Representation of Numbers on HP and VAX Computers
Representation of Numbers on HP and VAX Computers
Goals:This laboratory has the following purposes:

To develop an expanded understanding of the storage of
numeric data on both the HP 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 HP and VAX computers (both of which are 32bit 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 bitexam from HP directory ~walker/pascal .

Enter positive integers and check that the bit patterns
correspond to the binary representations you calculated before the lab.

Enter negative integers and determine which notation is used on
the HP computers. Be sure you can justify your answer by citing output
you obtained.

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.

Use your knowledge of storage of real numbers to determine what
real number comes ``immediately after'' 2.0 and 11.0 on this system.

Repeat the above steps running bitexam from VAX directory
[walker.modula2]
Work to be turned in:
Your lab writeup 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 HP 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.math.grin.edu/~walker/courses/211/labs/lab.datarep.html
created August 18, 1997
last revised August 29, 1997