For inclusion to hold between two cache levels $$L1$$ and $$L2$$ in a multilevel cache hierarchy, which of the following are necessary?

$$1.$$ $$L1$$ must be a write-through cache
$$2.$$ $$L2$$ must be a write-through cache
$$3.$$ The associativity of $$L2$$ must be greater than that of $$L1$$
$$4.$$ The $$L2$$ cache must be at least as large as the $$L1$$ cache

Consider a machine with a byte addressable main memory of $${2^{16}}$$ bytes. Assume that a direct mapped data cache consisting of $$32$$ lines of $$64$$ bytes each is used in the system. $$A\,\,50 \times 50$$ two-dimensional array of bytes is stored in the main memory starting from memory location $$1100H.$$ Assume that the data cache is initially empty. The complete array is accessed twice. Assume that the contents of the data cache do not change in between the two accesses.

Which of the following lines of the data cache will be replaced by new blocks in accessing the array?

Consider a machine with a byte addressable main memory of $${2^{16}}$$ bytes. Assume that a direct mapped data cache consisting of $$32$$ lines of $$64$$ bytes each is used in the system. $$A\,\,50 \times 50$$ two-dimensional array of bytes is stored in the main memory starting from memory location $$1100H.$$ Assume that the data cache is initially empty. The complete array is accessed twice. Assume that the contents of the data cache do not change in between the two accesses.

How many data cache misses will occur in total?

A $$CPU$$ has a cache with block size $$64$$ bytes. The main memory has $$k$$ banks, each bank being $$c$$ bytes wide. Consecutive $$c$$-byte chunks are mapped on consecutive banks with wrap-around. All the $$k$$ banks can be accessed in parallel, but two accesses to the same bank must be serialized. A cache block access may involve multiple iterations of parallel bank accesses depending on the amount of data obtained by accessing all the $$k$$ banks in parallel. Each iteration requires decoding the bank numbers to be accessed in parallel and this takes $$k/2$$ $$ns.$$ The latency of one bank access is $$80$$ $$ns.$$ If $$c=2$$ and $$k=24,$$ then latency of retrieving a cache block starting at address zero from main memory is