An access sequence of cache block addresses is of length $$N$$ and contains $$n$$ unique block address. The number of unique block addresses between two consecutive accesses to the same block address is bounded above by $$k.$$ What is the miss ratio if the access sequence is passed through a cache of associativity $$A\, \ge \,k$$ exercising least-recently-used replacement policy?

In a $$k$$-way set associative cache, the cache is divided into $$v$$ sets, each of which consists of $$k$$ lines. The lines of a set are placed in sequence one after another. The lines in set $$s$$ are sequenced before the lines in set $$(s+1).$$ The main memory blocks are numbered $$0$$ onwards. The main memory block numbered $$j$$ must be mapped to any one of the cache lines from

The amount of $$ROM$$ needed to implement a $$4$$ bit multiplier is

A main memory unit with a capacity of $$4$$ megabytes is built using $$1M \times 1$$-bit $$DRAM$$ chips. Each $$DRAM$$ chip has $$1K$$ rows of cells with $$1K$$ cells in each row. The time taken for a single refresh operation is $$100$$ nanoseconds. The time required to perform one refresh operation on all the cells in the memory unit is