trouble understanding

Hello all, I am new to arduino (as a matter of fact to programming). I am thinking to use arduino due for my academic projects. While going through it's datasheet(SAM3X8E datasheet from Atmel) I came across timers, and it is said that all are 32bit counters. And they count till 0xFFFF before going to 0x0000 again. I am confused a bit. Shouldn't they count till 0xFFFFFFFF(before going to zero) as they are 32bit counters. I think 16bit counters are one's which count till 0xFFFF. May be what i ask is silly but please throw some light on it.

Thanks in advance..