Can we add 1908+100, kids?
centennial and 100th birthday is 100 years after. That is, if birthdate was in 1908, 100th birthday is in 2008.
Maybe confused with that crap about centuries starting in '01 years? That's because dumb people (almost) 2007 years ago didn't know about, or use the number 0. Then you have historians back then screwing up and eating away 0 AD so "historic time" doesn't equate with "astronomic time", "ISO time" or any other mathematically useful date system.
So basically the century rollover is in '01 because first century was 1-100 instead of 0-99, not because of freaky counting. Oh, and that is because you're counting from the first day of first year, to last day of last year. Move over the "start pointer" one day, and you would get 0-100 or 1-101. ;)