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 _________ $$MB.$$

A processor has $$40$$ distinct instructions and $$24$$ general purpose registers. A $$32$$-bit instruction word has an opcode, two register operands and an immediate operand. The number of bits available for the immediate operand field is __________ .

Suppose the functions $$F$$ and $$G$$ can be computed in $$5$$ and $$3$$ nanoseconds by functional units $${U_F}$$ and $${U_G},$$ respectively. Given two instances of $${U_F}$$ and two instances of $${U_G},$$ it is required to implement the computation $$F\left( {G\left( {{X_i}} \right)} \right)$$ for $$1 \le i \le 10.$$ Ignoring all other delays, the minimum time required to complete this computation is _____________ nanoseconds.

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.