# Homework 3

1. [Makeup exam '99] Are there IEEE 32-bit floating point numbers a and b (b not zero), such that a + b = a? Show an example of such numbers if they exist, or explain why they cannot exist.

2. IEEE floating point numbers are in denormalized form if the exponent is 0 and the fraction part is not all 0. In 32-bit floating point numbers their value is xx..xx*2-23*2-126, where xx..xx is the fraction. What is the reason for multiplying with 2-126, but not 2-127?

3. [Makeup exam 2000] We can define 6-bit floating point numbers in the following way. The first bit (leftmost) is sign bit, next two are the exponent on Excess-form and the three rightmost bits are the fraction part (with one hidden bit). In all other ways the format is the same as the IEEE 754 standard (in denormalized numbers, zero, NaN, and infinity).
1. What floating point value is 100100?
2. What is the smallest gap between successive floating point numbers? How about the largest gap?
3. How many normalized floating point numbers can be represented in this format?

4. Problem 2.17 on page 59 in the textbook.

5. Problem 2.19 on page 59 in the textbook.

Hand these problems in on monday september 17th.

hh (hja) hi.is, 12. september, 2001.