CODEWITHSUNDEEP
bitwise-operatorsbit
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Reputation: 401

Why is ~x = -x -1

I don't understant why ~x = -x-1 is true. It seems counter-intuitive to me to take the inverse when negating a number. Shouldn't -x just be x with the -/+ bit as 1? Or is this ~x = -x-1 just a hard set rule...

Upvotes: 1

Views: 717

Answers (1)

David
David

Reputation: 8298

the ~ operator flip all the bits. While -x is taking the minus of a certain value which is different. This is because the bit-wise operator inverts each bit in the word. It is not an arithmetic operation, it is a logic operation.

Let's consider the following example that will emphasize this issue for words of length 3:

The range of values that you can represent is from -4 to 3. If you are not familiar with it read about 2's complementnt

011 represent the value 3 -> ~3 is 100 which is -4.

Where -3 is 101 and when subtracting 1 you get 100 which is 4.

so when taking the negative value we need to also subtract 1 because the range is -2^(B) - 2^(B) - 1 and we need to compensate.

Upvotes: 1

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