Can a native 64-bit CPU run 32-bit code ?

My laptop has a AMD Athlon 64 Processor 3700+, Architecture is x86_64. My problem is that I have to compile a code that will then be linked to pre-compile binaries produced on 32-bit machines. In short, everything must be compiled to generate 32-bit code for the sake of compatibility. There should be an option in the gcc compiler that forces it to generate 32-bit code.. But assuming I've got an executable for 32-bit machines, then can I run such an exectable on MY OWN laptop which is 64-bit ? If the answer is "yes" (I hope so) then I'd be grateful to know how I can do that . Thank you in advance for your help. Maura