User:YEAH TOAST4555/Redstone logic

Using redstone, one can implement logic  gates in Minecraft. As in digital electronic circuits, simple  redstone gates can be combined to form more complex redstone gates,  which can be combined into even more elaborate devices.

Logic Gates
A Boolean logic gate performs a logical operation on one or more logic inputs and produces a single logic output.

For an input of 2 binary variables, there are 16 possible Boolean algebraic  functions. These functions are shown below, together with the output given by each combination of inputs.

Implementations
For each of the most common logic gates, possible redstone implementations  are shown below. Note that most circuits have multiple valid implementations, each with various advantages and disadvantages. Important properties to consider are size (in each dimension), material requirements, location and isolation of the inputs and outputs, and  speed, measured by the worst case number of ticks required by the gate  to process the input.

Not (Inverter)
Along with the Or gate, this is one of the simplest possible gates in Minecraft.

Or
A simpler version of the Or gate is design A: merely a wire connecting all inputs and outputs. However, this causes the inputs to become "compromised", so that they can only be used in this OR gate. If you need to use the inputs elsewhere, version B is necessary.

Note that design B is a simple inversion of a Nor gate.

Nor
Due to the simplicity and compactness of the Not and Or gates in Minecraft,  the smallest and most efficient gates use the Nor as their fundamental  building blocks. Any gate can be built entirely out of Nor gates.

This is the  basic logic gate. A torch can have as many as 4 mutually  isolated inputs (design B), but 3 can fit comfortably  (design  A), and all are optional. A torch with 1 input is the Not gate,  and with no inputs is the True gate (i.e. a power source). If more  inputs than 4 are necessary, one must resort to the non-isolated Or   gate with a Not at the end (at expense of isolation), or multiple Nor   gates, according to the formula A ⊽ B ⊽ C = A ⊽ ¬(B ⊽   C) (at the expense of speed, due to the nested gates).

Nand
The  simplest possible Nand gate must be constructed from two Not gates and   an Or gate. This means that while it is possible to construct any gate using only Nand gates, the most efficient designs will revolve around  the Nor gate.

Implies
A device which represents material implication. Returns false only if the implication A → B is false, that is, if the conditional A is true, but the consequent B is false.