====== Digital gates ======
DeMorgan's theorem in graphical form:

{{:courses:phy305l:demorgan.png?nolink|}}

This is important because real world is full of 'active-low signals' and 'assertion-level symbols'.

An AND gate with active-high I/O is similar to an OR gate with active-low I/O.

Now-a-days we do not use small packages of gates, but ICs. A few dollars can buy an IC with 1600 gates; this is a gate array.

Gate arrays come in 2 forms: Application-specific ICs (ASICs) and Field-programmable gate arrays (FPGAs). Beside these we have something called Programmable Logic Devices or PLDs. PLDs are simpler than FPGAs.

===== Apparatus =====
{{https://upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Elenco_Logic_probe_LP-560.jpg/1024px-Elenco_Logic_probe_LP-560.jpg?nolink}}
Logic probe: a gizmo the size of a thin hotdog; a cord on one end, a sharp point on another. The cord takes power (+5 V or ground), the point indicates the logic level.

{{https://upload.wikimedia.org/wikipedia/commons/thumb/7/73/400_points_breadboard.jpg/1024px-400_points_breadboard.jpg?nolink}}
Breadboard with LED indicators.