How can I create a Boolean logic gate without the steam punk logic gates?

Solution 1:

The Steampunker NPC is available on console and mobile versions of the game, but unfortunately she only sells logic gates on the PC version.

However, you can still do some logic gates manually. They take up a lot of space, but it is possible. It's a bit of a complex topic, however, and it's not really something I'm particularly good at, so I'll leave this video to explain in a little more detail:

Wiring Logic using crab statues, faster bird gates

Though this video is from the PC version, you should have most of the necessary items to follow along on console/mobile.