Question

a. Assume our model requires \(10^{14}\) computations to simulate one hour of activity. We run the program on a desktop computer with a computation speed of 800 MIPS (millions of instructions per second). How long will it take to simulate one day of activity in the model? b. How fast a computer (in terms of MIPS) do we need to use if we want to complete the simulation of one day in five minutes of computing time?

Short answer

a. 34.72 days b. 8 million MIPS

Step-by-step solution

Calculate total computations for one day

Since one hour of activity requires \(10^{14}\) computations, and there are 24 hours in a day, the total computations needed for one day is \(10^{14} \times 24 = 2.4 \times 10^{15}\) computations.

Compute time required with current speed

The desktop computer runs at 800 MIPS, or \(800 \times 10^6\) instructions per second. To find out how long it takes to complete \(2.4 \times 10^{15}\) computations, divide the total computations by the speed: \(\frac{2.4 \times 10^{15}}{800 \times 10^6}\). Calculating this gives \(3 \times 10^6\) seconds.

Convert seconds to days

Convert \(3 \times 10^6\) seconds into days: \(\frac{3 \times 10^6}{60 \times 60 \times 24} = 34.72\) days. Thus, it takes approximately 34.72 days of computing time to simulate one day of activity.

Determine required speed for 5-minute simulation

If the simulation must complete in 5 minutes, convert 5 minutes to seconds: \(5 \times 60 = 300\) seconds. Rearrange the speed formula to find the necessary MIPS: \(\frac{2.4 \times 10^{15}}{300}\). Calculating gives \(8 \times 10^{12}\) instructions per second.

Convert instructions per second to MIPS

Convert \(8 \times 10^{12}\) instructions per second to MIPS by dividing by \(10^6\): \(\frac{8 \times 10^{12}}{10^6} = 8 \times 10^6\) MIPS. Thus, a computing speed of 8 million MIPS is needed to simulate one day of activity in 5 minutes.

Key concepts

MIPS (Millions of Instructions Per Second)

MIPS stands for Millions of Instructions Per Second and is a measure of a computer's processing speed. It denotes how many millions of instructions a computer can execute in one second. The higher the MIPS, the faster the computer performs. For example, a machine with a speed of 800 MIPS executes 800 million instructions every second.

Understanding MIPS helps in evaluating a computer's performance, especially when comparing different systems. It's important to note that while MIPS gives insights into processing speed, it doesn't always indicate overall system efficiency, as different computers might perform varied types of instructions.

• MIPS is useful for assessing computational tasks like simulations.
• It's particularly relevant when considering how much time a specific task would take on a given machine.
• Calculating the MIPS requirement helps in choosing or designing systems for specific performances.

Computational Simulation

Computational simulation uses computer systems to replicate a real-world process. It's a powerful technique to analyze complex systems that would be difficult to study directly. By conducting simulations, researchers and developers can predict behaviors and understand systems without needing a real-world experiment.

In computational simulation, knowing the required computational power is crucial. This is often defined by the number of computations needed to model an activity. For instance, in our exercise, simulating one hour of activity requires \(10^{14}\) computations. Multiplying this by 24 hours predicts the whole day's requirements.

• Simulations help save time and resources by avoiding real-world testing.
• They can be used across various fields, like science, engineering, and medicine.
• The efficiency and accuracy depend on both the model and the computational resources available.

Instruction Execution Time

Instruction Execution Time refers to the time a computer takes to complete a single instruction. It's a critical factor in understanding overall computer performance. Usually expressed in seconds or fractions, it provides insights into how swiftly a system processes tasks.

To calculate the instruction execution time, one would typically divide the time taken by the number of instructions processed. From the exercise, we find that with a desktop speed of 800 MIPS, 2.4 trillion computations take \(3 \times 10^6\) seconds to complete. This illustrates the direct connection between speed, instruction count, and execution time.

• Improving execution time often helps in faster and more efficient simulations.
• Understanding execution time assists in designing systems for optimal performance.
• The goal is to minimize this time, enhancing the system's efficiency in performing tasks.