The width of the physical address on a machine is $$40$$ bits. The width of the tag field in a $$512$$ $$KB$$ $$8$$-way set associative cache is _____________ bits.

A file system uses an in-memory cache to cache disk blocks. The miss rate of the cache is shown in the figure. The latency to read a block from the cache is $$1$$ $$ms$$ and to read a block from the disk is $$10$$ $$ms.$$ Assume that the cost of checking whether a block exists in the cache is negligible. Available cache sizes are in multiples of $$10$$ $$MB.$$

The smallest cache size required to ensure an average read latency of less than $$6$$ $$ms$$ is _________ $$MB.$$

In designing a computer’s cache system, the cache block (or cache line) size is an important parameter. Which one of the following statements is correct in this context?

A $$4$$-way set-associative cache memory unit with a capacity of $$16KB$$ is built using a block size of $$8$$ words. The word length is $$32$$ bits. The size of the physical address space is $$4$$ $$GB.$$ The number of bit for the TAG field is ____________.