ROLUAN: Ternary "AND" Gate

Today we will discuss about how a ternary "AND" gate can be represented in a logical circuit. 

What is "AND" gate? If in short, it represents the minimum value between two ternary inputs (trits, that can have one of the following states: "-1", "0" or "1"). So, if we will have two inputs, "A" and "B", then the ternary "AND" circuit should choose the minimal value of them and pass the result further. For more details, see the article on wikipedia. This result can be an input for another ternary gate, or a final result, stored in a memory circuit.

We already know the "AND" ternary formula, or, more correctly, ternary "AND" truth table:


Ok, let's see the general circuit schema (excluding additional components), that can implement at hardware level this truth table:


As we see in the picture, we have two inputs on the left (for convenience, we put there a switch between ground and voltage source to make testing more easy), two voltage sources and a light. If light will be on, it will mean that we will have voltage. If off - we can consider it as "0".

The schema represents 4 transistors: two of them are n-MOS and two are p-MOS. The n-MOS transistors are linked in series, the p-MOS - in parallel. It looks like we have one binary "AND" and one binary "OR" that are connected at the same inputs.

Ok, let's check each combination. According to the truth table we have in total 6 combinations, excluding inverted ones.

Case A: "1" and "-1":
At output we have "-1". The light is On.

Case B: "0" and "0":
No current. The output is "0". The light is Off. 

Case C: "1" and "0":
The output is "0". The light is Off. 

Case D: "1" and "1":
The output is "1". The light is On. 

Case E: "-1" and "0":
The output is "-1". The light is On. 

Case F: "-1" and "-1":

The output is "-1". The light is On. 

The emulator code that correspond to this gate is described on our GitHub repository here.

In this article we found how can be constructed a circuit that represents Ternary "AND" Gate. See you next time.