How does bitwise not operation give negative value

Question

I want to see how bitwise NOT works through a simple example:

int x = 4;
int y;
int z;
y = ~(x<<1);
z =~(0x01<<1);
cout<<"y = "<<y<<endl;
cout<<"z = "<<z<<endl;

This results in y = -9 and z = -3. I don't see how this happen. Anyone can educate me a bit?

Answer 1

(x<<1) will shift the bits one, so

00000000 00000000 00000000 00000100

will become:

00000000 00000000 00000000 00001000

Which is the representation of 8. Then ~ will invert all the bits such that it becomes:

11111111 11111111 11111111 11110111

Which is the representation of -9.

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0x01 is

00000000 00000000 00000000 00000001

in binary, so when shifted once becomes:

00000000 00000000 00000000 00000010

And then when ~ is applied we get:

11111111 11111111 11111111 11111101

Which is -3 in binary