为什么我们需要添加1，在做2的补 [英] Why we need to add 1 while doing 2's complement

问题描述

基于2的数值，即由重N位psented $ P $补为2 ^ N个。结果
例如：如果数字是7（0111），我再$ P $使用4位，然后它psenting，2对它的补充将是（2 ^ N个），即（2 ^ 4-7）= 9（1001 ）结果

The 2's complement of a number which is represented by N bits is 2^N-number.
For example: if number is 7 (0111) and i'm representing it using 4 bits then, 2's complement of it would be (2^N-number) i.e. (2^4 -7)=9(1001)

7==> 0111
1's compliment of 7==> 1000
1000
+  1
-------------
1001 =====> (9)

在计算2的一数目的补体，我们以下步骤：
1.做数的补
2.添加一个步骤1的结果。

While calculating 2's complement of a number, we do following steps: 1. do one's complement of the number 2. Add one to the result of step 1.

据我了解，我们需要做数的补，因为我们正在做一个否定操作。但是为什么我们添加了1？

I understand that we need to do one's complement of the number because we are doing a negation operation. But why do we add the 1?

这可能是一个愚蠢的问题，但我有一个很难理解的逻辑。用上面的例子解释（为7号），我们做一补，让-7，然后添加+1，所以-7 + 1 = -6，但我们仍然不能在正确的答案，即+9

This might be a silly question but I'm having a hard time understanding the logic. To explain with above example (for number 7), we do one's complement and get -7 and then add +1, so -7+1=-6, but still we are getting the correct answer i.e. +9

推荐答案

您错误是在我们做一个人的称赞，并得到-7。为了说明为什么这是错的，采取7人的补充和增加7到它。如果是-7，你应该为零，因为-7 + 7 = 0，你不会的。

Your error is in "we do one's compliment and get -7". To see why this is wrong, take the one's complement of 7 and add 7 to it. If it's -7, you should get zero because -7 + 7 = 0. You won't.

中7的补是 1000 。加入7到，你会得到 1111 。绝对不是零。你需要一个更添加它来获得零！

The one's complement of 7 was 1000. Add 7 to that, and you get 1111. Definitely not zero. You need to add one more to it to get zero!

一些负面的是你需要添加到它得到零数。

The negative of a number is the number you need to add to it to get zero.

如果您添加 1 到 ... 11111 ，你就会得到零。因此，-1，再presented所有1位。

If you add 1 to ...11111, you get zero. Thus -1 is represented as all 1 bits.

如果您添加一个数字，说 X ，其1的补〜X ，你得到所有1位

If you add a number, say x, to its 1's complement ~x, you get all 1 bits.

这样：结果
〜X + X = -1

Thus:
~x + x = -1

加1到两边：结果
〜X + X + 1 = 0

Add 1 to both sides:
~x + x + 1 = 0

从两边减去X：结果
〜X + 1 = -x

Subtract x from both sides:
~x + 1 = -x

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