My notes read "AND/OR exhibit duality"?

Question

In logic gates, if it is said that AND/OR gates exhibit duality, what exactly do they mean? and how about applying duality to gates? what does that mean plz? thnx so much guyz!!

Answer 1

The duality principle says that for every logic system, there is another form that will perform the same function.

Most theorems occur in pairs.
If you're given one theorem,
and you replace all the AND gates for OR gates,
and the OR gates for AND gates,
you'll get the other theorem.

Answer 2

There is Positive Logic and negative Logic. The difference between the two is wether or not a voltage is considered a high (1) or low (0)

Consider a Diode OR circuit where two diode cathodes are connected to a pull down resistor.
in Positive logic a voltage is considered a High so applying a voltage to either input places a voltage on the resistor as current flows through the forward basiased diode(s)

With this same circuit if we do not change a thing electrically except what we consider Hi and Lo are we can redefine the Positive logic OR into a Negative logic AND.

In negative logic the presence of a voltage is now considered a Low.

In negative logic when a low is applied to a single diode input you are applying a voltage which will pass through the diode as before and can be seen on the resistor. In this case the output voltage is now considered a logic Low. The other diode input can have a Negative Logic Hi (zero volts) on the other input the output is still showing voltage (Neg logic LOW) This same electrical circuit is now acting like an AND gate by mearly switching the convention of what voltage levels represent which logic state.

If you want to work this out using regular Positive logic do a truth table for a gate. Then add an inverter to each input and the out put and solve the truth table. you will fine that you can change between AND's and OR's by inverting the logic states at the input & outputs.