The perpetual license versions - download and disk (disk now discontiued, I understand) - are platform-specific. You would have to purchase what is called a 'Crossgrade' (PC to Mac). The Cloud versions of the programs will work on either platform.
If you purchased a traditional disc from a store, it was probably platform-specific.
If that's the case for you, I wouldn't even bother buying another physical copy. Go check out Adobe Creative Cloud - it will blow your mind. I've switched to the Creative Cloud ($40/month) and will never go back.
Hope this helps!
To elaborate on OldBob's post,
You would have to purchase what is called a 'Crossgrade' (PC to Mac)
The "purchase" price, from what I hear, is minimum, like less than $20. You will also have to give up all licensing rights to the Windows version.
For more info on Adobe platform swap:
If that's the case for you, I wouldn't even bother buying another physical copy.
Again, in the past, a same version platform swap has cost very little. Contact Adobe Customer Support to see what they say. If you need to use both PC and Mac, then the Cloud subscription might be best option.
Keep in mind you'll not be able to use a perpetual license on BOTH PC and Mac at the same time. Cloud subscriptions allow that.