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14 July, 16:03

An advanced computer sends information to its various parts via infrared light pulses traveling through silicon fibers (n = 3.50). 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 0.50 ns to process a request. If the information has to be obtained from memory in 2.00 ns, what is the maximum distance the memory unit can be from the central processing unit?

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  1. 14 July, 16:11
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    d = 6.43 cm

    Explanation:

    Given:

    - Speed resistance coefficient in silicon n = 3.50

    - Memory takes processing time t_p = 0.50 ns

    - Information is to be obtained within T = 2.0 ns

    Find:

    - What is the maximum distance the memory unit can be from the central processing unit?

    Solution:

    - The amount of time taken for information pulse to travel to memory unit:

    t_m = T - t_p

    t_m = 2.0 - 0.5 = 1.5 ns

    - We will use a basic relationship for distance traveled with respect to speed of light and time:

    d = V*t_m

    - Where speed of light in silicon medium is given by:

    V = c / n

    - Hence, d = c*t_m / n

    -Evaluate: d = 3*10^8*1.5*10^-9 / 3.50

    d = 0.129 m 12.9 cm

    - The above is the distance for pulse going to and fro the memory and central unit. So the distance between the two is actually d / 2 = 6.43 cm
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