Math for Computer Architecture Part 1

Notes

• We will be doing some computation this semester
• The first topic is the factor-label method
  • You can look up Conversion_of_units on wikipedia for a further disucssion
  • This method of computation
    • Requires that there be a conversion factor between different uints.
    • Has the computer include these units to assure accuracy and the ability to check correctness
      • Please search for articles about the Mars Climate Orbiter, (wikipedia Mars_Climate_Orbiter)
      • Lockheed Mrtin used US Customary Units
      • NASA used SI units (more on this later)
      • And so it burned up in Mars' upper atomsphere.
      • And so, $327.6 million was lost.
    • Allows the computer to use the rules of algebra
    • Keeps us from memorizing hundreds or more conversion formulas.
  • This works when there is a relationship between units.
    • 1 ft ≈ .3048 meter
    • 1 second = 1000 miliseconds
• Do I need to do this?
  • The Mars Climate Orbiter really makes me mad.
  • So Yes, you do
• But it is too much writing/typing
  • It is part of the problem solving required for this class.
  • And as such, I reserve the right to mark any solution not showing this method as wrong.
• The Method
  1. Setup
     1. State the units you have and the units you want.
     2. State any conversion factors, but this can be done as part of the solution as well.
  2. Perform a series of computations
     1. Starting with the original unit
     2. Multipltiply by a conversion factor containing
        • The original unit
        • The final unit
        • An intermediate unit
        that gets closer to the final unit.
     3. Include a dimension label with every number
     4. Cancel the labels, but keep them visible.
     5. Cary along the numbers, simplifying if necessary.