Why is abs(0x80000000) == 0x80000000?

Question

I just started reading Hacker\'s Delight and it defines abs(-2³¹) as -2³¹. Why is that?

I tried printf(\"%x\", abs(0x80000000)) on a f

Answer 1

Because integers are stored in memory as a two's complement binary number, the positive version of the minimum value overflows back to negative.

That is to say (in .NET, but still applies):

int.MaxValue + 1 == int.MinValue  // Due to overflow.

And

Math.Abs((long)int.MinValue) == (long)int.MaxValue + 1