Positive logic defines the high voltage level as 1 and the low voltage level as 0. Negative logic defines the high voltage level as 0 and the low voltage level as 1. Logic gates like NAND and NOR will have different truth tables under positive and negative logic systems. The characteristics of a logic family include speed, fan-in, fan-out, noise immunity, and power dissipation. Speed considers transition times, fan-in is the number of inputs, fan-out is the maximum number of output circuits, noise immunity is the tolerance for noise, and power dissipation should be minimized.