A certain processor uses a fully associative cache of size 16 kB. The cache block size is 16 bytes. Assume that the main memory is byte addressable and uses a 32-bit address. How many bits are required for the Tag and the Index fields resectively in the addresses generated by the processor?

A $$32$$-bit wide main memory unit with a capacity of $$1$$ $$GB$$ is built using $$256M\,\, \times \,\,4$$-bit $$DRAM$$ chips. The number of rows of memory cells in the $$DRAM$$ chip is $${2^{14}}.$$ The time taken to perform one refresh operation is $$50$$ nanoseconds. The refresh period is $$2$$ milliseconds. The percentage (rounded to the closest integer) of the time available for performing the memory read/write operations in the main memory unit is __________.

A processor can support a maximum memory of $$4$$ $$GB,$$ where the memory is word-addressable (a word consists of two bytes). The size of the address bus of the processor is at least ___________ bits.

Consider a machine with a byte addressable main memory of $${2^{20}}$$ bytes, block size of $$16$$ bytes and a direct mapped cache having $${2^{12}}$$ cache lines. Let the addresses of two consecutive bytes in main memory be $${\left( {E201F} \right)_{16}}$$ and $${\left( {E2020} \right)_{16}}$$. What are the tag and cache line address (in $$hex$$) for main memory address $${\left( {E201F} \right)_{16}}$$?