Can 32-bit Linux be installed on 64-bit laptop (and is it a good idea)?

[Reshat Sabiq]

>From what I remember 64-bit processors still support 32-bit exes, which
means I should be able to run all the 32-bit software, and for that
software the memory usage will not double. I.e., 256MB RAM for 64-bit box
running mostly 32-bit software is not like 128MB RAM for 32-bit box. I
suspect if the OS was 64-bit, then the OS pieces might be consuming twice
as much memory as on 32-bit box, but I think that XP it is shipped with
is 32-bit, which means it's not gonna be consuming twice the memory.

I'm
not sure if I would have to install 64-bit Linux, instead 32-bit though.
If i have to, then memory usage might be doubled by Linux OS pieces, and
perhaps even apps, if they are built for 64-bit, on Linux. Is that
correct?

Also, I should be able to add memory to it later, when it comes to that.
This is for my relatives, and 256MB should be enough for now.

P.S. Link:
http://www.shopping.hp.com/webapp/shopping/computer_series.do?series_name=ze2000z_series&catLevel=2&category=notebooks/hp_pavilion&storeName=computer_store

Thanks.