怎么办整数两者相辅相成，乘法和除法？ [英] how to do two complement multiplication and division of integers?

问题描述

我已阅读本帖子上使用两个二进制补码乘法。但对我来说并不很清楚。即使我很难理解维基在这篇文章。我想知道如何去计算负数的乘法：

I have read this post on binary multiplication using two complement. but it is not very clear to me. Even I have difficulty understanding the wiki article on this. I want to know how to go about calculating multiplications of negative numbers:

eg: -1 with -7 should give 7.
A 4-bit, 2's complement of -1 is : 1111
A 4-bit, 2's complement of -7 is : 1001

计算所述乘法会有所帮助的一些逐步方式。没有文章中，我遇到了关于分工会谈。如何处理呢？

some step-wise way of calculating the multiplication will be helpful. No article I came across talks about division. How to approach this?

推荐答案

第1步：符号扩展这两个整数的两倍位。这是安全的，但可能不总是必要的。

step 1: sign extend both integers to twice as many bits. This is safe to do, though may not always be necessary.

for 4-bit --> 1111, you would extend as 1111 1111
for 4-bit --> 0111,you would extend as 0000 0111

第2步：做乘法基本

step 2: do elementary multiplication

09月03日：取结果位的正确数量从结果的至少显著部

sep 3: take the correct number of result bits from the least significant portion of the result.

例如：乘法后，你最终为 0010011110 一些诸如取后8位，即 10011110

eg: after multiplication, you end up with something such as 0010011110take the last 8 bits i.e 10011110

让我说明你提供的例子： 1 X -7 4位再presentation

Let me illustrate with the example you provided: -1 X -7 in 4-bit representation

         1111 1111        -1
       x 1111 1001     x  -7
      ----------------    ------
          11111111         7
         00000000
        00000000
       11111111
      11111111
     11111111
    11111111
   11111111
   ----------------
1  00000000111       --->  7 (notice the Most significant bit is zer``o)
      --------  (last 8-bits needed) 

您可以得到更多的细节这里;

you could get more details here;

有关划分：转换为正，计算后调整迹象。我将离开这个锻炼，但你可以参考这个页面。

for division: convert to positive and after the calculation adjust the sign. I will leave this as exercise but you could refer this page.

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