3><ul><li>从<code>冯·诺依曼</code>体系结构中,我们知道,计算机中所有的<code>数据</code>和<code>指令</code>都是以<code>二进制</code>的形式表示的;所以,计算机中对于文本数据的数据也是以二进制来存储的,那么对应的流程如下:</li></ul><p><img src="/c/assets/34.CcDWE4nn.png" alt="" loading="lazy"></p><ul><li>我们知道,计算机是上个世纪 60 年代在美国研制成功的,为了实现字符和二进制的转换,美国就制定了一套字符编码,即英语字符和二进制位之间的关系,即 ASCII (American Standard Code for Information Interchange)编码: <ul><li>ASCII 编码只包括了英文字符、数字和一些特殊字符,一共 128 个字符,并且每个字符都分配了唯一的数字,范围是 0 - 127。</li><li>ASCII 编码中的每个字符都使用 7 位的二进制数字表示;但是,计算机中的存储的最小单位是 1 B = 8 位,那么最高位统一规定为 0 。</li></ul></li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><ul><li>① 其实,早期是没有字符集的概念的,只是后来为了解决乱码问题,而产生了字符集的概念。</li><li>② 对于英文体系来说,<code>a-zA-Z0-9</code>以及一些<code>特殊字符</code>一共 <code>128</code> 就可以满足实际存储需求;所以,在也是为什么 ASCII 码使用 7 位二进制(2^7 = 128 )来存储的。</li></ul></div><ul><li>在操作系统中,就内置了对应的编码表,Linux 也不例外;可以使用如下的命令查看:</li></ul><div class="language-shell vp-adaptive-theme line-numbers-mode"><button title="Copy Code" class="copy"></button><span class="lang">shell</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;">man</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> ascii</span></span></code></pre><div class="line-numbers-wrapper" aria-hidden="true"><span class="line-number">1</span><br></div></div><p><img src="/c/assets/35.B7y2_JVX.gif" alt="" loading="lazy"></p><ul><li>其对应的 ASCII 编码表,如下所示:</li></ul><p><img src="/c/assets/36.Btcc3rs2.gif" alt="" loading="lazy"></p><ul><li>但是,随着计算机的发展,计算机开始了东征之路,由美国传播到东方:</li></ul><p><img src="/c/assets/37.CR4ARW8y.png" alt="" loading="lazy"></p><ul><li>先是传播到了欧洲,欧洲在兼容 ASCII 编码的基础上,推出了 ISO8859-1 编码,即: <ul><li>ISO8859-1 编码包括基本的拉丁字母表、数字、标点符号,以及西欧语言中特有的一些字符,如:法语中的 <code>è</code>、德语中的 <code>ü</code> 等。</li><li>ISO 8859-1 为每个字符分配一个单字节(8 位)编码,意味着它可以表示最多 256 (2^8)个不同的字符(编号从 0 到 255)。</li><li>ISO 8859-1 的前 128 个字符与 ASCII 编码完全一致,这使得 ASCII 编码的文本可以无缝转换为 ISO 8859-1 编码。</li></ul></li></ul><p><img src="/c/assets/36.Btcc3rs2.gif" alt="" loading="lazy"></p><p><img src="/c/assets/39.DOX3ymYP.gif" alt="" loading="lazy"></p><ul><li>计算机继续传播到了亚洲,亚洲(双字节)各个国家分别给出了自己国家对应的字符集编码,如: <ul><li>日本推出了 Shift-JIS 编码: <ul><li>单字节 ASCII 范围:0 - 127。</li><li>双字节范围: <ul><li>第一个字节:129 - 159 和 224 - 239 。</li><li>第二个字节:64 - 126 和 128 - 252 。</li></ul></li></ul></li><li>韩国推出了 EUC-KR 编码: <ul><li>单字节 ASCII 范围:0 - 127。</li><li>双字节范围:从 41281 - 65278。</li></ul></li><li>中国推出了 GBK 编码: <ul><li>单字节 ASCII 范围:0 - 127。</li><li>双字节范围:33088 - 65278 。</li></ul></li></ul></li></ul><div class="note custom-block github-alert"><p class="custom-block-title">NOTE</p><p></p><ul><li>① 通过上面日本、韩国、中国的编码十进制范围,我们可以看到,虽然这些编码系统在技术上的编码范围存在重叠(特别是在高位字节区域),但因为它们各自支持的字符集完全不同,所以实际上它们并不直接冲突。</li><li>② 但是,如果一个中国人通过 GBK 编码写的文章,通过邮件发送给韩国人,因为韩国和中国在字符集编码上的高位字节有重叠部分,必然会造成歧义。</li></ul></div><h3 id="_3-3-3-unicode-编码" tabindex="-1">3.3.3 Unicode 编码 <a class="header-anchor" href="#_3-3-3-unicode-编码" aria-label="Permalink to "3.3.3 Unicode 编码""></a></h3><ul><li><p>在 Unicode 之前,世界上存在着数百种不同的编码系统,每一种编码系统都是为了支持特定语言或一组语言的字符集。这些编码系统,包括:ASCII、ISO 8859 系列、GBK、Shift-JIS、EUC-KR 等,它们各自有不同的字符范围和编码方式。这种多样性虽然在局部范围内解决了字符表示的问题,但也带来了以下几个方面的挑战:</p><ul><li><code>编码冲突</code>:由于不同的编码系统可以为相同的字节值分配不同的字符,因此在不同编码之间转换文本时,如果没有正确处理编码信息,就很容易产生乱码。这种编码冲突在尝试处理多种语言的文本时尤为突出。</li><li><code>编码的复杂性</code>:随着全球化的发展,软件和系统需要支持越来越多的语言,这就要求开发者和系统同时处理多种不同的编码系统。这不仅增加了开发和维护的复杂性,而且也增加了出错的风险。</li><li><code>资源限制</code>:在早期计算机技术中,内存和存储资源相对有限。不同的编码标准要求系统存储多套字符集数据,这无疑增加了对有限资源的消耗。</li><li>……</li></ul></li><li><p>针对上述的种种问题,为了推行全球化,Unicode 应运而生,Unicode 的核心规则和设计原则是建立一个全球统一的字符集,使得世界上所有的文字和符号都能被唯一地识别和使用,无论使用者位于何地或使用何种语言。这套规则包括了字符的编码、表示、处理和转换机制,旨在确保不同系统和软件间能够无缝交换和处理文本数据。</p><ul><li><code>通用字符集 (UCS)</code>:Unicode 为每一个字符分配一个唯一的编号(称为<code>“码点”</code>)。这些码点被组织在一个统一的字符集中,官方称之为 “通用字符集”(Universal Character Set,UCS)。码点通常表示为 <code>U+</code> 后跟一个十六进制数,例如:<code>U+0041</code> 代表大写的英文字母 <code>“A”</code>。</li><li><code>编码平面和区段</code>:Unicode 码点被划分为多个 “平面(Planes)”,每个平面包含 65536(16^4)个码点。目前,Unicode定义了 17 个平面(从 0 到16),每个平面被分配了一个编号,从 “基本多文种平面(BMP)” 的 0 开始,到 16 号平面结束。这意味着 Unicode 理论上可以支持超过 110万(17*65536)个码点。</li></ul></li><li><p>Unicode 仅仅只是字符集,给每个字符设置了唯一的数字编号而已,却没有给出这些数字编号实际如何存储,可以通过如下命令查看:</p></li></ul><p><img src="/c/assets/40.Cie9_tkP.gif" alt="" loading="lazy"></p><ul><li>为了在计算机系统中表示 Unicode 字符,定义了几种编码方案,这些方案包括 UTF-8、UTF-16 和 UTF-32 等。 <ul><li><strong>UTF-8</strong>:使用 1 - 4 个字节表示每个 Unicode 字符,兼容 ASCII,是网络上最常用的编码。</li><li><strong>UTF-16</strong>:使用 2 - 4 个字节表示每个 Unicode 字符,适合于需要经常处理基本多文种平面之外字符的应用。</li><li><strong>UTF-32</strong>:使用固定的 4 个字节表示每个 Unicode 字符,简化了字符处理,但增加了存储空间的需求。</li></ul></li><li><code>Unicode 字符集</code>和对应的<code>UTF-8 字符编码</code>之间的关系,如下所示:</li></ul><p><img src="/c/assets/41.DLjH9Ges.png" alt="" loading="lazy"></p></div></div></main><footer class="VPDocFooter" data-v-39a288b8 data-v-e257564d><!--[--><!--]--><div class="edit-info" 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<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">}</span></span></code></pre><div class="line-numbers-wrapper" aria-hidden="true"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br><span class="line-number">12</span><br><span class="line-number">13</span><br><span class="line-number">14</span><br><span class="line-number">15</span><br></div></div></div></div></main><footer class="VPDocFooter" data-v-39a288b8 data-v-e257564d><!--[--><!--]--><div class="edit-info" data-v-e257564d><!----><div class="last-updated" data-v-e257564d><p class="VPLastUpdated" data-v-e257564d data-v-e98dd255>上次更新: <time datetime="2024-08-06T08:32:38.000Z" data-v-e98dd255></time></p></div></div><nav class="prev-next" aria-labelledby="doc-footer-aria-label" data-v-e257564d><span class="visually-hidden" id="doc-footer-aria-label" data-v-e257564d>Pager</span><div class="pager" data-v-e257564d><a class="VPLink link pager-link prev" href="/c/notes/01_c-basic/03_xdx/" data-v-e257564d><!--[--><span class="desc" data-v-e257564d>上一篇</span><span class="title" data-v-e257564d>数据类型和运算符</span><!--]--></a></div><div class="pager" data-v-e257564d><a class="VPLink link pager-link next" href="/c/notes/01_c-basic/05_xdx/" data-v-e257564d><!--[--><span class="desc" data-v-e257564d>下一篇</span><span class="title" data-v-e257564d>数组</span><!--]--></a></div></nav></footer><!--[--><!--]--></div></div></div><!--[--><!--]--></div></div><footer class="VPFooter has-sidebar" data-v-5d98c3a5 data-v-e315a0ad><div class="container" data-v-e315a0ad><p class="message" data-v-e315a0ad>Released under the MIT License.</p><p class="copyright" data-v-e315a0ad>Copyright © 2024 许大仙</p></div></footer><!--[--><!--]--></div></div>
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<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> 0</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">;</span></span>
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<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">}</span></span></code></pre><div class="line-numbers-wrapper" aria-hidden="true"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br><span class="line-number">12</span><br><span class="line-number">13</span><br><span class="line-number">14</span><br></div></div><div class="warning custom-block github-alert"><p class="custom-block-title">WARNING</p><p></p><p>在上述示例中,<code>arr</code> 和 <code>&arr</code> 的值是一样的,但是对应的含义是不同的。</p><ul><li>① <code>arr</code> 是数组名,在大多数情况下会转换为数组第一个元素的地址,即:<code>arr</code> 等价于 <code>&arr[0]</code>,其数据类型是 <code>int *</code>。</li><li>② <code>&arr</code>是数组名的地址,即整个数组的地址,它指向数组本身,并不是数组第一个元素的地址,<code>&arr</code> 的数据类型是 <code>int(*)[3]</code>。</li></ul></div></div></div></main><footer class="VPDocFooter" data-v-39a288b8 data-v-e257564d><!--[--><!--]--><div class="edit-info" data-v-e257564d><!----><div class="last-updated" data-v-e257564d><p class="VPLastUpdated" data-v-e257564d data-v-e98dd255>上次更新: <time datetime="2024-08-12T02:47:17.000Z" data-v-e98dd255></time></p></div></div><nav class="prev-next" aria-labelledby="doc-footer-aria-label" data-v-e257564d><span class="visually-hidden" id="doc-footer-aria-label" data-v-e257564d>Pager</span><div class="pager" data-v-e257564d><a class="VPLink link pager-link prev" href="/c/notes/01_c-basic/04_xdx/" data-v-e257564d><!--[--><span class="desc" data-v-e257564d>上一篇</span><span class="title" data-v-e257564d>流程控制</span><!--]--></a></div><div class="pager" data-v-e257564d><a class="VPLink link pager-link next" href="/c/notes/01_c-basic/06_xdx/" data-v-e257564d><!--[--><span class="desc" data-v-e257564d>下一篇</span><span class="title" data-v-e257564d>指针</span><!--]--></a></div></nav></footer><!--[--><!--]--></div></div></div><!--[--><!--]--></div></div><footer class="VPFooter has-sidebar" data-v-5d98c3a5 data-v-e315a0ad><div class="container" data-v-e315a0ad><p class="message" data-v-e315a0ad>Released under the MIT License.</p><p class="copyright" data-v-e315a0ad>Copyright © 2024 许大仙</p></div></footer><!--[--><!--]--></div></div>
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<span class="line"><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;">printf</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">"Address of array: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">%p\n</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">"</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">, </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">&</span><span style="--shiki-light:#E36209;--shiki-dark:#FFAB70;">arr</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">);</span><span style="--shiki-light:#6A737D;--shiki-dark:#6A737D;"> // 返回整个数组的地址</span></span>
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<span class="line"><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;">printf</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">"Address of pointer: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">%p\n</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">"</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">, </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">&</span><span style="--shiki-light:#E36209;--shiki-dark:#FFAB70;">ptr</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">);</span><span style="--shiki-light:#6A737D;--shiki-dark:#6A737D;"> // 返回指针变量ptr的地址</span></span></code></pre><div class="line-numbers-wrapper" aria-hidden="true"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br></div></div></li></ol><p>综上所述,通过这些示例和解释,可以看出数组名虽然在某些场合下可以像指针一样使用,但它并不是一个真正的指针变量,而是一个常量,表示数组的首地址。</p></div></div></main><footer class="VPDocFooter" data-v-39a288b8 data-v-e257564d><!--[--><!--]--><div class="edit-info" data-v-e257564d><!----><div class="last-updated" data-v-e257564d><p class="VPLastUpdated" data-v-e257564d data-v-e98dd255>上次更新: <time datetime="2024-08-13T02:39:52.000Z" data-v-e98dd255></time></p></div></div><nav class="prev-next" aria-labelledby="doc-footer-aria-label" data-v-e257564d><span class="visually-hidden" id="doc-footer-aria-label" data-v-e257564d>Pager</span><div class="pager" data-v-e257564d><a class="VPLink link pager-link prev" href="/c/notes/01_c-basic/05_xdx/" data-v-e257564d><!--[--><span class="desc" data-v-e257564d>上一篇</span><span class="title" data-v-e257564d>数组</span><!--]--></a></div><div class="pager" data-v-e257564d><a class="VPLink link pager-link next" href="/c/notes/01_c-basic/07_xdx/" data-v-e257564d><!--[--><span class="desc" data-v-e257564d>下一篇</span><span class="title" data-v-e257564d>函数</span><!--]--></a></div></nav></footer><!--[--><!--]--></div></div></div><!--[--><!--]--></div></div><footer class="VPFooter has-sidebar" data-v-5d98c3a5 data-v-e315a0ad><div class="container" data-v-e315a0ad><p class="message" data-v-e315a0ad>Released under the MIT License.</p><p class="copyright" data-v-e315a0ad>Copyright © 2024 许大仙</p></div></footer><!--[--><!--]--></div></div>
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data-v-b7550ba0>数据类型和运算符</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/01_c-basic/04_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>流程控制</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/01_c-basic/05_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>数组</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/01_c-basic/06_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>指针</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/01_c-basic/07_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>函数</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/01_c-basic/08_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>预处理器</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/01_c-basic/09_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>自定义数据类型</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/01_c-basic/10_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>内存管理</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/01_c-basic/11_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>文件操作</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/02_c-basic/13_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>调试工具和调试技巧(gdb和make)</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/01_c-basic/13_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>常用库函数</p><!--]--></a><!----></div><!----></div><!--]--></div></section></div><div class="no-transition group" data-v-c40bc020><section class="VPSidebarItem level-0 collapsible collapsed" data-v-c40bc020 data-v-b7550ba0><div class="item" role="button" tabindex="0" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><h2 class="text" data-v-b7550ba0>C 语言高级</h2><div class="caret" role="button" aria-label="toggle section" tabindex="0" data-v-b7550ba0><span class="vpi-chevron-right caret-icon" data-v-b7550ba0></span></div></div><div class="items" data-v-b7550ba0><!--[--><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/02_c-advance/01_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>变量和内存分布</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/02_c-advance/02_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>指针强化</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/02_c-advance/03_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>结构体和文件的高级用法</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/02_c-advance/04_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>链表和回调函数</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/02_c-advance/05_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>编译过程和面向接口</p><!--]--></a><!----></div><!----></div><!--]--></div></section></div><div class="no-transition group" data-v-c40bc020><section class="VPSidebarItem level-0 collapsible collapsed" data-v-c40bc020 data-v-b7550ba0><div class="item" role="button" tabindex="0" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><h2 class="text" data-v-b7550ba0>项目构建工具</h2><div class="caret" role="button" aria-label="toggle section" tabindex="0" data-v-b7550ba0><span class="vpi-chevron-right caret-icon" data-v-b7550ba0></span></div></div><div class="items" data-v-b7550ba0><!--[--><section class="VPSidebarItem level-1 collapsible collapsed" data-v-b7550ba0 data-v-b7550ba0><div class="item" role="button" tabindex="0" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><h3 class="text" data-v-b7550ba0>meson</h3><div class="caret" role="button" aria-label="toggle section" tabindex="0" data-v-b7550ba0><span class="vpi-chevron-right caret-icon" data-v-b7550ba0></span></div></div><div class="items" data-v-b7550ba0><!--[--><div class="VPSidebarItem level-2 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/03_build/01_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>meson 入门</p><!--]--></a><!----></div><!----></div><!--]--></div></section><section class="VPSidebarItem level-1 collapsible collapsed" data-v-b7550ba0 data-v-b7550ba0><div class="item" role="button" tabindex="0" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><h3 class="text" data-v-b7550ba0>Cmake</h3><div class="caret" role="button" aria-label="toggle section" tabindex="0" data-v-b7550ba0><span class="vpi-chevron-right caret-icon" data-v-b7550ba0></span></div></div><div class="items" data-v-b7550ba0><!--[--><div class="VPSidebarItem level-2 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/03_build/01_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>Cmake 入门</p><!--]--></a><!----></div><!----></div><!--]--></div></section><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/03_build/01_${commonDirectoryName}/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>Conan </p><!--]--></a><!----></div><!----></div><section class="VPSidebarItem level-1 collapsible collapsed" data-v-b7550ba0 data-v-b7550ba0><div class="item" role="button" tabindex="0" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><h3 class="text" data-v-b7550ba0>Gradle</h3><div class="caret" role="button" aria-label="toggle section" tabindex="0" data-v-b7550ba0><span class="vpi-chevron-right caret-icon" data-v-b7550ba0></span></div></div><div class="items" data-v-b7550ba0><!--[--><div class="VPSidebarItem level-2 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/03_build/01_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>Gradle 入门</p><!--]--></a><!----></div><!----></div><!--]--></div></section><!--]--></div></section></div><div class="no-transition group" data-v-c40bc020><section class="VPSidebarItem level-0 collapsible collapsed" data-v-c40bc020 data-v-b7550ba0><div class="item" role="button" tabindex="0" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><h2 class="text" data-v-b7550ba0>Linux</h2><div class="caret" role="button" aria-label="toggle section" tabindex="0" data-v-b7550ba0><span class="vpi-chevron-right caret-icon" data-v-b7550ba0></span></div></div><div class="items" data-v-b7550ba0><!--[--><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/04_linux/01_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>Linux 初识和安装</p><!--]--></a><!----></div><!----></div><!--]--></div></section></div><div class="no-transition group" data-v-c40bc020><section class="VPSidebarItem level-0 collapsible collapsed" data-v-c40bc020 data-v-b7550ba0><div class="item" role="button" tabindex="0" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><h2 class="text" data-v-b7550ba0>C++ 基础</h2><div class="caret" role="button" aria-label="toggle section" tabindex="0" data-v-b7550ba0><span class="vpi-chevron-right caret-icon" data-v-b7550ba0></span></div></div><div class="items" data-v-b7550ba0><!--[--><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/01_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>C++ 入门</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/02_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>变量、数据类型、运算符</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/03_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>流程控制</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/04_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>数组</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/05_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>指针</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/06_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>函数</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/07_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>自定义数据类型</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/08_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>类和对象</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/09_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>C++ 引用</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/10_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>继承和派生</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/11_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>C++ 多态和虚函数</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/12_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>运算符重载</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/13_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>模板</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/14_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>C++ 异常</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/15_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>面向对象进阶</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/16_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>文件操作和 IO 流</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/17_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>STL(标准模板库)</p><!--]--></a><!----></div><!----></div><!--]--></div></section></div><div class="no-transition group" data-v-c40bc020><div class="VPSidebarItem level-0 collapsible collapsed" data-v-c40bc020 data-v-b7550ba0><div class="item" role="button" tabindex="0" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><p class="text" data-v-b7550ba0>C++ 高级</p><!----></div><!----></div></div><div class="no-transition group" data-v-c40bc020><div class="VPSidebarItem level-0 collapsible collapsed" data-v-c40bc020 data-v-b7550ba0><div class="item" role="button" tabindex="0" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><p class="text" data-v-b7550ba0>QT 桌面开发</p><!----></div><!----></div></div><div class="no-transition group" data-v-c40bc020><div class="VPSidebarItem level-0 collapsible collapsed" data-v-c40bc020 data-v-b7550ba0><div class="item" role="button" tabindex="0" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><p class="text" data-v-b7550ba0>Linux 高并发服务器开发</p><!----></div><!----></div></div><!--]--><!--[--><!--]--></nav></aside><div class="VPContent has-sidebar" id="VPContent" data-v-5d98c3a5 data-v-1428d186><div class="VPDoc has-sidebar has-aside" data-v-1428d186 data-v-39a288b8><!--[--><!--]--><div class="container" data-v-39a288b8><div class="aside" data-v-39a288b8><div class="aside-curtain" data-v-39a288b8></div><div class="aside-container" data-v-39a288b8><div class="aside-content" data-v-39a288b8><div class="VPDocAside" data-v-39a288b8 data-v-3f215769><!--[--><!--]--><!--[--><!--]--><nav aria-labelledby="doc-outline-aria-label" class="VPDocAsideOutline" data-v-3f215769 data-v-a5bbad30><div class="content" data-v-a5bbad30><div class="outline-marker" data-v-a5bbad30></div><div aria-level="2" class="outline-title" id="doc-outline-aria-label" role="heading" data-v-a5bbad30>目录</div><ul class="VPDocOutlineItem root" data-v-a5bbad30 data-v-b933a997><!--[--><!--]--></ul></div></nav><!--[--><!--]--><div class="spacer" data-v-3f215769></div><!--[--><!--]--><!----><!--[--><!--]--><!--[--><!--]--></div></div></div></div><div class="content" data-v-39a288b8><div class="content-container" data-v-39a288b8><!--[--><!--]--><main class="main" data-v-39a288b8><div style="position:relative;" class="vp-doc _c_notes_about_" data-v-39a288b8><div><h3 id="后端技术栈" tabindex="-1">后端技术栈 <a class="header-anchor" href="#后端技术栈" aria-label="Permalink to "后端技术栈""></a></h3><p><img src="https://img.shields.io/badge/-Spring-6DB33F?logo=Spring&logoColor=FFF" alt="Spring" style="display:inline-block;"> <img src="https://img.shields.io/badge/-Spring%20Boot-6DB33F?logo=Spring-Boot&logoColor=FFF" alt="Spring Boot" style="display:inline-block;"> <img src="https://img.shields.io/badge/-MySQL-4479A1?logo=MySQL&logoColor=FFF" alt="MySQL" style="display:inline-block;"> <img src="https://img.shields.io/badge/-MariaDB-A9A9A9?logo=MariaDB&logoColor=003545" alt="MariaDB" style="display:inline-block;"> <img src="https://img.shields.io/badge/-PostgreSQL-C0C0C0?logo=PostgreSQL&logoColor=4169E1" alt="PostgreSQL" style="display:inline-block;"> <img src="https://img.shields.io/badge/-Oracle-C0C0C0?logo=Oracle&logoColor=F80000" alt="Oracle" style="display:inline-block;"> <img 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data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/01_c-basic/04_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>流程控制</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/01_c-basic/05_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>数组</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/01_c-basic/06_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>指针</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/01_c-basic/07_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>函数</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/01_c-basic/08_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>预处理器</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/01_c-basic/09_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>自定义数据类型</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/01_c-basic/10_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>内存管理</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/01_c-basic/11_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>文件操作</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/02_c-basic/13_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>调试工具和调试技巧(gdb和make)</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/01_c-basic/13_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>常用库函数</p><!--]--></a><!----></div><!----></div><!--]--></div></section></div><div class="no-transition group" data-v-c40bc020><section class="VPSidebarItem level-0 collapsible collapsed" data-v-c40bc020 data-v-b7550ba0><div class="item" role="button" tabindex="0" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><h2 class="text" data-v-b7550ba0>C 语言高级</h2><div class="caret" role="button" aria-label="toggle section" tabindex="0" data-v-b7550ba0><span class="vpi-chevron-right caret-icon" data-v-b7550ba0></span></div></div><div class="items" data-v-b7550ba0><!--[--><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/02_c-advance/01_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>变量和内存分布</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/02_c-advance/02_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>指针强化</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/02_c-advance/03_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>结构体和文件的高级用法</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/02_c-advance/04_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>链表和回调函数</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/02_c-advance/05_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>编译过程和面向接口</p><!--]--></a><!----></div><!----></div><!--]--></div></section></div><div class="no-transition group" data-v-c40bc020><section class="VPSidebarItem level-0 collapsible collapsed" data-v-c40bc020 data-v-b7550ba0><div class="item" role="button" tabindex="0" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><h2 class="text" data-v-b7550ba0>项目构建工具</h2><div class="caret" role="button" aria-label="toggle section" tabindex="0" data-v-b7550ba0><span class="vpi-chevron-right caret-icon" data-v-b7550ba0></span></div></div><div class="items" data-v-b7550ba0><!--[--><section class="VPSidebarItem level-1 collapsible collapsed" data-v-b7550ba0 data-v-b7550ba0><div class="item" role="button" tabindex="0" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><h3 class="text" data-v-b7550ba0>meson</h3><div class="caret" role="button" aria-label="toggle section" tabindex="0" data-v-b7550ba0><span class="vpi-chevron-right caret-icon" data-v-b7550ba0></span></div></div><div class="items" data-v-b7550ba0><!--[--><div class="VPSidebarItem level-2 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/03_build/01_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>meson 入门</p><!--]--></a><!----></div><!----></div><!--]--></div></section><section class="VPSidebarItem level-1 collapsible collapsed" data-v-b7550ba0 data-v-b7550ba0><div class="item" role="button" tabindex="0" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><h3 class="text" data-v-b7550ba0>Cmake</h3><div class="caret" role="button" aria-label="toggle section" tabindex="0" data-v-b7550ba0><span class="vpi-chevron-right caret-icon" data-v-b7550ba0></span></div></div><div class="items" data-v-b7550ba0><!--[--><div class="VPSidebarItem level-2 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/03_build/01_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>Cmake 入门</p><!--]--></a><!----></div><!----></div><!--]--></div></section><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/03_build/01_${commonDirectoryName}/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>Conan </p><!--]--></a><!----></div><!----></div><section class="VPSidebarItem level-1 collapsible collapsed" data-v-b7550ba0 data-v-b7550ba0><div class="item" role="button" tabindex="0" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><h3 class="text" data-v-b7550ba0>Gradle</h3><div class="caret" role="button" aria-label="toggle section" tabindex="0" data-v-b7550ba0><span class="vpi-chevron-right caret-icon" data-v-b7550ba0></span></div></div><div class="items" data-v-b7550ba0><!--[--><div class="VPSidebarItem level-2 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/03_build/01_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>Gradle 入门</p><!--]--></a><!----></div><!----></div><!--]--></div></section><!--]--></div></section></div><div class="no-transition group" data-v-c40bc020><section class="VPSidebarItem level-0 collapsible collapsed" data-v-c40bc020 data-v-b7550ba0><div class="item" role="button" tabindex="0" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><h2 class="text" data-v-b7550ba0>Linux</h2><div class="caret" role="button" aria-label="toggle section" tabindex="0" data-v-b7550ba0><span class="vpi-chevron-right caret-icon" data-v-b7550ba0></span></div></div><div class="items" data-v-b7550ba0><!--[--><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/04_linux/01_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>Linux 初识和安装</p><!--]--></a><!----></div><!----></div><!--]--></div></section></div><div class="no-transition group" data-v-c40bc020><section class="VPSidebarItem level-0 collapsible collapsed" data-v-c40bc020 data-v-b7550ba0><div class="item" role="button" tabindex="0" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><h2 class="text" data-v-b7550ba0>C++ 基础</h2><div class="caret" role="button" aria-label="toggle section" tabindex="0" data-v-b7550ba0><span class="vpi-chevron-right caret-icon" data-v-b7550ba0></span></div></div><div class="items" data-v-b7550ba0><!--[--><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/01_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>C++ 入门</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/02_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>变量、数据类型、运算符</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/03_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>流程控制</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/04_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>数组</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/05_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>指针</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/06_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>函数</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/07_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>自定义数据类型</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/08_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>类和对象</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/09_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>C++ 引用</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/10_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>继承和派生</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/11_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>C++ 多态和虚函数</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/12_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>运算符重载</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/13_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>模板</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/14_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>C++ 异常</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/15_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>面向对象进阶</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/16_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>文件操作和 IO 流</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b7550ba0 data-v-b7550ba0><div class="item" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><a class="VPLink link link" href="/c/notes/05_cpp/17_xdx/" data-v-b7550ba0><!--[--><p class="text" data-v-b7550ba0>STL(标准模板库)</p><!--]--></a><!----></div><!----></div><!--]--></div></section></div><div class="no-transition group" data-v-c40bc020><div class="VPSidebarItem level-0 collapsible collapsed" data-v-c40bc020 data-v-b7550ba0><div class="item" role="button" tabindex="0" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><p class="text" data-v-b7550ba0>C++ 高级</p><!----></div><!----></div></div><div class="no-transition group" data-v-c40bc020><div class="VPSidebarItem level-0 collapsible collapsed" data-v-c40bc020 data-v-b7550ba0><div class="item" role="button" tabindex="0" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><p class="text" data-v-b7550ba0>QT 桌面开发</p><!----></div><!----></div></div><div class="no-transition group" data-v-c40bc020><div class="VPSidebarItem level-0 collapsible collapsed" data-v-c40bc020 data-v-b7550ba0><div class="item" role="button" tabindex="0" data-v-b7550ba0><div class="indicator" data-v-b7550ba0></div><p class="text" data-v-b7550ba0>Linux 高并发服务器开发</p><!----></div><!----></div></div><!--]--><!--[--><!--]--></nav></aside><div class="VPContent has-sidebar" id="VPContent" data-v-5d98c3a5 data-v-1428d186><div class="VPDoc has-sidebar has-aside" data-v-1428d186 data-v-39a288b8><!--[--><!--]--><div class="container" data-v-39a288b8><div class="aside" data-v-39a288b8><div 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