7404N and high output
What you are doing with the two outputs is not okay.

Basically if one of them wants to be high and the other wants to be low, they will compete and force limiting currents through each other, very likely damaging them, because you cannot guarantee in any case that they will go high or low at the same time, since then you'd have to tie both inputs together as well.

Depending on what you want to do exactly (not sufficiently clearly specified for me), in the sense of combining them you need OR, or AND, or NOR, or NAND gates, or diodes and/or transistors to do that for you.