Interaction term between two binary variables


When including an interaction term between two binary variables (e.g. sex X group) should one shift the binarizations to 1/2 instead of 0/1? It seems like if 0 is an option, then there are only two outcomes possible by the interaction term (0 and 1), despite their but with 1/2 binarization you can get three outcomes (1, 2 and 4). Or if the binarizations are different for terms (e.g. 1/2 and 3/4) then you can get all 4 permutations for the interaction term. Does anyone have a different/preferred approach? Any guidance is appreciated.