Quiz 7 will be on computer arithmetic.

Be able to:

-- Convert numbers from decimal (base 10) to binary (base 2), 
   and convert numbers from binary to decimal.

   Examples: Convert 42.625 to binary.
             Convert 11.101001 (base 2) to decimal

-- Represent a negative integer in 2's complement.

   Example:  Give the 6-bit 2's complement representation
             for -13.

-- Add two binary integers.

   Example:  Convert 12 and -6 to 6-bit 2's complement
             representation and add them.

-- Given a fixed point system, determine the integers
   that can be represented.

   Example:  In a 6-bit 2's complement computer, what
             integers can be represented?

-- Explain how the IA32 flags ZF, SF, OF, CF can be set
   based on the fixed point representation of the result of
   a computation.

   Example:  What condition sets the ZF? 
             How is overflow detected?

(This changed from "two's-complement" to "sign-magnitude" 12/09/13
-- Give the (sign-magnitude) mantissa and the biased or 
   unbiased exponent for a given number.
   (I will remind you of d, m, M, and the bias.)

   Example:  What is the IEEE single precision representation 
             for 12.0625?

             What is the IEEE single precision representation 
             for -12.0625?

-- Add two floating point numbers.

   Example:  What is the result of adding the floating point
             numbers with  mantissa +1.010, unbiased exponent 4
                           mantissa +1.011, unbiased exponent 2

-- Given a floating point system, determine the largest and
   smallest positive numbers that can be stored, and machine
   epsilon (which is not the same as the smallest).

   Example: If d=7, m = -30, M = 31, what are the largest
   and smallest positive numbers that have an exact representation,
   and what is machine epsilon?

-- Explain what a guard digit is and why it is needed.

-- Give the floating point representation for 0, Inf, -Inf, and NaN
   for a given floating point system.

   Example: If d=7, m = -30, M = 31, represent 0, Inf, -Inf, and NaN.

-- Use your knowledge of floating point to predict computational
   results.

   Example:  Consider this Matlab code.

      x = 1;
      delta = 1 / 2^(53);
      for j1=1:2^(20),
      x = x + delta;
      end
   
    What is the final value of x, knowing that Matlab uses double
    precision?


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For more sample questions, see the quizzes numbered "Quiz 1" at
http://www.cs.umd.edu/users/oleary/c660quizzes/index.html
They contain questions on error analysis (which you can ignore)
and machine arithmetic.