what's the difference between 32bit/64bit architecture?

hiho@ll

shortly i'll explain what i know and think about the topic:
a cpu has registers to work with
on 32bit these registers are a maximum of 32bit in size
on 64bit they are 64bit in size
so they can store larger values which means they can mostly (for example) be faster or use better hardware (larger harddisk, more ram)

why i ask the question:
if you compile a prog for example a C prog which uses integer
the int value on a 32bit architecture will be 32bit in size on 64bit it's 64bit
ok
now what if i write a prog where i know i don't need to store creater values than 32bit

if i compile the prog on a 32bit architecture, will it run on 64bit?
if not, why? i think the cpu registers are just bigger, why shouldn't work 32bit code on a 64 machine?

maybe it's simple and my direction of thinking is right
but i don't think so, that's why i'm asking ;-)
thx@ll

I think it will depend on the OS, and how the OS is configured to run. I see your logic - but I know for sure that there are 64bit systems that can't touch 32bit code - and others that will pad it, or alter it to make it compatible. I'm sure the new version of Windows will allow for this - so the public doesn't freak out when they can't use something cheesy - like Corel and what not.

I believe that some x86_64 Distros will allow you to run 32bit binaries as well.