The size of the physical address space of a processor is $${2^P}$$ bytes. The word length is $${2^W}$$ bytes. The capacity of cache memory is $${2^N}$$ bytes. The size of each cache block is $${2^M}$$ words. For a $$K$$-way set-associative cache memory, the length (in number of bits) of the tag field is

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 _________ $$MB.$$

The memory access time is $$1$$ nanosecond for a read operation with a hit in cache, $$5$$ nanoseconds for a read operation with a miss in cache, $$2$$ nanoseconds for a write operation with a hit in cache and $$10$$ nanoseconds for a write operation with a miss in cache. Execution of a sequence of instructions involves $$100$$ instruction fetch operations, $$60$$ memory operand read operations and $$40$$ memory operand write operations. The cache hit-ratio is $$0.9.$$ The average memory access time (in nanoseconds) in executing the sequence of instructions is___________________.