By 16 billion things you mean 16 billion bytes? If you are talking about physical memory, then no, you can't occupy the entire memory. If you are talking about virtual memory, then you can store more data.
Actually, CPU processes things in words, not bytes. On 64-bit architecture the word is 64 bit or 8 bytes.
But there is a lot of things that CPU can do even faster than that, because this limitation only relates to actual instruction execution (and even then there are instructions that can process multiple words at a time).
