Why does -INT_MIN = INT_MIN in a signed, two's complement representation?

Question

I still haven\'t found a reason why the lowest signed negative number doesn\'t have an equivalent signed positive number? I mean in a 3 digit binary number for simplicity 10

Answer 1

The missing digit is 0. In a mathematical sense, 0 is neither positive nor negative. But in a binary sense, since 0 has no negative bit, it's considered positive. In other words, if you wanted -128 to 128, there couldn't be a 0.