What are the implications of section 922(g)(1) of the 18.22(b) section of the Federal Criminal Code for possessing firearms that have been shipped or transported in interstate or foreign commerce?

Title 18 U.S.C. 922(g)(1) makes it unlawful for any person "who has been convicted in any court of [ ] a crime punishable by imprisonment for a term exceeding one year" from possessing firearms that have been shipped or transported in interstate or foreign commerce. Murillo's two predicate offenses do not fall within section 922(g)(1)'s exceptions (certain business practice violations and state misdemeanors), see 18 U.S.C. 921(a)(20), and his guilty pleas constitute convictions, see United States v. Marks, 379 F.3d 1114, 1117-18 (9th Cir.2004), cert. denied, ___ U.S. ___, 125 S.Ct. 1355, 161 L.Ed.2d 148 (2005). Thus, the issue is whether his convictions were of crimes punishable by a term exceeding one year.