Question

For a given CPU, the cycle latency for a set of operations are given as follows:

Addition: 4

Subtraction: 8

Multiplication: 64

Division: 80

If the clock of this CPU runs at 3GHz, find the following

How many operations of each of the list above can this CPU perform in 5 minutes?

If we have a set of operations that contains 10^9 of each operation in the list in part 1, compute the required time in seconds to execute the set. Please explain the formula used.

Answer 1

A CPU frequency of 3 GHz means that the CPU runs (3 * 10⁹) cycles per second.

Thus, the number of instructions of a particular type that can be run in a second

= (Number of CPU cycles per second) / (Number of cycles for the particular instruction type)

Thus, the number of instructions of a particular type that can be run in 5 minutes (300 seconds)

= [300 * (Number of CPU cycles per second)] / (Number of cycles for the particular instruction type)

Thus, number of instructions in 5 minutes for

Addition :

= [300 * (3 * 10⁹)] / 4

= (225 * 10⁹) additions

Subtraction :

= [300 * (3 * 10⁹)] / 8

= (112.5 * 10⁹) subtractions

Multiplication :

= [300 * (3 * 10⁹)] / 64

= (14.0625 * 10⁹) multiplications

Division :

= [300 * (3 * 10⁹)] / 80

= (11.25 * 10⁹) divisions

Now, if we are given number of instructions, then execution time (in seconds)

= [(Number of instructions) * (Cycles per instruction type)] / (Number of CPU cycles per second)

Since we are given that there are 10⁹ operations of each kind, so the total time (in seconds) for

Addition :

= [10⁹ * 4)] / (3 * 10⁹)

= 1.333 seconds

Subtraction :

= [10⁹ * 8)] / (3 * 10⁹)

= 2.667 seconds

Multiplication :

= [10⁹ * 64)] / (3 * 10⁹)

= 21.333 seconds

Division :

= [10⁹ * 80)] / (3 * 10⁹)

= 26.667 seconds

Thus, total execution time (in seconds) for the set

= 1.333 + 2.667 + 21.333 + 26.667

= 52 seconds