Tutorials/Basic logic gates

Logic gates in Minecraft are a way of using redstone circuits in a manner that a certain combination of inputs, or redstone signals, achieves a certain output. They are similar to computer logic gates in a way, but are slightly different in their constructs.

Basic Info
Some basic info about Minecraft needed to understand redstone circuits and gates:
 * There are ten items that can provide an input charge into redstone. These are levers, pressure plates, redstone torches, redstone blocks, buttons, detector rails, tripwire hooks, trapped chests, observers, and daylight sensors.
 * Switches are most commonly used with gates because of their ease of use and the fact that they are easily made.
 * When redstone torches are powered, they go into an "off" state and stop providing power themselves.
 * Any block can have redstone placed on it except leaves and glass, with a few more exceptions.
 * Glowstone can have redstone wire placed on it, but not torches or repeaters.

Using Logic Gates


Logic gates are used to create circuits more complex than a single on/off switch. For instance, if you wanted to have a redstone lamp light only when two switches were both toggled to the "on" position, you would use an AND gate. If you wanted no signal when a switch is on, but wanted a signal when a switch is off, you would use a NOT gate. Lighting in modern buildings controlled by two or more switches (for example: a light in a hallway with a switch at each end) use XOR gates.

Gates can be used in combinations to create complex signal patterns, and some have even successfully created redstone computers using logic gates. See Tutorials/Advanced redstone circuits for more info.

NOT Gate


A NOT gate (¬A), also known as an inverter, is a gate used when an opposite output is wanted from the input given. For instance, when the switch, or input, is set to "on", the output will be toggled to "off", and when the switch is toggled to "off", the output will be toggled to "on".

AND Gate


An AND gate (A ∧ B) is used with two or more switches or other inputs. The output is toggled to "on" ONLY when both switches, or inputs, are toggled to "on". Otherwise, the output will remain "off". In reality, the image provided is a NOR gate with inverted inputs. By taking the logic of A and B, the first two torches (top and bottom from the image) invert them into ¬A ∨ ¬B, then the third torch (the center-right one) applies a NOT to that statement. Thus it becomes ¬(¬A ∨ ¬B), which can be interpreted as A ∧ B by De Morgan's Law.

NAND Gate


A NAND gate (¬(A ∧ B)) is the opposite to the AND gate. The output is toggled to "off" ONLY when both switches are toggled to "on". Otherwise, the output is set to "on". This gate also requires two or more inputs. (By De Morgan's Law, (¬(A ∨ B)) is identical to (¬A ∧ ¬B)

OR Gate
An OR gate (A ∨ B) uses two or more inputs. Whenever any input is "on", the output is to "on". The only time the output is "off" is when all inputs are "off".

NOR Gate


A NOR gate (¬(A ∨ B)) is the opposite of the OR gate. Whenever at least one switch is toggled to "on", the output is toggled to "off". The only time the output is "on" is when all inputs are toggled to "off". This gate also uses two or more inputs.

XOR Gate


An XOR gate (A ⊻ B) is a gate that uses two inputs. In this gate, the output is toggled to "on" when one switch is "on" and one switch is "off". If both switches are in the same position, the output is toggled to "off". Because of these properties, XOR gates are commonly found in complex redstone circuits. In some cases, it is possible to get an OR gate output and an AND gate output on different channels. (The reason why it is possible is because, the circuit above is composed out of AND gates, OR gates and NOT gates. The whole circuit is ¬(¬(A ∨ B) ∨ A) ∨ ¬(¬(A ∨ B) ∨ B), which can be further simplified into (¬A ∧ B) ∨ (A ∧ ¬B) )

XNOR Gate
An XNOR gate (A ↔ B) is the opposite of an XOR gate. It uses two inputs. When both switches are in the same state (both switches are "on" or both switches are "off"), then the output is toggled to "on". Otherwise, if the switches differ, the output is toggled to "off".

NOTE: The capital N in every gate listed above means NOT. For example, the NAND gate means NOT AND, thus anytime an AND gate would output an "on" signal, a NAND gate would output "off." And anytime an AND gate would output "off," a NAND gate would output an "on" signal. Important Note for beginners to the concept of logic gates: Some explanations use terms like "low-power" and "high-power" to describe signal inputs and outputs of logic gates. "Low-power" is akin to "off," and "high-power" is akin to an "on" signal.

ONLY / NON-IMPLY Gate
NOTE: This 'gate' is just a special case of a NOR gate where one of the inputs is inverted.

In this gate, the output is toggled to "on" only when input A is "on" and input B is "off". If input A is "off" and input B is "on", the output will remain "off". If both inputs are "off" or "on", the output will remain "off". This makes this gate useful when needing a specific order of inputs to trigger the output.



Diodes
Diodes prevent power from flowing backwards in a circuit. This can be very useful if the player needs to isolate an input wire to avoid feedback, or need to merge two inputs into one (such as in the OR gate above). There are three flavors of diodes: The one-block one (up to four) tick delay repeater, the three-block two tick delay redstone torch repeater that is also called a classic or traditional repeater, and the two-block, zero tick delay glowstone diode.



Repeater
Repeater based diodes are the easiest to make, by simply placing a repeater in a line of redstone, the player have a simple one-tick delay diode. This simple mechanism can be seen demonstrated in the image to the right.

Torch Repeater
Torch based repeaters are effective for making diodes (at a heavy cost of two ticks, however) because torches do not go out if you power them from a block they are not attached to. They are simply two NOT gates (and can be spaced much wider, allowing more transmission range at a lower cost than repeaters), by placing two solid blocks (not glass, glowstone, leaves, etc.) then a torch on the top of the block you're sending power to you create the first NOT gate, you then lay wire on the second block and place a torch on one side, this second torch will be switched off after a brief pulse, by the torch on the first block. If the player like, they can also lay wire instead of placing the torch immediately, up to 15 blocks of it; after 15 blocks, however, you must place a third block at the very end and place the second torch on one side of that before you continue laying wire.

A possible alternative to placing two blocks for the first torch if you're doing long distance transmission is to dig one block down, and place wire in the hole then place a torch on the block the wire in the hole connects to. This will give you the final block for the other NOT gate as well, so you don't need to carry spare blocks for the repeaters or diodes.

Glowstone, Stairs, and Slabs
Glowstone, stairs, and slabs are utilities in redstone circuits due to a few interesting features of how they transmit power. They all:


 * Allow power to go through their lower and upper edges (see vertical transmission below)
 * Allow power to transmit up to a wire on its surface (top).
 * Do not allow power to transmit from its surface to a block below.

That last feature is the most used. Among other things, it allows the use of these to construct a diode. Placing redstone up to one of these blocks, across to a normal block on the same level, then back down (see figure), creates a zero-tick-delay diode that prevents feedback loops in time-sensitive circuits.

That same feature also allows for 1-wide, 2-deep instant vertical redstone transmission.