Computer Science 211 Lab: Representation of Numbers on PC/Linux and Vax Computers

Representation of Numbers on PC/Linux and Vax Computers

Goals:This laboratory has the following purposes:

To develop an expanded understanding of the storage of numeric data on both the PC/Linux and Vax computers through experimentation,
To clarify integer data type,
To give students experience with real data type, and
To allow for comparison of the storage of numeric data on both the PC/Linux and Vax computers (both of which are 32-bit machines).

Preparation Before the laboratory session, write binary patterns for

integers ± 1, ± 2, ± 3, ± 6, ± 9 using sign/magnitude notation, ones complement notation, and twos complement notation, and
real numbers ± 1.0, ± 2.0, ± 3.0, and 4.0, 5.0, ..., 11.0 .

In the Laboratory:

Run program data-rep from PC/Linux directory ~walker/c .
(Click here to view the source code for this C program.)
1. Enter positive integers and check that the bit patterns correspond to the binary representations you calculated before the lab.
2. Enter negative integers and determine which notation is used on the PC/Linux computers. Be sure you can justify your answer by citing output you obtained.
3. Enter real numbers, and conduct experiments to determine:
  - which bit is the sign bit,
  - which bits are used for the mantissa,
  - which bits are used for the exponent, and
  - what bias is used in the storage of exponents.
4. Use your knowledge of storage of real numbers to determine what real number comes ``immediately after'' 2.0 and 11.0 on this system.
Program data-rep-vax in directory ~walker/c simulates the running of the data-rep program for Vax computers. Repeat the above steps running data-rep-vax.
Explain any differences you identify between the representation of numbers on PC/Linux machines and on Vax computers.

Work to be turned in: Your lab write-up should contain both your computations from the lab preparation and your results from the lab itself. Further, you should document how both negative integers and real numbers are stored in both the PC/Linux and Vax computers based on your experiments in the lab. Finally, you should compare how the two machines store numbers. Are the storage algorithms the same? If so, justify your conclusions. If not, explain how the storage is different.

This document is available on the World Wide Web as

     http://www.cs.grinnell.edu/~walker/courses/211.fa01/labs/lab.data-rep.html

created August 18, 1997 last revised September 14, 2001


For more information, please contact Henry M. Walker at walker@cs.grinnell.edu.