How to find out if the input of a logic gate is negative in two's complement?
In two’s complement, the most significant bit (MSB) of all \$ N \$ bits involved is the sign indicator, so it would be sufficient to just look at the MSB of the bits going into your logic gate. Is it 0, then the number is positive. Is it 1, then the number is negative and you have to subtract \$ 2^{(N-1)} \$ from the number represented by the other \$ N-1 \$ bits in order to get the value.

A NOT gate's output of which the input is fed with the MSB will reflect the state of the input number. 0 means positive, 1 means negative.