Although virtual addresses are 64 bits wide in 64-bit mode, current implementations (and all chips known to be in the planning stages) do not allow the entire virtual address space of 264 bytes (16 EB) to be used. This would be approximately four billion times the size of virtual address space on 32-bit machines. Most operating systems and applications will not need such a large address space for the foreseeable future, so implementing such wide virtual addresses would simply increase the complexity and cost of address translation with no real benefit. AMD therefore decided that, in the first implementations of the architecture, only the least significant 48 bits of a virtual address would actually be used in address translation (page table lookup). See https: //en.wikipedia.org/wiki/X86-64#Virtual_address_space_details (a) How big (in GiB) is the virtual memory in the AMD 64-bit architecture? (b) A midrange server-grade motherboard today can fit Four AMD Opteron 6000 series processors (Socket G34) with 16/12/8/4-Cores each and up to 1TB of DDR3 RAM. How many bits are needed for physical addresses in this case?