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I hate to use wiki, but in a hurry it sometimes does the job.

On July 2, 1980, however, President Carter signed Proclamation 4771, Registration Under the Military Selective Service Act in response to the Soviet Union’s invasion of Afghanistan,[14] retroactively re-establishing the Selective Service registration requirement for all 18–26 year old male citizens born on or after January 1, 1960.[15] Only men born between March 29, 1957, and December 31, 1959, were completely exempt from Selective Service registration.[16] The first registrations after Proclamation 4771 took place on Monday, July 21, 1980, for those men born in January, February and March 1960 at U.S. Post Offices. Tuesdays, Wednesdays and Thursdays were reserved for men born in the later quarters of the year, and registration for men born in 1961 began the following week.[17]

If you were born between 3-39-57 and 12-31-59 you were completely exempt from selective service. If you turned 18 in 78, you were born in 60 and 18 in 79, you were born in 61. Neither which are during 1957-1959. Barry had to register in 1980 unless he skipped by using his Indonesian passport to register and he would have used an international 999-xx-xxxx student ID.