Boolean Logic Game

This applet allows you to play a game using boolean logic. The idea is to create all of the numbers 0 to 15 using only four boolean operators (AND, OR, NOT, XOR) and a few given starting numbers.

Further Questions

1. Using the applet, generate "proofs" that the numbers 0 through 15 can be generated from any starting state of (number, number, [number], AND, OR, NOT, XOR). List a set.

Example, given (2, 3, 5, AND, OR, NOT, XOR):
• 0 = 2 AND 5
• 1 = 3 AND 5
• 2 = given
• 3 = given
• 4 = 1 XOR 5
• ...

2. Using the applet, or just paper and pencil (whichever you find easiest), determine the minimum number of starting numbers needed to generate the set U = {0,...,15}, using only the four given boolean operators.

3. Boolean logic of this sort makes for fun games! What does this mean for breeding Pokemon characters in the Gameboy game? Go to the following web site to learn about Pokemon breeding: http://www.pojo.com/videogames/GoldSilver/PokemonBreedingInfo.html.

Created by Andrew Freed, arf132@psu.edu on April 29, 2002.
Modified by Andrew Freed, arf132@psu.edu on April 29, 2002.

Development of this applet was sponsored by the Penn State Fund for Excellence in Learning and Teaching (FELT), project "Java-based Teaching of Mathematics in Information Sciences and Technology", supervised by Frank Ritter and David Mudgett.