An advanced computer sends information to its various parts via infrared light pulses traveling through silicon fibers. To acquire data from memory, the central processing unit sends a light-pulse request to the memory unit. The memory unit processes the request, then sends a data pulse back to the central processing unit. The memory unit takes 0.5 ns to process a request. If the information has to be obtained from memory in 2.0 ns, what is the maximum distance the memory unit can be from the central processing unit?

Verified step by step guidance

1. Determine the total time available for the light pulses to travel between the central processing unit (CPU) and the memory unit. Subtract the processing time of the memory unit (0.5 ns) from the total time (2.0 ns). This gives the time available for the round trip of the light pulses.
2. Divide the time available for the round trip by 2 to find the time available for a one-way trip of the light pulse.
3. Recall that the speed of light in a medium is given by \( v = \frac{c}{n} \), where \( c \) is the speed of light in a vacuum (approximately \( 3.0 \times 10^8 \ \text{m/s} \)) and \( n \) is the refractive index of the medium. For silicon, the refractive index \( n \) is approximately 3.5. Use this to calculate the speed of light in silicon.
4. Use the formula \( d = v \cdot t \), where \( d \) is the distance, \( v \) is the speed of light in silicon, and \( t \) is the one-way travel time calculated in step 2. This will give the maximum distance the memory unit can be from the CPU.
5. Express the final result in meters or convert it to a more convenient unit, such as millimeters, if necessary.

Key Concepts

Speed of Light

The speed of light in a vacuum is approximately 299,792 kilometers per second (or about 300,000 km/s). In materials like silicon, light travels slower due to the medium's refractive index. Understanding the speed of light is crucial for calculating how far light can travel in a given time, which is essential for determining the maximum distance between the central processing unit and the memory unit.

Time Delay

Time delay refers to the total time taken for a signal to travel from one point to another and back. In this scenario, the total time for the round trip of the light pulse must account for both the processing time of the memory unit (0.5 ns) and the time taken for the light to travel to and from the memory unit. This concept is vital for calculating the maximum allowable distance based on the total time constraint of 2.0 ns.

Distance Calculation

Distance can be calculated using the formula: distance = speed × time. In this context, once the total time for the light pulse's round trip is determined, the maximum distance can be calculated by considering the speed of light in silicon. This calculation is essential for understanding the physical limitations of the system's architecture and ensuring efficient data transfer.