For binary data, I would recommend using a category encoder with string categories of “0” and “1”. This will assure they have no overlap between them. I have an example of this in my cellular automata prediction project. Have a look in this video:
Also, I noticed when I built this project that I could have used better n and w values for the category encoders I created. They should be adjusted so that w takes up roughly half of the n input space because there are only 2 possible inputs.