Scientific Computing

This module graphically illustrates the finite, discrete nature of
floating-point number systems. A floating-point number system is
characterized by four integer parameters: the base *β*,
precision *p*, lower exponent limit *L*, and upper exponent
limit *U*. The total number of normalized floating-point numbers
in such a system is *β* − 1)
*β*^{ p−1} (*U* − *L* +
1) + 1.*underflow level*, is given by *β*^{L}*overflow level*, is given by *β*^{U+1} (1 − *β*^{
− p})

The user selects values for the base, precision, and lower and upper limits for the exponent range. The machine numbers in the resulting floating-point number system are indicated by tick marks on the real number line. The largest and smallest positive machine numbers, as well as the total number of machine numbers, are also printed. Clicking the mouse anywhere on the number line highlights in red the corresponding rounded value, and both the selected value and rounded result are printed below.

**Reference:** Michael T. Heath,
*Scientific Computing,
An Introductory Survey*, 2nd edition, McGraw-Hill, New York,
2002. See Section 1.3, especially Example 1.9 and Figure 1.3.

**Developers:** Nicholas Exner and Michael Heath