Consider the case of a $44$ two$-$dimensional array of numbers, A$.$ Assume that each number in the array occupies one word and that the array elements are stored row$-$major order in the main memory from location $1000$ to location $1015.$ The cache consists of four blocks each consisting of just two words. Assume also that whenever needed, FIFO replacement policy is used. We would like to examine the changes in the cache as the following code: for i: $0$ to $3$ do sum: $=0$ for j :$=0$ to $3$ do sum:$=$ sum $+$ a$($i$,$j$)$ end for ave$($i$)$ :$=$ sum$/8$ end for assume that the cache memory access time is $10$ns and that the memory access time is $100$ns$.$ Compute the average access time per element of the array A and the changes in the cache if each of the following mapping techniques is used: a$)$ Direct mapping b$)$ Fully associative Mapping