Due: Thursday, January 30, 2003, 11AM

1. What is the smallest positive integer that is not exactly representable as a floating point?

2. Using a toy number system
with only 3 bits in the mantissa (not including the hidden bit), and with
the only allowable exponents equal {-1,0,1}:

(a) Draw all possible floating
point numbers on a line.

(b) What can you say about the
gaps between floating point numbers?

3. Repeat the computation on p. 9 in Heath, but using the more accurate finite difference formula f'(x) = (f(x+h)-f(x-h))/(2h). Make a table of your approximation and the error for the different values of h, and plot the results. Could you predict the best value of h to use?

4. Do problems 1.4, 1.5, 1.6 in the Heath text on p. 42.