Q53

A computer uses $46\text{-bit}$ virtual address, $32\text{-bit}$ physical address, and a three–level paged page table organization. The page table base register stores the base address of the first-level table $\text{(T1)},$ which occupies exactly one page. Each entry of $\text{T1}$ stores the base address of a page of the second-level table $\text{(T2)}.$ Each entry of $\text{T2}$ stores the base address of a page of the third-level table $\text{(T3)}.$ Each entry of $\text{T3}$ stores a page table entry $\text{(PTE)}.$ The $\text{PTE}$ is $32\;\text{bits}$ in size. The processor used in the computer has a $1\;\textsf{MB}\; 16$ way set associative virtually indexed physically tagged cache. The cache block size is $64$ bytes. What is the minimum number of page colours needed to guarantee that no two synonyms map to different sets in the processor cache of this computer?