The OP doesn't say but I'm going to assume 8 bits to a symbol, for a total of 24 bits per packet (this is an unusual packet length but we'll roll with it. ATM frames are 424 bits, so it's not too weird.)
An alien can't automatically translate a given binary pattern to a given symbol. Remember that everything in a computer is binary, all the instructions, all the data...it's all binary. What matters is the context of a particular binary sequence. For example "0x30" (hex) or "0011 0000" (binary) can mean a lot of different things depending on where you find it. If it's an instruction on an Intel x86 cpu then it's an 'XOR' command. If it's in ASCII, then it's '0'. Translating binary strings into symbols isn't automatic.
Progression of Concepts
Binary first. This should be painfully obvious from watching the radio amplitude or frequency graphs. Two groups with sufficient technology to detect and utilize a wormhole will certainly understand binary.
Endianness next. Endianness determines if the first bit in the stream is the largest value or if it is the smallest value. This should be able to establish with some simple addition. Adding '001' to '001' is '010' establishes big-endianness.
Operations next. Sending through strings of basic operations like '000001 000001 000001 000010' and '000010 000001 000001 000000' would be enough to establish 'add' and 'subtract'. Each operation string will ensure that the aliens know how to execute a specific command.
They would send back a similar set of operations from which a primitive CPU and memory model can be derived. With that CPU model, we can start running their programs and they can start running ours. Distinguishing between programs and data can be specified by specific binary sequences. Essentially, we're telling them we both know about and know how to build a Universal Turing Machine.
Programs and Data
Eventually, when you've established a set of operations, then you can start sending them programs and data. With a program, you can convey pretty much anything. Images, maps, 3D models, anything you want. Any data we send them will be subjected to statistical analysis so over time, we could teach them English and they can teach us Alien. This would be a very lengthy process but ultimately doable.
We require more bandwidth
Bandwidth is going to be a real problem very quickly. The search will be on for faster means of transmitting data. Every scientific profession under the sun is going to want to ask questions. The cosmologists will want to know if the aliens can see a place where there are no stars or the cosmological microwave background is different than ours. They will have similar questions to us too.