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浮点数的二进制存储形式及c语言验证 | 雅乐网 </title>
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<a href="http://www.yalewoo.com/programming">编程</a> » <a href="http://www.yalewoo.com/programming/c_cpp">C/C++</a> » 浮点数的二进制存储形式及c语言验证 </div>
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<span class="meta-time meta-ico"> 最后修改于 2016-03-28</span>
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<ul id="content-index-contents"><li class="content-index-level-1"><a href="http://www.yalewoo.com/float.html#浮点数的存储步骤：" title="浮点数的存储步骤："><em>1</em><span>浮点数的存储步骤：</span></a></li><li class="content-index-level-1"><a href="http://www.yalewoo.com/float.html#5.75的二进制表示" title="5.75的二进制表示"><em>2</em><span>5.75的二进制表示</span></a></li><li class="content-index-level-1"><a href="http://www.yalewoo.com/float.html#-161.875的二进制表示" title="-161.875的二进制表示"><em>3</em><span>-161.875的二进制表示</span></a></li><li class="content-index-level-1"><a href="http://www.yalewoo.com/float.html#1 10010100 00000000111000100001111表示为实数" title="1 10010100 00000000111000100001111表示为实数"><em>4</em><span>1 10010100 00000000111000100001111表示为实数</span></a></li><li class="content-index-level-1"><a href="http://www.yalewoo.com/float.html#c语言验证" title="c语言验证"><em>5</em><span>c语言验证</span></a></li></ul></div>
<p>我们经常听说浮点数，其实浮点数是和定点数对应的。定点数就是小数点固定的数，而且他的小数点在最右边，所以定点数用来表示整数。</p>
<p>浮点数表示方法允许小数点的浮动，一个浮点数分为三个部分：第一部分是符号，可以是正数可以是负数；第二部分是小数点应该左移或右移的位移量；第三部分是小数点位置固定的定点表示法。</p>
<p>下面介绍常用的IEEE标准定义的浮点数的标准。</p>
<p><a target="_blank" href="http://7d9rd6.com1.z0.glb.clouddn.com/wp-content/uploads/2014/06/搜狗截图20140627191037.png"><img class="alignnone size-full wp-image-415" data-original="http://7d9rd6.com1.z0.glb.clouddn.com/wp-content/uploads/2014/06/搜狗截图20140627191037.png" src="http://www.yalewoo.com/wp-content/themes/YLW3_lite/img/loading.gif" alt="搜狗截图20140627191037" width="872" height="177" /></a></p>
<noscript><img class="alignnone size-full wp-image-415" src="http://7d9rd6.com1.z0.glb.clouddn.com/wp-content/uploads/2014/06/搜狗截图20140627191037.png" alt="搜狗截图20140627191037" width="872" height="177" /></a></p></noscript>
<p>符号部分： 0表示正数 1表示负数</p>
<p>位移量部分：采用余127码表示。在余码系统中，正数和负数都用无符号数储存，而且可以保持原有的大小关系，只需要将所有的数字整体右移。即该部分看做无符号整数，127表示0 126表示-1 128表示1</p>
<p>尾数部分：是将某数字化为1.xxxxxxx * 2^n的形式后的xxxxxx部分.小数点和其左边的1并不存储。</p>
<h3 id="浮点数的存储步骤：">浮点数的存储步骤：</h3>
<p>1. 看符号位</p>
<p>2.将数字转化成二进制</p>
<p>3.将二进制规范化为 1.xxxxxxxx*2^n</p>
<p>4. 将n转化为指数（加上127） 尾数xxxx后面补零</p>
<p>5.写出</p>
<p>下面举几个例子：</p>
<h3 id="5.75的二进制表示">5.75的二进制表示</h3>
<p>1. 是正数，因此符号位为0</p>
<p>2. 十进制转化二进制 5.75 = 101.11（二进制）</p>
<p>3. 将二进制规范化：101.11 = 1.0111 * 2^2</p>
<p>指数部分为2 尾数部分为0111</p>
<p>4. 根据余127码 指数部分为 2+127 = 129 = 10000001（二进制） 尾数部分后面补零 01110000000000000000000</p>
<p>5. 表示如下</p>
<p>0 10000001 01110000000000000000000</p>
<h3 id="-161.875的二进制表示">-161.875的二进制表示</h3>
<p>1. 符号位为1 （负数）</p>
<p>2.转化为二进制 161.875 = 10100001.111（二进制）</p>
<p>3.二进制规范化： 10100001.111 = 1.0100001111 * 2^7</p>
<p>4.指数部分E = 7+127 = 134 = 10000110（二进制） 尾数部分0100001111</p>
<p>5.表示如下</p>
<p>1 10000110 01000011110000000000000</p>
<h3 id="1 10010100 00000000111000100001111表示为实数">1 10010100 00000000111000100001111表示为实数</h3>
<p>1. 首位为1 是负数</p>
<p>2. 指数部分10010100 = 148 148-127 = 21</p>
<p>3. 尾数去规范化 1.00000000111000100001111</p>
<p>4.二进制为 1.00000000111000100001111 * 2^21</p>
<p>5. 十进制为2104378.75</p>
<p>6.该数字是 -2104378.75</p>
<h3 id="c语言验证">c语言验证</h3>
<p><a target="_blank" href="http://7d9rd6.com1.z0.glb.clouddn.com/wp-content/uploads/2014/06/搜狗截图20140627200725.png"><img class="alignnone size-full wp-image-417" data-original="http://7d9rd6.com1.z0.glb.clouddn.com/wp-content/uploads/2014/06/搜狗截图20140627200725.png" src="http://www.yalewoo.com/wp-content/themes/YLW3_lite/img/loading.gif" alt="搜狗截图20140627200725" width="460" height="145" /></a></p>
<noscript><img class="alignnone size-full wp-image-417" src="http://7d9rd6.com1.z0.glb.clouddn.com/wp-content/uploads/2014/06/搜狗截图20140627200725.png" alt="搜狗截图20140627200725" width="460" height="145" /></a></p></noscript>
<p>源代码如下</p>
<div id="crayon-5a3a8bcbaf0f9414302482" class="crayon-syntax crayon-theme-classic crayon-font-consolas crayon-os-mac print-yes notranslate" data-settings=" minimize scroll-mouseover disable-anim wrap" style=" margin-top: 12px; margin-bottom: 12px; font-size: 20px !important; line-height: 30px !important;">
<div class="crayon-plain-wrap"><textarea class="crayon-plain print-no" data-settings="dblclick" readonly style="-moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4; font-size: 20px !important; line-height: 30px !important;">
#include <stdio.h>
int main(void)
{
float fnum = 1;
int i;
int * p = (int *)&fnum;
while (fnum != 0)
{
printf("input a num: ");
scanf("%f", &fnum);
for (i = 31; i >= 0; i--)
{
printf("%d", (*p & (1 << i) ? 1: 0));
}
printf("\n");
}
return 0;
}</textarea></div>
<div class="crayon-main" style="">
<table class="crayon-table">
<tr class="crayon-row">
<td class="crayon-nums " data-settings="show">
<div class="crayon-nums-content" style="font-size: 20px !important; line-height: 30px !important;"><div class="crayon-num" data-line="crayon-5a3a8bcbaf0f9414302482-1">1</div><div class="crayon-num" data-line="crayon-5a3a8bcbaf0f9414302482-2">2</div><div class="crayon-num" data-line="crayon-5a3a8bcbaf0f9414302482-3">3</div><div class="crayon-num" data-line="crayon-5a3a8bcbaf0f9414302482-4">4</div><div class="crayon-num" data-line="crayon-5a3a8bcbaf0f9414302482-5">5</div><div class="crayon-num" data-line="crayon-5a3a8bcbaf0f9414302482-6">6</div><div class="crayon-num" data-line="crayon-5a3a8bcbaf0f9414302482-7">7</div><div class="crayon-num" data-line="crayon-5a3a8bcbaf0f9414302482-8">8</div><div class="crayon-num" data-line="crayon-5a3a8bcbaf0f9414302482-9">9</div><div class="crayon-num" data-line="crayon-5a3a8bcbaf0f9414302482-10">10</div><div class="crayon-num" data-line="crayon-5a3a8bcbaf0f9414302482-11">11</div><div class="crayon-num" data-line="crayon-5a3a8bcbaf0f9414302482-12">12</div><div class="crayon-num" data-line="crayon-5a3a8bcbaf0f9414302482-13">13</div><div class="crayon-num" data-line="crayon-5a3a8bcbaf0f9414302482-14">14</div><div class="crayon-num" data-line="crayon-5a3a8bcbaf0f9414302482-15">15</div><div class="crayon-num" data-line="crayon-5a3a8bcbaf0f9414302482-16">16</div><div class="crayon-num" data-line="crayon-5a3a8bcbaf0f9414302482-17">17</div><div class="crayon-num" data-line="crayon-5a3a8bcbaf0f9414302482-18">18</div><div class="crayon-num" data-line="crayon-5a3a8bcbaf0f9414302482-19">19</div></div>
</td>
<td class="crayon-code"><div class="crayon-pre" style="font-size: 20px !important; line-height: 30px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="crayon-5a3a8bcbaf0f9414302482-1"><span class="crayon-p">#include <stdio.h></span></div><div class="crayon-line" id="crayon-5a3a8bcbaf0f9414302482-2"> </div><div class="crayon-line" id="crayon-5a3a8bcbaf0f9414302482-3"><span class="crayon-t">int</span><span class="crayon-h"> </span><span class="crayon-e">main</span><span class="crayon-sy">(</span><span class="crayon-t">void</span><span class="crayon-sy">)</span></div><div class="crayon-line" id="crayon-5a3a8bcbaf0f9414302482-4"><span class="crayon-sy">{</span></div><div class="crayon-line" id="crayon-5a3a8bcbaf0f9414302482-5"><span class="crayon-h"> </span><span class="crayon-t">float</span><span class="crayon-h"> </span><span class="crayon-v">fnum</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-cn">1</span><span class="crayon-sy">;</span></div><div class="crayon-line" id="crayon-5a3a8bcbaf0f9414302482-6"><span class="crayon-h"> </span><span class="crayon-t">int</span><span class="crayon-h"> </span><span class="crayon-v">i</span><span class="crayon-sy">;</span></div><div class="crayon-line" id="crayon-5a3a8bcbaf0f9414302482-7"><span class="crayon-h"> </span><span class="crayon-t">int</span><span class="crayon-h"> </span><span class="crayon-o">*</span><span class="crayon-h"> </span><span class="crayon-v">p</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-sy">(</span><span class="crayon-t">int</span><span class="crayon-h"> </span><span class="crayon-o">*</span><span class="crayon-sy">)</span><span class="crayon-o">&</span><span class="crayon-v">fnum</span><span class="crayon-sy">;</span></div><div class="crayon-line" id="crayon-5a3a8bcbaf0f9414302482-8"><span class="crayon-h"> </span><span class="crayon-st">while</span><span class="crayon-h"> </span><span class="crayon-sy">(</span><span class="crayon-v">fnum</span><span class="crayon-h"> </span><span class="crayon-o">!=</span><span class="crayon-h"> </span><span class="crayon-cn">0</span><span class="crayon-sy">)</span></div><div class="crayon-line" id="crayon-5a3a8bcbaf0f9414302482-9"><span class="crayon-h"> </span><span class="crayon-sy">{</span></div><div class="crayon-line" id="crayon-5a3a8bcbaf0f9414302482-10"><span class="crayon-h"> </span><span class="crayon-r">printf</span><span class="crayon-sy">(</span><span class="crayon-s">"input a num: "</span><span class="crayon-sy">)</span><span class="crayon-sy">;</span></div><div class="crayon-line" id="crayon-5a3a8bcbaf0f9414302482-11"><span class="crayon-h"> </span><span class="crayon-e">scanf</span><span class="crayon-sy">(</span><span class="crayon-s">"%f"</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-o">&</span><span class="crayon-v">fnum</span><span class="crayon-sy">)</span><span class="crayon-sy">;</span></div><div class="crayon-line" id="crayon-5a3a8bcbaf0f9414302482-12"><span class="crayon-h"> </span><span class="crayon-st">for</span><span class="crayon-h"> </span><span class="crayon-sy">(</span><span class="crayon-v">i</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-cn">31</span><span class="crayon-sy">;</span><span class="crayon-h"> </span><span class="crayon-v">i</span><span class="crayon-h"> </span><span class="crayon-o">>=</span><span class="crayon-h"> </span><span class="crayon-cn">0</span><span class="crayon-sy">;</span><span class="crayon-h"> </span><span class="crayon-v">i</span><span class="crayon-o">--</span><span class="crayon-sy">)</span></div><div class="crayon-line" id="crayon-5a3a8bcbaf0f9414302482-13"><span class="crayon-h"> </span><span class="crayon-sy">{</span></div><div class="crayon-line" id="crayon-5a3a8bcbaf0f9414302482-14"><span class="crayon-h"> </span><span class="crayon-r">printf</span><span class="crayon-sy">(</span><span class="crayon-s">"%d"</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-sy">(</span><span class="crayon-o">*</span><span class="crayon-v">p</span><span class="crayon-h"> </span><span class="crayon-o">&</span><span class="crayon-h"> </span><span class="crayon-sy">(</span><span class="crayon-cn">1</span><span class="crayon-h"> </span><span class="crayon-o"><<</span><span class="crayon-h"> </span><span class="crayon-v">i</span><span class="crayon-sy">)</span><span class="crayon-h"> </span><span class="crayon-sy">?</span><span class="crayon-h"> </span><span class="crayon-cn">1</span><span class="crayon-o">:</span><span class="crayon-h"> </span><span class="crayon-cn">0</span><span class="crayon-sy">)</span><span class="crayon-sy">)</span><span class="crayon-sy">;</span></div><div class="crayon-line" id="crayon-5a3a8bcbaf0f9414302482-15"><span class="crayon-h"> </span><span class="crayon-sy">}</span></div><div class="crayon-line" id="crayon-5a3a8bcbaf0f9414302482-16"><span class="crayon-h"> </span><span class="crayon-r">printf</span><span class="crayon-sy">(</span><span class="crayon-s">"\n"</span><span class="crayon-sy">)</span><span class="crayon-sy">;</span></div><div class="crayon-line" id="crayon-5a3a8bcbaf0f9414302482-17"><span class="crayon-h"> </span><span class="crayon-sy">}</span></div><div class="crayon-line" id="crayon-5a3a8bcbaf0f9414302482-18"><span class="crayon-h"> </span><span class="crayon-st">return</span><span class="crayon-h"> </span><span class="crayon-cn">0</span><span class="crayon-sy">;</span></div><div class="crayon-line" id="crayon-5a3a8bcbaf0f9414302482-19"><span class="crayon-sy">}</span></div></div></td>
</tr>
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