Use 64 bit key on 32 bit laptop?

i've got a copy of DOpus (64 bit) for my windows 7 64 bit machine. but i've also got a windows XP laptop (32 bit). i remember reading somewhere that i could use my key for 1 desktop & 1 laptop. does this mean i can install a 32 bit version of DOpus on my lappy & - when i type in the license key i use for my 64 bit desktop machine - it'll work???? or not? in which case, i'll have to buy another copy of DOpus? (which won't happen, as i rarely use my laptop)

additionally, if i do manage to install another copy of DOpus on the laptop with the same license key - and then get a different laptop (perhaps a better one - a 64 bit one or something) - could i remove DOpus from my 32 bit machine & then install a 64 bit version on the laptop & then use the license key again??????

answers appreciated

Keys work equally well with either version, so you shouldn't run into any problems.

That's how I work with DOpus, albeit with Vista 32-bit. (XP is now a dangerous piece of software that should be allowed nowhere near the Internet without strict supervision.)