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It’s just a random thought.
The two’s complement of 100…(31 zeros) is also 100…
So, the value must be 0. But we know that the binary representation of 0 is 000…
I know it can’t be a -0 and a +0 because every binary representation should map to a unique value.
It’s −231. Two’s complement has only a single zero and the negative range extends one number further than the positive. And yes, that means that there is a single negative number that has no positive equivalent – this is sometimes called the »weird number« since it is an exception of how two’s complement numbers are built.