Consider two processors $P_1$ and $P_2$ executing the same instruction set. Assume that under identical conditions, for the same input, a program running on $P_2$ takes 25% less time but incurs 20% more CPI (clock cycles per instruction) as compared to the program running on $P_1$. If the clock frequency of $P_1$ is 1GHz, then the clock frequency of $P_2$ (in GHz) is _______.

The CPU execution time formula is:

where:

• $I$ is the instruction count,

• $\text{CPI}$ is the average cycles per instruction,

• $f$ is the clock frequency.

Since both processors run the same program with the same instruction set and input, the instruction count is the same for both:

From the problem statement:

• $T_2 = (1 - 0.25) T_1 = 0.75 \, T_1$

• $\text{CPI}_2 = (1 + 0.20) \text{CPI}_1 = 1.20 \, \text{CPI}_1$

• $f_1 = 1\text{ GHz}$

Expressing the ratio of execution times:

Substitute the given values:

Thus, the clock frequency of $P_2$ is 1.6 GHz.