Astronomical year numbering
Cassini gave the following reasons for using a year 0:
Fred Espanak of NASA lists 50 phases of the moon within year 0, showing that it is a full year, not an instant in time. Jean Meeus gives the following explanation:
Although he used the usual French terms "avant J.-C." (before Jesus Christ) and "après J.-C." (after Jesus Christ) to label years elsewhere in his book, the Byzantine historian Venance Grumel used negative years (identified by a minus sign, −) to label BC years and unsigned positive years to label AD years in a table. He did so possibly to save space and put no year 0 between them.
Year 2000 problem
Although only two digits are allocated for the birth year in the Bulgarian national identification number, the year 1900 problem and subsequently the Y2K problem were addressed by the use of unused values above 12 in the month range. For all persons born before 1900, the month is stored as the calendar month plus 20, and for all persons born after 1999, the month is stored as the calendar month plus 40.