I think the answer depends on whether you only need to draw the operation or truly simulate it.

For simply drawing:
Code:

...
void draw() {
  background(255);
 
  noFill();
  rect(20,20,40,40);
  
  if (inputvalue) {
    //Z shape
    line(20,30,50,30);
    line(30,50,60,50);
    line(50,30,30,50);
  } else {
    //draw default state
    line(10,30,40,30);
    line(40,50,70,50);
    line(40,30,40,50);
  } 
  
} 
...
 

For simulation, you may want to look into the BoxWrap2D library:
http://jbox2d.nfshost.com/processing/

It would be more complex to program, but would provide an animated operation of your NOT gate.

Yes.
There are a couple animation examples that come with processing or at:

http://processing.org/learning/topics/sequential.html

and
http://processing.org/learning/topics/animatedsprite.html

Yep.
If your images have the same width as the length of the lines, all you have to do is use the same first x and y coordinate of the horizontal lines.

If they are a difference size, you will have to scale those values.

For the angled line (the one that appears to rotate), using two images may be easier. You can rotate images if you want to try that though.

See this link for an example of rotating an image by a set amount.

http://processing.org/discourse/yabb_beta/YaBB.cgi?board=Programs;action=display;num=1213532886

Hello  I have kept it in the class named NOT .I want to export it into the library .How can i do that ?

the final code is like this :

class NOT {
boolean inputvalue = false;//store the input state
PImage a;
PImage b;
PImage c;

void setup() {
 size(500,500);
 
 
}

void mouseReleased() {
 //toggle the input state
 inputvalue = !inputvalue;
}
void draw() {
 background(255);

 noFill();
 rect(20,20,40,40);
 a= loadImage("nanotube1.jpg"); // load image
 
 if (inputvalue) {
   //Z shape
   line(20,30,50,30);
   line(30,50,60,50);
   line(50,30,30,50);
 } else {
   //draw default state
   //line(10,30,40,30);
   image(a,10,30);
   line(40,50,70,50);
   line(40,30,40,50);
 }  
 
}  
}

Thank you

In reverse order:

The 'export as application' will create an *.exe. Java is still required and will direct the user to download if necessary.

An example of using a custom class is found here:

http://processing.org/reference/class.html

To have one 'feed' another like a circuit, you could use a reference to your NOT class inside that class.

Code:

class Not {
  Not connectedTo;

  Not {
    //setup
  }

  void connectMeTo(Not cn) {
    connectedTo = cn;
  }

  //to match the example
  void update() {
    //check the output of connectedTo
    //change state based on that
    //
    //draw stuff
  }

}
 

Now, to control more than one Not gate, you would have to add a test within the mouseReleased method to see if the mouse is over the gate. Similar to making your own button.

I would probably follow this example:

http://processing.org/learning/topics/buttons.html

and create buttons for each NOT gate that you would like to display.

After clicking on one, make sure to update any that reference the gate that was clicked.

May not be exactly what you need:
Code:

//when NOT gate has been clicked
clickedGate.updateState();

...
//inside Not class
void updateState() {
  //do update code for this gate

  if (pointsTo != null)
    pointsTo.updateState();

}
 

That way, any click will update the input of the next.

If you have specific questions, feel free to ask.