Homework 4

Details

For each problem make sure you clearly and neatly show all of your work! Each part/problem is worth 5 points.

1. Add the floating-point numbers 00110101100001001000111110001000 and 00101101010110010010111111110100 by converting to fixed point, doing the appropriate shift, adding, performing an appropriate shift (if necessary), and converting back to floating-point.
2. Let x = 1.23456×10¹² and y = 9.87654×10^-5.
   1. What is x+y?
      (Compute it by hand or use something like WolframAlpha to compute the exact answer directly using this representation)
   2. If x and y where stored in 32-bit floating-point notation and we computed x+y and stored the result in 32-bit floating point, what would the answer be and why? (Hint: You should not have to actually do the conversion, but just enough work to justify what is happening.)
3. Compute the sum of the following 2 numbers that are represented in 12 bit two's complement: 111100001010 and 110011010111. Clearly indicate whether or not overflow occurred and explain how you know.