The memory architecture of a machine X is summarized in the following parameters: Virtual Address: 54 bits Page Size: 16 Kbytes PTE Size: 4 bytes a) Assume that there are 8 bits reserved for the operating system functions (protection, replacement, valid, modified, and Hit/Miss- All overhead bits) other than required by the hardware translation algorithm. Derive the largest physical memory size (in bytes) allowed by this PTE format. Make sure you consider all the fields required by the translation algorithm b) How large (in bytes) is the page table