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📁 浙江大学计算机学院计算机组成教材《计算机组成与设计》（潘学增）的课堂教学课件。
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<h3 align="center"><font color="#000000" size="6"><b>4.7 Division 除法运算</b></font></h3>                                         
<p align="right"><font color="#000000"><a href="chapter4.htm"><img border="0" src="images/BACK.GIF" width="60" height="45" align="left"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;        
<a href="4-6.htm"><img border="0" src="images/PREV.GIF" width="60" height="45"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;         
<a href="4-8.htm"><img border="0" src="images/FORW.GIF" width="60" height="45"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</font></p>                                    
<p align="left"><font color="#000000" size="4">本节问题：</font></p>                                  
<p align="left"><font color="#000000" size="4"><img border="0" src="images/SUB.GIF" width="26" height="27"><a href="#除法的基本原理">除法的基本原理</a><br>                                
<img border="0" src="images/SUB.GIF" width="26" height="27"><a href="#第一代除法算法和硬件设计">第一代除法算法和硬件设计</a><br>                                
<img border="0" src="images/SUB.GIF" width="26" height="27"><a href="#第二代除法算法和硬件设计">第二代除法算法和硬件设计</a><br>                               
<img border="0" src="images/SUB.GIF" width="26" height="27"><a href="#第三代除法算法和硬件设计">第三代除法算法和硬件设计</a><br>                      
<img border="0" src="images/SUB.GIF" width="26" height="27"><a href="#加减交替法">加减交替法</a><br>                      
<img border="0" src="images/SUB.GIF" width="26" height="27"><a href="#带符号数除法运算">带符号数除法运算</a><br>                      
<img border="0" src="images/SUB.GIF" width="26" height="27"><a href="#MIPS机除法的实现">MIPS机除法的实现</a></font></p>                               
<p align="left"><font color="#000000" size="4">一：<a name="除法的基本原理">除法的基本原理</a></font></p>                               
<p align="left"> <font color="#000000" size="4">&nbsp;&nbsp;&nbsp; 我们根据十进制手工运算方法回忆除法基本原理，divide 1001010<sub>ten</sub>                                       
by 1000<sub>ten</sub>。<br>                                      
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;                                   
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;  
1001<sub>ten</sub>&nbsp;&nbsp; Quotient<br>                                   
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;   
__________<br>                                  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Divisor1000<sub>ten</sub>|1001010<sub>ten</sub>&nbsp;&nbsp;&nbsp;&nbsp;                                   
Dividend<br>                                  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;   
-1000<br>                                 
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;   
________<br>                                 
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;  
001010<br>                                 
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;  
-1000<br>                                 
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<br>                                 
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<br>                                 
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;                                   
_______ <br>                                  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;                                   
10<sub>ten</sub>&nbsp;&nbsp;&nbsp;&nbsp; Remainder<br>                                
&nbsp;&nbsp;&nbsp; Dividend=Quotient × Divisor + Remainder<br>                                 
&nbsp;&nbsp;&nbsp; 这里Remainder要小于Divisor,二进制除法的原理同上。</font></p>                                
<p align="left"><font color="#000000" size="4">二：<a name="第一代除法算法和硬件设计">第一代除法算法和硬件设计</a></font></p>                              
<p align="left"><font color="#000000" size="4">&nbsp;&nbsp;&nbsp; 具体的算法和流程图如下，同时我们需要32-bit Quotient register并将其初始化为0，每一步需要将divisor向右移动一位，因此我们还需要64-bit                                  
Divisor rigister并将Divisor赋于Divisor register的左半部分并每一步向右移动一位。</font></p>                                 
<p align="center"><font color="#000000" size="4"><img border="0" src="images/4-7-pic1.gif" width="721" height="406"></font></p>                              
<p> <font color="#000000" size="4">&nbsp;&nbsp;&nbsp; Example: Using a 4-bit                                  
version of the algorithm to save pages, let's try dividing 7<sub>ten</sub> by&nbsp;&nbsp;<br>                                
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;                 
&nbsp;&nbsp;&nbsp;&nbsp; 2<sub>ten</sub> or 0000 0111<sub>two</sub> by 0010<sub>two</sub>.<br>                                 
&nbsp;&nbsp;&nbsp; Answer:这种方法需要运行n+1步，每一步中的step2通过检测remainder                                 
register 的符号位来看<br>                                
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;                 
&nbsp;&nbsp; remainder是正还是负。如下表：</font></p>                                
<p align="center">　</p>                                
<div align="center">                                
  <center>                                
  <table border="1" cellpadding="0" cellspacing="0" width="648" height="231" bordercolordark="#CC9966" bordercolorlight="#FFCC66">                                
    <tr>                                
      <td width="87" height="17" bgcolor="#CCFF99">                                
        <p align="center"><font color="#000000" size="4">Iteration</font></td>                               
      <td width="243" height="17" bgcolor="#CCFF99">                               
        <p align="center"><font color="#000000" size="4">Step</font></td>                               
      <td width="99" height="17" bgcolor="#CCFF99">                               
        <p align="center"><font color="#000000" size="4">Quotient</font></td>                               
      <td width="116" height="17" bgcolor="#CCFF99">                               
        <p align="center"><font color="#000000" size="4">Divisor</font></td>                               
      <td width="91" height="17" bgcolor="#CCFF99">                               
        <p align="center"><font color="#000000" size="4">Remainder</font></td>                               
    </tr>                               
    <tr>                               
      <td width="87" height="19">                               
        <p align="center"><font color="#000000" size="4">0</font></td>                               
    </center>                               
    <td width="243" height="19">                               
      <p align="left"><font color="#000000" size="4">Initial Values</font></td>                                
    <center>                                
    <td width="99" height="19">                                
      <p align="center"><font color="#000000" size="4">0000</font></td>                               
    <td width="116" height="19">                               
      <p align="center"><font color="#000000" size="4">0010 0000</font></td>                                
    <td width="91" height="19">                                
      <p align="center"><font color="#000000" size="4">0000 0111</font></td>                                
    </tr>                                
    <tr>                                
      <td width="87" height="56" rowspan="3">                                
        <p align="center"><font color="#000000" size="4">1</font></td>                               
    </center>                               
    <td width="243" height="18">                               
      <p align="left"><font color="#000000" size="4">1: Rem=Rem-Div</font></td>                               
    <center>                               
    <td width="99" height="18">                               
      <p align="center"><font color="#000000" size="4">0000</font></td>                               
    <td width="116" height="18">                               
      <p align="center"><font color="#000000" size="4">0010 0000</font></td>                                
    <td width="91" height="18">                                
      <p align="center"><font color="#000000" size="4">1110                                 
      0111</font></td>                                
    </tr>                                
  </center>                                
  <tr>                                
    <td width="243" height="17">                                
      <p align="left"><font color="#000000" size="4">2b:Rem&lt;0 =&gt;+Div,sll                                 
      Q,Q0=0&nbsp;</font></td>                                
    <center>                                
    <td width="99" height="17">                                
      <p align="center"><font color="#000000" size="4">0000</font></td>                               
    <td width="116" height="17">                               
      <p align="center"><font color="#000000" size="4">0010 0000</font></td>                                
    <td width="91" height="17">                                
      <p align="center"><font color="#000000" size="4">0000 0111</font></td>                                
    </tr>                                
  </center>                                
  <tr>                                
    <td width="243" height="21">                                
      <p align="left"><font color="#000000" size="4">3: Shift Div right</font></td>                                
    <center>                                
    <td width="99" height="21">                                
      <p align="center"><font color="#000000" size="4">0000</font></td>                               
    </center>                               
    <td width="116" height="21">                               
      <p align="center"><font color="#000000" size="4">0001 0000</font></td>                                
    <center>                                
    <td width="91" height="21">                                
      <p align="center"><font color="#000000" size="4">0000 0111</font></td>                                
    </tr>                                
    <tr>                                
      <td width="87" height="56" rowspan="3">                                
        <p align="center"><font color="#000000" size="4">2</font></td>                               
    </center>                               
    <td width="243" height="19">                               
      <p align="left"><font color="#000000" size="4">1: Rem=Rem-Div</font></td>                               
    <center>                               
    <td width="99" height="19">                               
      <p align="center"><font color="#000000" size="4">0000</font></td>                               
    <td width="116" height="19">                               
      <p align="center"><font color="#000000" size="4">0001 0000</font></td>                                
    <td width="91" height="19">                                
      <p align="center"><font color="#000000" size="4">1111                                 
      0111</font></td>                                
    </tr>                                
  </center>                                
  <tr>                                
    <td width="243" height="18">                                
      <p align="left"><font color="#000000" size="4">2b:Rem&lt;0 =&gt;+Div,sll                                 
      Q,Q0=0&nbsp;</font></td>                                
    <center>                                
    <td width="99" height="18">                                
      <p align="center"><font color="#000000" size="4">0000</font></td>                               
    <td width="116" height="18">                               
      <p align="center"><font color="#000000" size="4">0001 0000</font></td>                                
    <td width="91" height="18">                                
      <p align="center"><font color="#000000" size="4">0000 0111</font></td>                                
    </tr>                                
  </center>                                
  <tr>                                
    <td width="243" height="19">                                
      <p align="left"><font color="#000000" size="4">3: Shift Div right</font></td>                                
    <center>                                
    <td width="99" height="19">                                
      <p align="center"><font color="#000000" size="4">0000</font></td>                               
    <td width="116" height="19">                               
      <p align="center"><font color="#000000" size="4">0000 1000</font></td>                                
    <td width="91" height="19">                                
      <p align="center"><font color="#000000" size="4">0000 0111</font></td>                                
    </tr>                                
    <tr>                                
      <td width="87" height="51" rowspan="3">                                
        <p align="center"><font color="#000000" size="4">3</font></td>                               
    </center>                               
    <td width="243" height="17">                               
      <p align="left"><font color="#000000" size="4">1: Rem=Rem-div</font></td>                               
    <center>                               
    <td width="99" height="17">                               
      <p align="center"><font color="#000000" size="4">0000</font></td>                               
    <td width="116" height="17">                               
      <p align="center"><font color="#000000" size="4">0000 1000</font></td>                                
    <td width="91" height="17">                                
      <p align="center"><font color="#000000" size="4">1111                                 
      1111</font></td>                                
    </tr>                                
  </center>
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