The use of "not" in a sentence

I would understand this sentence to read "not knowing and not willful." There is no concrete rule stating that it must be understood this way, but if someone meant "not knowing but also willful," he would certainly word the phrase differently to prevent the inherent ambiguity. A sentence meaning the latter would more likely be worded: "His failure to register was not knowing but was indeed willful."

Checking this context, it should read more like this:

His failure to register was not "knowing and willful".

...which means that it was either not knowing, not willful, or both not knowing and not willful.

EDIT: This does not constitute legal opinion, by the way, just ordinary interpretation of the negation of a phrase with two conditions joined by "and". There were several places I found the phrase, and they all hinge on interpretation of legal phrase "knowing and willful", so if the OP can post the original context, it may be helpful.