That really only matters at higher levels of communication, not the barebone basics that we're talking about here. When we are referring to 1, 2, 3, etc., we're not referring to our ASCII representations of the numbers. We're referring to literal pulses or some kind of other countable thing. While sending what a layman would call a simple message would be difficult, the kind of simple message we are talking about is very doable.

that they might not use binary logic, but tertiary logic instead. They might not use 8 bits as a smallest package of data.

People did both of those things in computers. They have also decoded encrypted messages where they didn't know the algorithm or the key. And, as others have said, in this case you start with simple messages, establishing the basic boundaries of transmission, before trying to communicate most primitive ideas.

I confess, I was kind of baiting with the "decode the transmission" part. As someone else mentioned, the way we send the info doesn't have to be as complicated as what you're thinking. Many books and movies have been made about the subject... Contact and Project Hail Mary come to mind immediately. SETI is dedicated to being on the receiving end and makes assumptions about what ET would be sending based on assumptions about what we would send (filtering for repeating patterns and mathematical structures on narrow frequency bands).

In any case, how we transmit and what we transmit are two different things. What we transmit will likely be math and/or cosmos related, things we have in common with our galactic cousins (we assume). How we transmit... There are a million ways, so we narrow it down to what we think is the most likely to reach the target and be something they're listening for. And cross our fingers.