CS220 Spring 2016 Homework 3 Due Feb. 19, 2016

Name:



1. Give your answers in both abstract decimal and concrete hexadecimal format.
	a. What is the largest number less than infinity that can be represented in a 32 bit IEEE floating point number?  
   
   
	b. What is the smallest positive number greater than +0 that can be represented in a 32 bit IEEE floating point number? 
   
   
2. Given the following code:

	constant float onethird=1.0/3.0;
	float sum=0.0;
	int i=0;
	for(i=0; i<3000; i++) sum=sum+onethird;
	if (sum == 1000.0) printf (“Just as I expected, 3000 * 1/3 is 1000\n”);
	else printf(“That did not work!\n”);
	
   What will get printed?  Why? 
	
3. Given the following code:

	constant float x=1e20;
	constant float pi=3.14;
	float y = (x + (-x))+pi;
	float z = x + ((-x) + pi);
	if (y==z) printf("This is an example of the associative property.\n");
	else printf("This is a counter-example.. the associative property does not hold!\n");
	
   Which message will get printed?  Why?
   
4. If you are on a little-endian machine that uses 32 bit integers, the professor defines a "palindromic" number as a number
   for which x==htonl(x), and the professor argues that 16,843,009 is a "palindromic" number.  Is he correct?  Why?
   
5. The standard library function "float powf(float a,float b)" returns the value of "a" to the power of "b".  
   For instance, powf(2.0,3.0) return 2.0 x 2.0 x 2.0 = 8.0.  Find an integer value for "exp" for which the 
   FRAC bits of the expression "powf(2.0,exp)" is non-zero. (Warning: the representation of INFINITY in floating
   point has zero FRAC bits.)