Java KV diagram and logic minimization demonstration

This applet requires Java version 1.0 or higher. Because different colors are used for the "loops", it will only display correctly on a color display. For a short help about the applet see below.

KV diagram diagram applet for JAVA 1.0 (JDK appletviewer, Netscape 2.x or higher, MSIE 3.x or higher)

All comments, hints and bug reports are welcome: Please contact Norman Hendrich.

Applet basics:

• The applet on this page demonstrates KV diagrams and logic minimization. For a detailed explanation of KV (Karnaugh Veitch) diagrams see any standard computer science or electrical engineering textbook. The applets supports disjunctive (AND-OR) and conjunctive (OR-AND) forms. Minimiziation of multiple-output functions, however, is only supported in disjunctive form.

• The basic idea of a KV diagram is to represent a given boolean function as a kind of function table. At first, the function is represented using minterms. In order to minimize the function, one has to combine minterms to larger terms.

  The applet demonstrates how this works, because the current two-level logic realization of the function is plotted in a seperate window and updated whenever you combine terms. You can watch how the function schematic gets simpler (and the logic realization gets cheaper) while you minimze the function.

• The way to minimze a logic function using a KV diagram is to draw loops, in order to combine several minterms to larger terms. Larger terms are cheaper than minterms in the logic realization!

  Two examples of an initial logiv function KV diagram, its circuit realization and the optimized versions can be found here:

  • Example 1
  • Example 2

Applet usage:

• The applet consists of the main window, and two seperate PLA windows. The main window contains a menu bar on top, the KV diagram frame in the center, and a status area on the bottom.

  The two seperate PLA windows are used to display the schematic for the current function (that is, a two level AND-OR realization for the function), and the PLA table in the standard PLA (Espresso.5) format.

  The status line displays a kind of 'one line help messages' on what kind of mode the applet is in, and what you can (and should) do with the applet.

• Select the File: menu item to create a random, user-defined, or predefined example logic function with 2 to 6 inputs. The corresponding KV diagram without loops is drawn, and the PLA frame window displays the function realized with minterms.

  If you want to enter your own function, select a new function of the desired size (number of inputs and outputs). Afterwards use Edit Mode to enter your function.

• Click on the Edit function button to enter Edit Mode. In this mode, the value of f[i] is toggled between 0 and 1 when you click on the KV diagram field i.

  This mode also allows you to enter a desired function bit by bit, if you want to use the KV diagram applet for actual logic minimization.

• Click on the Add Loops button to enter Add Loop Mode. In this mode, you can start a new loop with index i, when you click on the KV diagram field i. In disjuntive mode, you can combine the '1' terms, in conjunctive form the '0' terms.

  To enlarge the loop, hold down the SHIFT key on your keyboard and click on the field you want to add to the current loop. The applet will automatically calculate all fields enclosed in the current loop (or warn you, if the clicked field cannot be added to the current loop).

  Loops are drawn in different colors (which repeat after 8 loops), in order to allow easy recognition of loops.

  Any time a loop is drawn, the PLA schematic and table are updated. Loops and the correspondings AND-gates are drawn in the same color.

• If you want to undo a loop, or to delete all loops, click on the Delete Loop button to enter Delete Loop Mode.

  On each click, this will delete the last loop drawn. Each deleted loops is split into the corresponding minterms, and the PLA schematic and table are updated.

• Click on the Index button to enter Index Mode. When you click on a field of the KV diagram in Index Mode, the active AND terms for this field (for all loops enclosing this field) are highlighted in the PLA schematic.

  Also, the numerical index (0 .. 63) of the KV diagram field in displayed in the Status Line on the bottom of the applet. This makes it easy to find a certain index field in the diagram, just by clicking a few times.

  (Note for Computer Science profs: The layout of the diagrams was deliberately modified somewhat from the standard layout. Using the applet for doing the homework will therefore still need some understanding...)

last update: Thu Jan 28 16:19:43 MET 1999 Norman Hendrich