Newly Adopted Cat is Biting

I adopted a cat on Christmas Eve - he was from the ASPCA and had been found at the zoo, so there was no way to tell if he was handled by people. Now that I've had him for a month, he has adapted well, has gained weight, uses the litter without issue and is now playing with toys (which he had no interest in when I first bought him home) - the only issue is that he wants to play all the time. When he isn't playing (and even when he is) he bites my hands and feet. If I am in bed and he wants to be pet, he will bite my hand. I've tried giving him new toys to divert his attention but it hasn't worked. Hes about a year or so old so I was hoping it;s a phase. But its not looking like it. Any thoughts? Words of advice? 

Does he bite or nip? Is he a kitten or a young cat? If he's a kitten or a young cat and nips, he's being playful, and it's likely to be a phase. If he's an adult cat and chomps on you, then there is probably a behavioral problem based on how he was treated by previous owners.

I'm hoping you haven't used your hands as toys... we're all very tempted to do it, but they'll keep on attacking fingers if they've ever been allowed to.  Same, of course, for feet.

Age really is a consideration..

Also, when male cats /kittens get overstimulated, they tend to nip, or bite, but do not usually break skin. Most kittens like to chase and "catch" anything that moves, even if it is your hand! When they are being playful, they should not be biting you and breaking any skin or drawing blood.

He bites - as if he were playing. I think he thinks I am a cat sometimes (who feeds him and throws his toys). He's my third cat and have learned early on that hands and feet are not toys! Learned that one the hard way back in my teens! The ASPCA said he's about 2 years old, however my vet thinks he's younger. Id say he is closer to a year maybe year and a half. He never knew what toys were until I brought him home. He didn't know what to do with them. He's not drawing blood - thankfully but his claws dig in as if I were prey! It's only been a month since I've had him and I feel that he's adjusting well. But if you all have any thoughts on deterrents on this behavior it would be appreciated! He is super friendly and trusting and I think it is a stimulation thing. I just want to make sure I am managing it correctly to change his behaviors.