加减补码 [英] Adding and subtracting two's complement

问题描述

使用六位 1 和 2 的补码表示我试图解决以下问题:

Using six-bit one's and two's complement representation I am trying to solve the following problem:

12 - 7 

现在，我先取二进制的 12 和二进制的 7.

Now, i take 12 in binary and 7 in binary first.

12 = 001100 - 6 bit 
7 =  000111 - 6 bit

那么，我是否会翻转二进制补码的位并加一个?

Then, would I then flip the bit for two's complement and add one?

12 = 110011 ones complement 
     +    1
    -------
     001101

7  = 111000 ones complement 
    +     1
   ---------
      111001

然后，将这两个补码相加

then, add those two complement together

 001101
+111001
-------
1000110 = overflow? discard the last digit?  If so I get 5

现在，如果我有类似的数字

Now, if I have a number like

-15 + 2

如果 MSB 为零，我会在 MSB 上添加一个符号幅度?

I would then add a sign magnitude on the MSB if it's a zero?

喜欢:

-15 = 001111 6 bit

在我翻转位之前我会在最后添加一个 1 吗?

Would I add a 1 at the end here before I flip the bits?

  = 101111

推荐答案

用补码表示负数的好处是减法和加法是一样的.在您的情况下，您可以将 12 - 7 视为 12 + (-7).因此，您只需要找到 -7 的二进制补码表示并将其添加到 +12:

Using two's complement to represent negative values has the benefit that subtraction and addition are the same. In your case, you can think of 12 - 7 as 12 + (-7). Hence you only need to find the two's complement representation of -7 and add it to +12:

12  001100
-7  111001   -- to get this, invert all bits of 7 (000111) and add 1
----------
 5 1000101

然后丢弃进位(表示溢出)，得到结果:000101，如预期的那样等于 5.

Then discard the carry (indicates overflow), and you have your result: 000101 which equals to 5 as expected.

对于您的 -15 + 2 示例，只需按照相同的过程即可获得 -15 的二进制补码表示:

For your example of -15 + 2, simply follow the same procedure to get the two's complement representation of -15:

15  001111
    110000   -- inverted bits
    110001   -- add 1

现在像往常一样添加:

-15  110001
  2  000010
-----------
res  110011

要看到 res 确实等于 -13，您可以看到它是负数(MSB 集).对于幅度，转换为正数(反转位，加 1):

To see that res indeed equals -13, you can see that it is negative (MSB set). For the magnitude, convert to positive (invert bits, add 1):

res  110011
     001100  -- inverted bits
     001101  -- add 1

因此，如预期的那样，震级为 13.

Hence the magnitude is 13 as expected.

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