I wouldn't worry to much. It's probably just a phase and more than likely just him testing a way to get your attention, or it could just be excitement on his part. At 16 months they can't control themselves and don't really understand that , that is wrong. I wouldn't worry to much about it...lots of kids go through that and turn out to be wonderful children. :)
This is what I did...it worked well for me. After the hit to my face. I would grab their offending arm, and hold it. (this usually surprises them and puts them on pause) I would then look them in their eye, and say "No" (they understand that word very well) "We don't hit, that hurts mommy". I would put them down immediatly and walk away. If they go into a tantrum, I ignore and find something to occupy my time. Eventually they realize that hitting and having a tantrum won't get responses. After they have calmed down a bit...I usually try to distract them, by offering to read a book or something after they have calmed down. That is my way of reinforcing positive behavior. I react to the good behavior, not the bad.
It really should clear up on it's own if you stick to a universal reaction to his hitting or tantrums. Time outs won't really work at his age, he's to young to stay still. BUT, walking out of the room into a room that maybe has a gate in front of it, means you have removed yourself from the situation, but he can still see you, but can't get to you.