Homework 1- Floating Point Arithmetic

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.