What determines if it's a 64 bit machine? Dual core?
Dual core = 2 CPUs effectively. Quad core = 4 CPUs on the same piece of Silicon
64 bit = more advance instruction set which replaces all the older 32 bit instruction set CPUs. 64 bit is more modern than 32 bit and that is the way software is going.
64bit doesn't specifically make it "more advanced." 64bit CPU's just support for a larger memory addressing space then 32bit CPU's, beyond the 4GB limit of 32bit addresses.