Floating-point mathematics

Modern processors usually support integer data types in widths of 8, 16, 32, and 64 bits. Some smaller embedded processors may not directly support 64-bit or even 32-bit integers, while more sophisticated devices may support 128-bit integers. Integer data types are appropriate for use in a wide range of applications, but many areas of computing, particularly in the fields of science, engineering, and navigation, require the ability to represent fractional numbers with a high degree of accuracy.

As a simple example of the limitations of integer mathematics, suppose you need to divide 5 by 3. On a computer restricted to using integers, you can perform an integer calculation of this expression as follows, in C++:

#include <iostream>
int main(void)
{
    int a = 5;
    int b = 3;
    int c = a / b;
    std::cout << "c = " << c << std::endl;
    return 0;
}

This program produces the following output:

c = 1

If you...