64-bits has little to do with amount of addressable memory. In fact, 32-bit and 64-bit processors can address just as much. For example, 32-bit ARMv7 Cortex A15 can address up to 1TB of memory.
The only difference is amount of physical RAM you can map at once. Only virtual address space is limited in 32-bit processors. But even then, you can change the virtual-to-physical mappings at runtime. It's only inconvenient.