MA580/CSC580 Homework 1
due 23 January 2013 in class

Read chapter 4 in the book by Higham & Higham, as well as the IEEE Standard for Binary Floating Point Arithmetic.

Try out Cleve Moler's Matlab program floatgui.m.

The program shows you the spacing of floating point numbers. The parameter t specifies the number of bits in the fraction, and the parameters e_min and e_max specify the range of the exponent.
(This is for self-study only. You do not need to hand in anything.)

1. [10 points]   Determine the exact distance between 17 and the next largest floating point number in IEEE double precision arithmetic. Please justify your answer.
2. [10 points]   In the IEEE double precision floating point representation of the numbers 10 and -100 determine: the sign bit, the fraction (in binary) and the exponent (in decimal).
3. [10 points]   The expressions 2^(-1024) and 1/(2^1024) are equal in exact arithmetic. Explain precisely what happens when they are evaluated in IEEE double precision arithmetic, and why.
4. [10 points]   What is the largest integer p such that all integers in the interval [-p,p] are exactly representable in IEEE double precision arithmetic? Please justify your answer, and give p in terms of powers of 2.