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.

These pages were written by Steven H. VanderLeest and Jeffrey Nyhoff and edited by Nancy Zylstra
©2005 Calvin College, All Rights Reserved

If you encounter technical errors, contact rit@calvin.edu.