加减二的补 [英] Adding and subtracting two's complement
问题描述
使用六位一个人的和补重presentation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，我拿12二进制和7进位争先。
Now, i take 12 in binary and 7 in binary first.
12 = 001100 - 6 bit
7 = 000111 - 6 bit
然后，我会然后翻转两个的补位和添加一个？
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
那么，加这两个互补在一起
then, add those two complement together
001101
+111001
-------
1000110 = overflow? discard the last digit? If so I get 5
现在，如果我有一个像
-15 + 2
我会再上MSB添加一个标志幅度，如果它是一个零？
I would then add a sign magnitude on the MSB if it's a zero?
这样的：
-15 = 001111 6 bit
我将在这里就结束了加1之前，我翻转位？
Would I add a 1 at the end here before I flip the bits?
= 101111
推荐答案
使用二的补重新present负值具有减法和加法是相同的好处。你的情况，你能想到的 12 - 7 为 12 +（-7）。因此，你只需要找到补重-7 presentation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（表示溢出），你有你的结果： 000101 如预期相等于5
有关你的的例子-15 + 2 ，只需按照相同的步骤，得到-15补重presentation：
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
现在做加法和往常一样：
Now do the addition as usual:
-15 110001
2 000010
-----------
res 110011
要看到 RES 确实等于-13，你可以看到它是负（MSB集）。对于大小，转换为正（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，幅度为13预期。
Hence the magnitude is 13 as expected.
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