CODEWITHSUNDEEP
c++bit-manipulation
Anirban Sinha
Anirban Sinha

Reputation: 23

Why does ~n give -(n+1)?

I wanted to test what happens when I write this code. I can not explain the following case:

Input: 5 Output: -6

#include <iostream>

int lastBit(int n){   return ~(n); }

int main() {   std::cout << lastBit(5); }

Upvotes: 0

Views: 133

Answers (3)

Anirban Sinha
Anirban Sinha

Reputation: 23

I found out the following

5 = 0101 Therefore, ~(5) = 1010

  1. The 1 at the most significant bit denotes negativee (-)
  2. 010 = 6

Therefore, output is -6 Since this is a 2's complement machine

Upvotes: 0

Spook
Spook

Reputation: 25927

Computers express negative numbers in quite a specific way. Values are always stored as series of bits and there is no way of introducing negative sign, so this has to be solved differently: one of bits plays role of a negative sign.

But this is not all - the system must be designed to handle maths properly (and ideally, the same way as for positive numbers).

So for instance 0 == 0b00000000. If you subtract 1 from 0, you get -1, but from the binary perspective, due to "binary underflow", 0b00000000 - 0b00000001 == 0b11111111, hence 0b11111111 == -1.

If you then subtract 1 from -1, you get 0b11111111 - 0b00000001 == 0b11111110 == -2. But 2 == 0b00000010, which shows, why -2 != ~2 (and the same rule applies to next values).

The very short, but maybe more intuitive answer might be: "-5 != ~5, because there is only one zero binarily (eg. 0 == -0), so there is always one more negative value than positive ones"

Upvotes: 3

Swift - Friday Pie
Swift - Friday Pie

Reputation: 14589

Not on all systems but on systems that use complement of two for signed values. By definition there, the binary representation of negative X = -n, where n is a positive integer, is ~n + 1, which allows signed and unsigned addition operations to be same.

Until C++20 result of ~(n) for signed negative n here would be undefined, because it depends on platform and compiler. In C++20 it's required to behave as if complement of two is used.

Upvotes: 2

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