CS 473 - HW1

Floating Point

Due Friday, August 30, 2002

For this assignment, you need to show all your work. In particular, for the number base conversions you need to show the table you use for the conversion; for the floating point arithmetic you need to divide the numbers into sign-exponent-mantissa fields and manipulate the fields explicitly. Yes, I really mean it, and the TA will take points off if you don't do it.

1. (32 points) Conversion from decimal to binary fractions.

   None of these result in a repetend.
   a) 0.25	b) 0.125	c) 0.375	d) 0.5625

2. (32 points) Conversion from binary to decimal fractions.

   a) 0.1010

   b) 0.1011

   c) 0.0111

   d) 0.0011

3. (32 points) Floating Point Interpretation

   What are the values, in decimal, of the following IEEE floating point numbers?
   a) 40700000	b) c1560000	c) 00000000	d) 3f800000

4. (32 points) Conversion to Floating Point

   What is the IEEE floating point representation of the following decimal floating point numbers?
   a) 37.25	b) -9.125	c) 0.375	d) -15.75

5. (64 points) Floating Point Arithmetic

   Perform the following arithmetic operations in IEEE floating point (use the algorithms as presented in class; don't convert to decimal, calculate the result, and convert back.
   a) 41100000 / 40400000	b) 41080000 * 40e80000	c) 3fe00000 + 3f000000	d) 40700000 - 40200000