Hello Kadkins,
The highest number we need to send to communicate months would be 12 (December). This could be represented like so in binary: 1100
The highest day we might need to send would be 31. In binary that could be: 11111
The protocol could state that the first four bits indicate the month and the last five bits indicate the day.
We need a total of at least nine bits in order to communicate the biggest possibility (12/31).
12/31: 110011111
Other examples:
1/5: 000100101 (0001 = 1, 00101 = 5)
5/25: 010111001 (0101 = 5, 11001 = 25)
Hope this helps!
~ Hannah