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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.

Latches and Flip-Flops
Latches and Flip-Flops are effectively  1-bit memory cells. They allow circuits to store data and deliver it at a later time, rather than acting only on the inputs at the time they are  given. Functions using these components can be built to give different outputs in subsequent executions even if the inputs don't change, and so  circuits using them are referred to as "sequential logic". They allow for the design of counters, long-term clocks, and complex memory  systems, which cannot be created with combinational logic gates alone.

The common feature at the heart of every redstone latch or flip-flop is the  RS NOR latch, built from two NOR gates whose inputs and outputs are  connected in a loop (see below). The basic NOR latch's symmetry makes the choice of which state represents 'set' an arbitrary decision, at  least until additional logic is attached to form more complex devices. Latches usually have two inputs, a 'set' input and a 'reset' input, used to control the value that is stored, while flip-flops tend to wrap  additional logic around a latch to make it behave in different ways.

RS NOR latch


A device where Q will stay on forever after input is received by S. Q can be turned off again by a signal received by R.

This is probably the smallest memory device that is possible to make in  Minecraft. Note that Q means the opposite of Q, e.g. when Q is on, Q is off and  vice-versa. This means that in certain cases, you can get rid of a NOT gate by simply picking the Q output instead of  putting a NOT gate after the Q output.

A very basic example of use would be making an alarm system in which a warning light  would stay turned on after a pressure plate is pressed, until you hit a  reset button.

In the truth table, S=1, R=1 is often referred to as forbidden, because it breaks the inverse relationship  between Q and Q. Also, some designs where the input is not isolated from the output, such as B and D, will  actually result in Q and Q both apparently being  1 in this case. As soon as either S or R becomes 0, the output will be correct again. However, if S and R both become 0 on the exact same tick, the resulting state could be either Q or Q, depending on quirks  of game mechanics. In practice, this input state should be avoided.

RS NAND latch
Since NOR is the basic logic gate in Minecraft, a design for an RS NAND latch  is just an RS NOR with inverters applied to the inputs and outputs.

When S and  R are both  off, Q and Q  are on. When S is on, but R  is off, Q will be on. When R is on, but S is off, Q will be on. When S and R are both on, it does  not change Q and Q. They will be the same as they were before S and R were both turned on.

D Flip-Flop
A D flip-flop, or "data" flip-flop, sets the output to D only on certain conditions. The basic level-triggering D flip-flop (design A), also known as a gated D latch, sets the output to D as long as the clock is set to OFF, and ignores changes in D as long as the clock is ON. Design B includes an edge-trigger, and will set the output to D only at the moment the clock goes from OFF to ON.

In these designs, the output is not isolated; this allows for asynchronous R  and S inputs (which override the clock and force a certain output  state). To get an isolated output, instead of using Q simply connect an inverter to Q.

Design C is a one block wide version of A, except for using a  non-inverted clock. It sets the output to D as long as the clock is ON (turning the torch off). This design can be repeated in parallel every other block, giving it a much smaller footprint, equal to the minimum  spacing of parallel data lines (when not using a "cable"). A clock signal can be distributed to all of them with a wire running  perpendicularly under the data lines, allowing multiple flip-flops to  share a single edge-trigger if desired. The output Q is most easily accessed in the reverse direction, toward the source of input. Q can be inverted or repeated to isolate the latch's Set line (the unisolated Q  and Q wires  can do double duty as R and S inputs, as in design A).

JK Flip-Flop
An unclocked JK Flip-Flop works a lot like a RS NOR Latch. When the input J is ON and the input K is OFF, the output Q is ON. It will then hold that state until only K or both is ON. When only K is ON the Q is OFF. When both inputs are on they will start a race condition. This means that the output will keep changing until one of the inputs is turned OFF  (It doesn't race fast enough to burn out the torches).

''NOTE: Some of the illustrated JK Flip-Flops to the right don't include the  typical inverse Q output. If you want to use the inverse Q then just add an inverter to the Q.''

T Flip-Flop
T Flip-Flops are also known as "toggles". Whenever T changes from 0 (off) to 1 (on), the output will toggle its state.

A useful way to use T Flip-Flops in Minecraft could for example be a button connected to the input. When you press the button the output toggles (a door opens or closes), and does not toggle back when the button pops out. (Designs C and D do not have an incorporated edge trigger and will toggle multiple times unless the input is passed through one first.)

It is also the core of all binary counters and clocks, as it functions as a "period  doubler", turning two input pulses into one output pulse.

Design A has a large footprint, but is easy to build. It (and B, which is a slightly compacted version of A) is essentially a JK  flip-flop with the inputs for J and K removed so that it relies on the  edge trigger (right side of the diagram) to keep it in the stable state  and only allow a single operation per input.

Design C has a smaller footprint and an easily accessible inverse output,  but lacks an edge trigger. If the input is kept high, it will repeatedly toggle on and off, cycling quickly enough to burn out its  torches. For example, if the button mentioned above is wired directly to its input, the device can toggle several times before the button shuts  off. Even a 4-clock is too slow to reliably result in only one toggle.

Adding an edge trigger by routing input through a separate pulse generator  (design B' seems to work best) will prevent this problem, as will  any other means of sending it a short (2-3 tick) pulse of power.

Designs D and E are much taller than the others, but only a single  block wide, making them good for situations where floorspace is limited. D is level-triggered like design C, which can save space when distributing one input pulse to multiple flip-flops. E has a single block wide edge trigger added on, making it easy to daisy-chain  multiple units to create a binary counter or period-doublers for a slow  clock. These designs are based on the vertical gated D latch (design C) with the inverse output looped back to the input.

''NOTE: Some of the illustrated T Flip-Flops to the right don't include the  typical inverse Q outputs. If you want to use the inverse Q then just add an inverter to Q.''

Repeater
Using two Redstone torches in series can effectively extend your running wire  length past the 15-block limitation. As of 1.0.2 (the July 6th update), there must be a strip of wire between the two Redstone torches. Repeaters makes it possible to send long-distance signals around the map, but in the proccess slow down the speed of transfer. To reduce delays, you can stretch out the repeater so that some areas of the wire  are consistently in the opposite state, but as long as the amount of  Redstone torches, or, effectively, NOT Gates is even,  the signal will be correct.

The North/South Quirk
A specific arrangement of torches which would normally be expected to behave identically to a repeater, causing a 2-tick delay in signal transmission, instead causes only a 1-tick delay. (See figure 1.) When constructed with the torches facing east and west, this arrangement causes the expected 2-tick delay, but when facing north and south, the second (top) torch changes state at the same time as the first, after only a single tick. The quirk can cause unexpected bugs in complicated circuit designs when not accounted for, but it does have  several practical uses. For example, double doors require opposite power states, but inverting one signal delays that door's response by 1 tick. The only known way to perfectly synchronize them is with this 1-tick repeater. Another application is in creating a clock circuit (see below) with an even pulse width and period.

Finally, as a generalization of the double-door use, the North/South Quirk can be used  to obtain two signals which are always inversely related without the  additional 1-tick delay a NOT gate normally causes in the second signal. (See figure 2.) This can be especially useful in circuits where precise timing is important, such as signal processing that relies on the  transition of an input from high to low and low to high (on to off and  back), for example by sending each of the inverse signals through  separate edge detectors (see pulse generators below) and then ORing  their outputs.

Delay Circuit
Sometimes it is desirable to induce a delay in your redstone circuitry. Delay circuits aim to do this in a compact manner. These two delay circuits utilize torches heavily in favor of compactness, but  in doing so the builder must be aware of the North/South Quirk. For maximum signal delay, construct these designs so that the stacked  torches face east and west. For a fine-tuned delay, adjust the design to rotate one of the alternating-torch stacks to face north and south, or  add an additional stack in that orientation.

Clock generators
Clock generators are devices where the output is toggling on/off constantly. The simplest stable clock generator is the 5-clock (designs B and  C). Using this method, 1-clocks and 3-clocks are possible to make but they will "burn out" because of their speed, which makes them  unstable. Redundancy can be used to maintain a 1-clock, even as the torches burn out; the result is the so-called "Rapid Pulsar" (design  A). Slower clocks are made by making the chain of inverters longer (designs B'  and C'  show how such an extension process can  be achieved).

Using a different method, a 4-clock can be made (design D). A 4-clock is the fastest clock which will not overload the torches.

A 4-clock with a regular on/off pulse width is also possible as seen in design E. This design uses five torches, but can be constructed so that it has a pulse width of 4  ticks by employing the North/South Quirk. It is important that the orientation of this design (or at least the portion containing the  stacked torches) be along the north/south axis.

The customary name x-clock is derived from half of the period length,  which is also usually the pulse width. For example, design D will produce a sequence   on  the output.

Pulse Generators
A device that creates a pulsed output when the input changes.

Design A will create a short pulse when the input turns off. By inverting the input as shown in B, the output will pulse when the input turns on. The length of the pulse can be increased with extra inverters, shown in B'. This is an integral part of a T flip-flop, as it prevents the flip-flop changing more than once in a single operation. Designs A and B can be put together to represent both the increase of A and the decrease of A  as separate outputs, these can then be ORed to show when The input  changes, regardless of its state.

A pulse generator which causes a short pulse of low power instead of high can be made by  removing the final inverter in design B' and replacing it with a wire  connection. This is the type used in designs A and B of the T and JK flip-flops (when J=1 and K=1) to briefly place these devices in the  'toggle' state, long enough for a single operation to take place.

Vertical transmission
Sometimes it's necessary or desirable to transmit a redstone state vertically,  for example to have a central control or status for several circuits  from a single observation point. To transmit a state vertically, a 2×2 spiral of blocks with redstone can be used to transmit power in either  direction, and the spiral is internally navigable (i.e. one can climb or  descend within the tower).

If repeaters are necessary, there is a 1×1 design for transmitting a state upward, and a 1×2 design  for transmitting a state downward. Internal navigability of these designs inside a 2×2 tower interior can be maintained using ladders.

Related pages

 * Redstone
 * Redstone (wire)
 * Redstone (ore)
 * Redstone (dust)
 * Redstone Torch
 * Advanced Electronic Mechanisms
 * Mechanisms
 * Traps

Redstone-Schaltkreise