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Packets, like I said before is communication between the server and the client. If the server wants the client to know they have a HC subscription of 12 days left. The server will send a packet and the client will display some text.
The structure has changed throughout the decade and more of how long Habbo has been around for but we'll talk about present day packet structure.
Structure:
It's important to know that 8 bits go into 1 byte, so 32 bits is 4 bytes. That represents an integer.
[length of packet - not including the length itself] - a 32 bit integer or 4 bytes.
[packet header] - which is 16 bits (2 bytes) and it's called a short in most programming languages
[the rest of the the packet]
If you wanted to write a string, it's UTF8 encoded (normal text like you're reading right now). The structure goes as follows;
[length of string] - short/int16
[string]
If you wanted to write a normal number (the count of rooms) it would be a 32 int or a normal integer. The only time a 16 bit integer is used when you're writing the length of a string or a packet.
Let's not forget booleans, they're just 1 byte, a boolean is either 0 or 1, 0 meaning false and 1 meaning true.
You can see how these are added by looking at sources such as BCStorm for a C# version and Sierra for a Java version.
Glaceon wrote a neat tutorial on how to get packets. As well as Droppy released a program for getting out going ones. Basically, they tell the emulator what to do when something happens and then send that information back to the Habbo.swf to display what you wanted it to do.