1. In addition to LRU, there is a similar page replacement algorithm called Least Frequently Used (LFU). Under LFU, when the memory is full and a new page will be brought into memory, the page with the least reference frequency will be replaced. Describe a situation in which a least frequently used (LFU) page replacement algorithm generates fewer page faults than the least recently used (LRU) page replacement algorithm?

2. A given system provides three frames to a program. The system uses single-layer paging (one page table) stored in memory but also has a TLB. TLB hit rates are 88%. Assume a TLB access takes 20ns, a memory access requires 200ns, and a page fault costs 8,000,000ns. Provide the amount of time a program with the reference string below spends accessing memory when using second chance FIFO.

Reference String: 7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1

3. We use 5-bit logical addresses which allows 32 possible locations. The higher 3 bits are used for the page number and the lower 2 bits are used for the page offset. What is the size of a frame? How many pages are in the page table?