Does being was convicted of bigamy and adjudicated guilty in 1996 mean that my second marriage is automatically annulled?

Generally, if one person in a couple purporting to become married is not legally eligible to be married, such as by having a previously existing and non-terminated marriage to another person, then the subsequent purported marriage would be null and void. Significantly more information would be needed, however, to analyze the situation described in the message you posted. It would be wise for you to consult with a domestic relations attorney about the issue, and, if the question is being asked in the context of an immigration legal matter, it would be wise for you to consult with an immigration attorney too.