Let me try some (original and prone to huge error) calculations and try to find your birthday in the Attic Calendar (that's your birthday isn't it), according to the Wiki articles Nickel mentioned above (for Ancient Greek calendar and numerals):
May 2nd was the middle of month Thargelion, sο the 16th day of the Full Moon.
Now about 1983. How many Olympiads had passed since 776BC, the first year of the first Olympiad? (1983+776)/4=689.75 says the calculator, hence the third year of the 690th Olympiad, since we have 689 completed + 3 years into the 690th
In Ancient Greek, all this would be. Note I'm using Attic Numerals to be consistent with the Attic calendar:
ΔΠΙ ΘΑΡΓΗΛΙΩΝΟΣ ΠΙΗΔΗ ΟΛΥΜΠΙΑΣ ΕΤΟΣ ΙΙΙ