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___________________.

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?

Consider a main memory system that consists of 8 memory modules attached to the system bus, which is one word wide. When a write request is made, the bus is occupied for $$100$$ nanoseconds ($$ns$$) by the data, address, and control signals. During the same $$100$$ $$ns$$, and for $$500$$ $$ns$$ thereafter, the addressed memory module executes one cycle accepting and storing the data. The (internal) operation of different memory modules may overlap in time, but only one request can be on the bus at any time. The maximum number of stores (of one word each) that can be initiated in $$1$$ millisecond is ____________.