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POComputer logic problem
 

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    <p>Consider a multilevel computer in which all the levels are different. Each level has instructions that are m times as powerful as those of the level below it; that is, one level r instruction can do the work of m level r – 1 instructions, If a level 1 program requires k seconds to run, how long would equivalent programs take at levels 2, 3, and 4, assuming n level r instructions are required to interpret a single r+1 instruction?</p> <p>This is the solution I came up with. Can anyone confirm or comment?</p> <p>This is the solution I wound up coming up with. Can anyone verify or comment?</p> <pre><code>Level (r) Level-1 Instructions (m) Time 4 m^3 t(q) ==(m^3q+n+nm+nm^2) (k/q) 3 m^2 t(q) =(m^2q+n+nm)(k/q) 2 m t(q) = (mq+n)(k/q) 1 1 t(q) = k </code></pre> <p>In order to calculate runtime t(q) for a given program containing q level-1 instructions, we must take into account both the exponentially-increasing number of level-1 instructions each level r instruction represents (shown as m^(r-1)) and the additional number of level-1 instructions required for interpretation for each layer on which the program is executed (shown as nm^(r-1)). The additional level-1 instructions used for interpretation by the lower levels must also be added into the final equations for r>2. Finally, for each equation we can determine the number of seconds the program takes to run by multiplying the total number of level-1 instructions used by the execution time of one level-1 cycle, as calculated by (k/q).</p> <p>Disclaimer: This IS homework, the assignment has already been handed in. I simply cannot get the semantics of this problem, and I would really like to understand it.</p>
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    1. COHint: Make a table whose columns are labeled as follows: Level, NumInstructionsInProgram, InstructionsPerSecond, TotalTime. The first row will be 1, N, N/k, k. Continue filling it out row by row.
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    2. COI don't think the problem specifies whether all instructions take the same number of clocks to execute.
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    3. COI've been filling out a table, I'm just having problems with the semantics of exactly what is meant by each of the variables and how I can factor them into the table values.
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