The game criteria is intentionally very open-ended. The goal is to make a game that incorporates logic into a fun challenge. Thus far, many students are opting to adapt a game that already exists, but one could design a game from scratch if they so desired.
Game ideas one could make are Dr.Mario where the colors are logic gates and you have to modify the pills so that when a certain number are together they disappear.
One could also make the hit Commodore 64 game Number Builder but instead of numbers it is bits. Where each “tile” color is a different logical operation that affects your current number until you can get to the target number.
One could also make a tower defense game where you place towers that relate to each kind of logic and that shoot a certain number to an “enemy” number that then changes that enemy's “value.” And you keep shooting at that enemy until they become a certain number, probably zero would be the easiest.
One could also do a shooting game where you and the enemies have bullets and you shoot their bullets with different logic to turn their bullets into zero's so that they can't hurt you.
One could do a rhythm game where you have to press the right key (logic) for the right note (some number) to make it zero.
For refresher, there are seven logic operations one will want to make use of. This includes:
AND OR XOR
NOT
NAND NOR XNOR
A B | Y ----|-- 0 0 | 0 1 0 | 0 0 1 | 0 1 1 | 1
A B | Y ----|-- 0 0 | 0 1 0 | 1 0 1 | 1 1 1 | 1
A B | Y ----|-- 0 0 | 0 1 0 | 1 0 1 | 1 1 1 | 0
A | Y --|-- 0 | 1 1 | 0
A B | Y ----|-- 0 0 | 1 1 0 | 1 0 1 | 1 1 1 | 0
A B | Y ----|-- 0 0 | 1 1 0 | 0 0 1 | 0 1 1 | 0
A B | Y ----|-- 0 0 | 1 1 0 | 0 0 1 | 0 1 1 | 1