# 1. [M] ( a ) A program consisting of a total of 300 instructions contains a 50-instruction loop…

1. [M] (a) A program consisting of a total of 300 instructions contains a 50-instruction loop that is executed 15 times. The processor contains a cache, as described in Section 1.2.2. Fetching and executing an instruction that is in the main memory requires 20 time units. If the instruction is found in the cache, fetching and executing it requires only 2 time units. Ignoring operand data accesses, calculate the ratio of program execution time without the cache to execution time with the cache. This ratio is called the speedup due to the use of the cache. Assume that the cache is initially empty, that it is large enough to hold the loop, and that the program starts with all instructions in the main memory.

(b) Generalize part (a) by replacing the constants 300, 50, 15, 20, and 2 with the variables w, x, y, m, and c. Develop an expression for speedup.

(c) For the values w = 300, x = 50, m = 20, and c = 2 what value of y results in a speedup of 5?

(d) Consider the form of the expression for speedup developed in part (b). What is the upper limit on speedup as the number of loop iterations, y, becomes larger and larger?

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