CS 2734 Computer Organization II

For this laboratory, you are to experiment with the bit pattern used to represent a double by computers that adhere to the IEEE standard for doubles. (See text, Section 4.8, pages 275-280. Sun hardware follows the standard.)

Given either an "ordinary" floating point number or a bit pattern, it is easy to get the other representation, say, with a simple program like the following:

#include <stdio.h>
#include <ctype.h>
void main(void){
   union {
      double d; 
      struct {
         int p;
         int q;
      } b;   } r;
   char ch;
   for( ; ; ) {
      while (isspace(ch = getchar()))
         ;
      if (ch == 'x') {
         scanf("%x %x", &r.b.p, &r.b.q);
         printf("  Decimal: %20.16e\n", 
            r.d);
         printf("  Bits: %08x %08x\n",
            r.b.p, r.b.q);
      }
      else if (ch == 'f') {
         scanf("%lf", &r.d);
         printf("  Decimal: %20.16e\n",
            r.d);
         printf("  Bits: %08x %08x\n",
            r.b.p, r.b.q);
      }
      else break;
   }
}

f 16.0
  Decimal: 1.6000000000000000e+01
  Bits: 40300000 00000000
f .75
  Decimal: 7.5000000000000000e-01
  Bits: 3fe80000 00000000
f 1.5
  Decimal: 1.5000000000000000e+00
  Bits: 3ff80000 00000000
x 3fe80000 00000000
  Decimal: 7.5000000000000000e-01
  Bits: 3fe80000 00000000
f -0.75
  Decimal: -7.5000000000000000e-01
  Bits: bfe80000 00000000
x bfffffff ffffffff
  Decimal: -1.9999999999999998e+00
  Bits: bfffffff ffffffff

• Create a new directory for this assignment.
• Copy, compile, and run the C program above. Try out some of the simple inputs shown.
• Complete the four items below.
  1. Check out the number -0.75 above. Convince yourself that you agree with the text, page 279. (Convert the hex numbers to binary by hand and see that your fields agree with those in the text.)
  2. Determine the bits for the numbers -1.0, -2.0, -4.0, and -8.0. Give an explanation for them. (In each case, determine the different floating point fields and see that you really have a representation for the number shown.)
  3. Determine the bits for the number -6.25, and give a careful explanation for them. (Again, determine the fields, and verify that this bit pattern really does represent the number -6.25.)
  4. Determine the bits for the number 0.1, that is, the number 1/10. Are you surprised? Again, give a careful explanation. (This is quite a bit more challenging to do. For a really good answer, you would have to use formulas for geometric series that you may have learned in college algebra.)
• Show your answers and results to the lab TA for checkout.