Answer:

Because decimal-based floating point numbers have similar problems, but with different numbers. For example 1.0/3.0 == 0.3333... without end. All floating point schemes have similar problems. Since binary has so many other advantages, most computers use it. Electronic calculators sometimes use hardware decimal-based calculations since they always present their results to humans. Also, mainframe computers usually include hardware decimal-based instructions for use in financial calculations.

Sin(x) Applet

(The rest of this chapter may be safely skipped.)

Let us graph the sine of x, for x in the range of 0.0 to 2 PI radians. Here is a start on doing this. The value of PI is part of the class Math. You get it with Math.PI. To get accurate results, let us use an increment of 1 over a power of two. (If you have not read the chapters on applets, you can skip the rest of this chapter with little loss.)

// assume that the drawing area is 600 by 400
public class sineWave extends Applet
{

    public void paint ( Graphics gr )
    {
        double inc = 1.0/32.0;
        for ( double x = 0.0; x <= 2*Math.PI; x = x + inc )
        {
          int startX = (int)x;
          int startY = (int)Math.sin( x );
          int endX   = (int)x + inc;
          int endY   = (int)Math.sin( x+inc );
          gr.drawLine( startX, startY, endX, endY );
        }
    }
}

The idea is that each iteration of the loop will compute two points on the curve sin(x) and connect them with a line. If the separation between all the points is small, all the straight lines will look like a curve. The various floating point values (such as x) are cast into int because that type is what drawLine() expects.

QUESTION 9:

(Debugging Practice: ) There is a problem with the code as it is so far. Can you find it? Hint: consider the values that sin(x) will have.