Redstone circuits/Logic

A logic gate can be thought of as a simple device that will return a number of outputs, determined by the pattern of inputs and rules that the logic gate follows. For example, if both inputs in an AND gate are in the 'true'/'on'/'powered'/'1' state, then the gate will return 'true'/'on'/'powered'/'1'.

There are many different kinds of logic gate, each of which can be implemented with many different designs. Each design has various advantages and disadvantages, such as size, complexity, speed, maintenance overhead, or cost. The various sections will give many different designs for each gate type.

Concepts
The output of each logic circuit reflects the state of its inputs at all times (though possibly with some delay incurred by the circuit).


 * Swapping inputs


 * For most of these gates, you can swap A and B without changing the output.


 * Swapping the inputs of the IMPLIES gate will affect its output, and the NOT gate has only one input.


 * Stacking inputs


 * The AND, OR, and XOR gates can each be used in arrays to perform their operation on more than two inputs, by combining two inputs at a time, then combining the results with each other and/or other inputs. For these gates, the order in which the inputs are combined doesn't matter.


 * When an XOR gate is combined in this way, its output is on when an odd number of inputs is on.


 * Choosing a logic gate


 * When unsure which logic gate to use, try building a table like the one on the right but with just one row of outputs. List the known inputs coming in and the possible combinations of power, and for each combination write down what the output should be for the structure to work. Then compare that to the table on the right and see which gate matches the desired outputs.


 * If the the output needs to change when the input is stable, or needs to be remembered after the input has ended, you may also need to look at pulse circuits or memory circuits.

Logic gate
A logic gate is a basic logic circuit.

NOT gate
A NOT gate (¬A), 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".


 * Torch Inverter


 * 1-wide, flat (horizontal only), silent, tileable
 * circuit delay: 1 tick


 * The torch inverter is the most commonly used NOT gate, due to its small size, versatility, and easy construction.


 * One drawback of the torch inverter is that it will "burn out" if run on a clock cycle faster than a 3-clock (3 ticks on, 3 ticks off). A burnt out torch inverter will turn back on after a random time, which may produce undesired pulses in a circuit.


 * Subtraction Inverter


 * flat, silent
 * circuit delay: 1 tick


 * The subtraction inverter offers little advantage over the torch inverter except that it can run on a 2-clock cycle without burning out. Faster clocks will not work though — the comparator simply won't react to them.


 * Variations: The powered lever can be replaced with another always-on power component (e.g., redstone torch, block of redstone), or with a full container if a power component would be inconvenient in that location.


 * The repeater is required to ensure the input signal is strong enough to overcome the comparator's rear source, but can be removed in a number of ways. If the input power level is known (because the circuit design is fixed, so it can be calculated), the repeater can be removed by replacing the powered lever with a container which will produce the same power level. Alternatively, the repeater can be removed if the output continues to a length of redstone wire which will reduce the subtracted signal enough that the signal is inverted eventually.


 * Instant Inverter


 * instant
 * circuit delay: 0 ticks


 * The instant inverter is a basic building block of larger instant circuits.


 * The "ground" version has the largest volume, but is shorter and fits easily with flatter circuits. The "tall" version (not actually tallest) is the smallest in volume and resources, but has an input and output at inconvenient locations (though not necessarily for "in-the-sky" builds). The "long" version is larger but has input and output at a convenient ground level.


 * With the "tall" version, it can be tempting to take the output from the lower block below the slabs, but that output is only instant on the input's rising edge.


 * Behavior (i.e., how it works): An instant inverter has two sticky pistons -- one to move a block to cut off the output, and one to move a block of redstone power source.


 * When the input is off, the block of redstone powers the output. When the input turns on, the block of redstone is immediately moved, cutting off the output's power (instantly inverting the input). At the same time, the redstone repeater gets powered, but before it can power the output, the other block has moved into place to cut off the output.


 * While the input is on, the redstone repeater is trying to power the output, but the output is cut off by the moving block. As soon as the output turns off, the block starts to retract, immediately allowing the power through (instantly inverting the input). The repeater will only continue to power the output for 2 tick before it turns off, but by that time the block of redstone has arrived back in its original position to continue powering the output.


 * Variations: When fitting an instant inverter into a larger build which may require the inputs or outputs to be moved around, there are three components that need to be powered simultaneously: the two sticky pistons and the redstone repeater. Getting the input line to all three can be tricky. The "tall" version solves this problem by placing all three components next to a single input block, while the other versions need to split the input line to reach all components.


 * In addition, the block of redstone and its sticky piston can be moved around, as long as it is powered without delay by the input, and powers the output wire after the repeater and before the dust-cut in its retracted state only (it shouldn't power anything in the circuit when extended). The three circuits shown below illustrate ways of powering the output line from above, below, and from the side.

OR gate
An OR gate (A ∨ B) is a gate which uses two or more inputs and whenever any input is "on", the output is to "on". The only time the output is "off" is when all inputs are "off". Note that since the OR operation is associative and commutative, OR gates can be combined freely: The player can compare huge numbers of inputs by using small OR gates to collect groups of inputs, then comparing their results with more OR gates. The result will not depend on the arrangement of the inputs, or on which ones were combined first.

The simplest 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. The introduction's example, using a solid block instead of wire, does not suffer the same hazard.

If you need to use the inputs elsewhere, the inputs need to be "isolated", by passing them through a block as above, or a device such as a torch or repeater. Torches yield version B. Note that this is in fact a NOR gate with an inverter on the output.

Version C isolates the inputs with repeaters. It can be expanded horizontally up to 15 inputs. Besides the isolated inputs, it is one tick faster than B. Additional repeaters can be used to add new groups of inputs, or to strengthen the output signal. This design is more expensive, as each repeater costs 3 redstone dust to craft (along with smooth stone).

Version D is a 1-wide version designed for vertical use, such as in walls. The repeater serves to isolate the outputs from the inputs. This version can only take two inputs, though of course the inputs can be stacked with multiple gates.

Version E utilizes the properties of light-transparent blocks: glowstone, and upside-down stairs or slabs. These send signals up, but not down. It is expandable, like design C.

NOR gate
A NOR gate turns its output off when at least one of the inputs are on. All logic gates can be made from some combinations of the NOR and NAND gates. In Minecraft, NOR is a basic logic gate, implemented by a torch with two or more inputs. (A torch with 1 input is the NOT gate, and with no inputs is the TRUE gate, that is, a power source.)

A torch can easily accommodate 3 mutually isolated inputs, as in design A. Design B goes to greater lengths to squeeze in a fourth input. If more inputs are necessary, it is simplest to use OR gates to combine them, then use an inverter (NOT) at the end. It is also possible to combine OR and NOR gates, by using the inversion of OR gates as inputs to NOR gates.

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 all inputs are "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.

A 3-input AND gate is shown, but, like OR gates, AND gates can be freely "ganged", combining groups of inputs and then combining the results.

A typical use for an AND gate would be to build a locking mechanism for a door, requiring both the activating button and the lock (typically a lever) to be on.

Many AND gates act similarly to a "tri-state buffer", in which input B acts like a switch, connecting or disconnecting input A from the rest of the circuit. Such designs have one input feeding a circuit, which is opened or closed by a sticky piston driven by the other input. The difference from real-life tri-state buffers is that one cannot drive a low current in Minecraft.

NAND gate
A NAND gate (¬(A ∧ B)) turns the output off only when both inputs are on, the reverse of an AND gate. All logic gates can be made from NAND gates. As with NOR, large numbers of inputs are probably best handled by stacking up AND gates, then inverting the result. By De Morgan's Law, (¬(A ∨ B)) is identical to (¬A ∧ ¬B).

XOR gate
An XOR gate turns on if the inputs are different from each other (one on, the other off).

The XOR gate is useful for controlling a mechanism from multiple locations. When controls (such as levers) are combined in an XOR gate, toggling any control will toggle the XOR gate's output (like a light bulb controlled by two light switches—you can flip either one to turn the light on or off).

An XOR gate is a device which activates when the inputs are not the same, when only one is on. XOR is pronounced "zor" or "exor," a shortening of "exclusive or," because each input is mutually exclusive with the output. The output will be on only when exactly 1 of the inputs is on. Adding or removing a NOT gate to the end, or to either input will produce an XNOR gate, which activates when the inputs are equal to each other. A useful feature is that an XOR (or XNOR) gate will always change its output when one of its inputs changes. This lets you set up 2 switches, either of which can always open or close a door, or turn some other device on or off. (In the real world, such arrangements are common for light switches, such as a stairway light with switches at top and bottom.)

Like AND and OR gates, XOR gates can freely be "stacked" together, with gates gathering groups of inputs and their outputs being gathered in turn. The result of XORing more than two inputs is called "parity"—the result is 1 if and only if an odd number of inputs are 1.

Design D is tiny, but only useful if you want the levers to be fixed to the circuit. The shaded block indicates the block the levers and the lit torch are attached to, along with the block that one is resting on.

Design F is the most widely used of the torch-only designs, but newer components can do much better. Design H uses pistons, and is both faster and more compact.

Beyond torches and pistons, various diodes can be used to produce fairly compact and cheap XOR gates. Design I can have its input repeaters coming in from either side or underneath, changing its size accordingly to fit tight spaces. Design J uses transparent blocks for a cheaper option.

The introduction of the comparator allows for several variations of a new design, the "subtraction XOR gate", which is flat, fast and silent (also easy to remember). The catch in survival mode, is that making comparators requires access to Nether Quartz.

Each input is the same distance to the rear and side of the comparator closest to it, so will suppress its own signal there, but travels farther to get to the side of the further comparator, so won't suppress its signal in the further comparator. Only if both inputs are on will both comparators get suppressed by a side input.

However, that is only true if the inputs are the same power level (or at least not different by more than 1), otherwise one signal could overwhelm the other's attempt to suppress its signal. If this circuit is sure to receive inputs of the same power level (because the system it's part of has been designed that way), then the "basic" version can be used. Otherwise, some method should be used to ensure the inputs are equal—for example, with repeaters (the "repeated" version) or with torches (the "inverted" version).

XNOR gate
In logic, this is commonly referred to as "if and only if," ("iff" for short), "bi-conditional," or "equivalence". An XNOR gate activates only when the inputs are equal to each other—both on, or both off. Like the XOR gate, when either input changes, the output changes.

An XNOR gate can be built by inverting either the output, or one input, of an XOR gate.

Design A is a pure-torch design. If external input isn't needed, the back-facing torches can be replaced with levers, yielding B. Design F is larger but highlights the logic, while I is an inverted variant of XOR gate H. Note that the output inverter can also be placed in line with the rest of the gate, or even in a pit attached to one of the output redstone's support blocks.

IMPLY gate
An IMPLY gate turns on either if both inputs are on, or if the first input is off. (Unlike the other gates here, the inputs are not interchangeable.) This represents material implication or a conditional statement, "if A then B", or "A implies B, also written A → B.  This is false only if the antecedent A is true, but the consequent B is false.  It is the logical equivalent of "B or NOT A", and the mathematical equivalent of (A≤B) (less than or equal to).

Design C has a speed of 2 ticks if output is 1, but 1 tick if the output is 0. Similarly, the other designs take 1 tick if the output is 0, but are immediate (and not isolated) if the output is 1. If you must synchronize (or isolate) the output, consider placing a 1-tick repeater in front of the "fast" input (input A for C, input B for the others).