Preliminary Concepts: Special Binary Numbers
A computer
can not represent every number. There will always be a number so large
that we do not have enough bits to represent it. However, we can reserve
certain patterns of 1s and 0s to represent certain values that have
special use. For example, even though we cannot represent very large numbers
that take more bits than we have available, we can reserve one pattern
of 1s and 0s to represent infinity. This is similar to you writing the
mathematical symbol for infinity 
on a piece of paper. Even though you might not be able to write enough
digits on the page to represent a very, very large number, you can write
a single, special symbol to represent infinity. We can do the same thing
with a special pattern of 1s and 0s. That is exactly what is done in
the IEEE floating-point standard used in most modern computers. Notice
that the computer treats every string of bits according to the program—i.e., according to the human programmer's intent.
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These pages were written by Steven H. VanderLeest and Jeffrey Nyhoff and
edited by Nancy Zylstra
©2005 Calvin University (formerly Calvin College), All Rights Reserved
If you encounter technical errors, contact computing@calvin.edu.