A logic board with two inputs where the state of the output changes upon changes in any of the inputs
You describe the operation of an XOR gate - readily available as four two-input gates in one IC.

Edit

An XOR gate will output True if the outputs are different, and False if the inputs are the same.  If the outputs are different, and one of them changes state, the output will also change state.  Similarly, if the inputs are the same, and one changes state, the output will also change state.

Thinking harder, if both inputs change state at the same time, the output will not change.  If that will happen, then an XOR gate won't meet your requirements.