Consider contiguous allocation of physical memory to processes using variable partitioning scheme. Suppose there are 8 holes in the memory of sizes $20 \mathrm{~KB}, 4 \mathrm{~KB}$, $25 \mathrm{~KB}, 18 \mathrm{~KB}, 7 \mathrm{~KB}, 9 \mathrm{~KB}, 15 \mathrm{~KB}$, and 12 KB . Assume that no two holes are adjacent. Two processes P1 of size 16 KB and P2 of size 9 KB arrive in that order, and they are allocated memory using the best-fit technique. After allocating space to P1 and P2, the number of holes of size less than 8 KB is $\_\_\_\_$ . (answer in integer)

Note: $1 \mathrm{~K}=2^{10}$

Consider a system that has a cache memory unit and a memory management unit (MMU). The address input to the cache memory is a physical address. The MMU has a translation lookaside buffer (TLB). Assume that when a page is evicted from the main memory, the corresponding blocks in the cache are marked as invalid.

For a given memory reference, which of the following sequences of events can NEVER happen?

Consider a demand paging system with three frames, and the following page reference string: 1 2 3 4 5 4 1 6 4 5 1 3 2 . The contents of the frames are as follows initially and after each reference (from left to right):

The *-marked references cause page replacements.

Which one or more of the following could be the page replacement policy/policies in use?

A computer system supports a logical address space of 232 bytes. It uses two-level hierarchical paging with a page size of 4096 bytes. A logical address is divided into a b-bit index to the outer page table, an offset within the page of the inner page table, and an offset within the desired page. Each entry of the inner page table uses eight bytes. All the pages in the system have the same size. The value of $b$ is _________ . (Answer in integer)