The message is pretty clear: binary returns a String, and you want to assign to an array of strings, which cannot work: an element isn't an array, at least in Java.
Perhaps what you want to do is:

1.   String[] bin = new String[data.length];
   
2.   for (int i = 0; i < data.length; i++) {
3.     receivedFromUDP += str(data[i]) + " ";
4.     bin[i] = binary(data[i]);
5.   }

1) Don't make duplicate threads. I deleted the "saving string into array" topic because it was basically the same thing than this one, with just another attempt of fixing the code. It is better to post another message here, or to edit your message to add information.
2) No need to post everything in General Discussion. I move there messages without code, but you show some code here. See the https://forum.processing.org/topic/where-to-place-threads-and-other-forum-practices thread.