The clock rate of a processor is improved by 20% - this improvement comes at the cost of a 24% increase in CPI. What is the speedup in overall execution time (assuming that the processor executes the same number of dynamic instructions in both scenarios) ?

Required speedup = 0.9677

Explanation:

Before improvement:-

suppose before any modification was done clock rate = f, CPI = c and number of instructions = n.

now, execution time without any improvement = number of instructions * number of cycles required to execute per instruction * one cycle time = n*c * (1/f) = nc / f

now after improvement:-

clock rate has increased by 20% means new clock rate = f + 0.2f = 1.2f

but due to this, CPI has increased by 24% means new CPI = c + 0.24c = 1.24c

now, execution time with improvement = n * (1.24c) * (1/1.2f) = 1.03334 nc / f

speedUp = execution time without improvement / execution time with improvement = (nc / f) / (1.03334 nc/f) = 1/1.034 = 0.9677

required speedup = 0.9677