A 32-bit machine CANNOT execute a 64-bit binary and this statements also holds the other way around.
But what would happen if you try that? If you are working on a ubuntu system, mostly likely a message will spit out:
What you can do is to use
file command to figure out the binary type:
a.out: ELF 32-bit LSB executable tells you that this is a 32-bit executable. Perhaps you want to read more
about ELF format.