Assignment 1: Numerical Precision

Assignment 1: Numerical Precision

The
storage and representation of numbers in a computer can lead to costly mistakes
because of precision errors. When using floating point numbers, one must make
sure that the correct number of digits is used in a calculation because rounding
errors can produce values that lead to errors. Consider the floating point
format, exponential format, and binary coded decimal (BCD).

Write a four
to five (4-5) page paper in which you:

  1. Analyze the floating point format in order to:
    • Determine how floating point numbers are stored in memory.
    • Discuss the ease or difficulty of manipulating and using floating point
      numbers in arithmetic calculations.
  2. Determine whether or not you believe that the floating point format is
    memory efficient. Provide a rationale to support your answer.
  3. Analyze the format used to store numbers using the binary coded decimal
    format. Determine whether the BCD format is more or less memory efficient than
    the floating point format.
  4. Compare and contrast the BCD format to the floating point format in terms
    of:

    • precision
    • performance in calculations
    • memory usage
  5. Select the format (floating point format, binary coded decimal (BCD), or
    exponential format) that you would recommend for processing efficiency and
    explain why.
  6. Floating point numbers can introduce rounding errors in the banking
    industry, which may lead to financial benefit for the bank but not for the
    customer. Analyze the ethics of knowingly benefitting from rounding errors.
    Propose a plan on how the rounding error should be handled.
  7. Differentiate between the exponential format and the floating point format
    in terms of:

    • format
    • processing speed
    • accuracy
  8. Use at least three (3) quality resources in this assignment. Note: Wikipedia
    and similar Websites do not qualify as quality resources.

Your
assignment must follow these formatting requirements:

  • Be typed, double spaced, using Times New Roman font (size 12), with one-inch
    margins on all sides; citations and references must follow APA or
    school-specific format. Check with your professor for any additional
    instructions.
  • Include a cover page containing the title of the assignment, the student’s
    name, the professor’s name, the course title, and the date. The cover page and
    the reference page are not included in the required assignment page length.

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