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Comparator Minecraft

depends on the Rayleigh range of the input beam. For the image beam waist to appear at this distance, the object beam waist should be separated from the lens by a distance one Rayleigh range larger than the focal length, ().

Comparator circuit

Unique Behavior of Gaussian BeamsThe behavior of Gaussian beams can be surprising, especially when compared with the predictions of the ray optics model and the conventional thin-lens equation.

Generally speaking, the comparator output signal strength represents the average fullness of the slots, based on how many of that item form a full stack (64, 16, or 1 for non-stackable items).

In the modified thin-lens equation, these distances refer to the separations between the lens and the input and output beam waists, respectively (Figure 1). The radius of a beam is smallest at its waist and increases with distance. A lens placed in the beam outputs a new beam with its own waist and divergence characteristics. The input beam waist radius (Wo ) is treated as the object size, and output beam waist radius (Wo' ) as the image size.

For a more in-depth breakdown of changes to repeater textures and models, including a set of renders for each state combination, see /Asset history

Comparator in digital Electronics

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A redstone comparator can be placed on the top of any opaque block with a solid full-height top surface (including upside-down slabs and upside-down stairs). In Bedrock Edition, a comparator can also be placed on walls and fences. For more information about placement on transparent blocks, see Opacity/Placement.

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A redstone comparator in subtraction mode (front torch up and powered) subtracts the signal strength of the higher side input from the signal strength of the rear input.

Comparator in research

Example 4: To produce a signal strength of 10 from a hopper, one requires a full-stack-equivalent of at least 3s + 14 = 206 but strictly less than than 3s + 37 = 229. This can be done with 3 minecarts, and 14 dirt.

Items that stack to a max of 16 (snowballs, signs, ender pearls, etc.), contribute +4 to the full-stack-equivalent for each unity (count of 1 item). Similarly, items that stack to 1 (minecart, boat, etc.) contribute +64, and items that stack to 64 contribute +1.

A redstone comparator in comparison mode (front torch down and unpowered) compares its rear input to its two side inputs. If either side input is greater than the rear input, the comparator output turns off. If neither side input is greater than the rear input, the comparator outputs the same signal strength as its rear input.

When a comparator measures a large chest or large trapped chest, it measures the entire large chest (54 slots), not just the half directly behind the comparator. A chest or trapped chest that cannot be opened (either because it has an opaque block, ocelot, or cat above it) always produces an output of 0 no matter how many items are in the container — shulker boxes can always be measured, even if they cannot open.

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If the laser beam is not perfectly Gaussian, its Rayleigh range will be shorter than the Rayleigh range of an ideal Gaussian beam with the same waist radius. The ratio of the two values, M2 (M-squared), is often specified for laser beams. Multiply the beam's Rayleigh range by the M2 value, and then use this product as zR or zR ' in the modified thin-lens equation to find s ' or s , respectively.

Comparator Machine

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For example, the conventional thin-lens equation (see table), predicts the image will appear at infinity when the object is placed at the lens' front focal point. However, for Gaussian beams, when the object beam waist is one focal length away from the input side of the lens, the image beam waist is one focal length away from the output side.

Redstone comparators check their power state before their scheduled ticks update. This results in redstone comparators not usually responding to 1-tick fluctuations of power or signal strength — for example, a 1-clock input is treated as always off from the side, and always on from the rear. This happens because the signal changes back to its original state before the redstone comparator checks its input states. However, certain setups such as powering any input with two separate observer pulses at the same time causes a redstone comparator to respond to 2 gametick pulses.

The redstone comparator has four functions: maintain signal strength, compare signal strength, subtract signal strength, and measure certain block states (primarily the fullness of containers).

Modified Thin-Lens EquationThe incident and output light are assumed to propagate as Gaussian beams (Figure 2). The modified thin-lens equation was derived by relating the input and output beam properties (table, center) across the lens:

In the case of laser light, a modified thin-lens equation that takes diffraction into account is recommended instead of the conventional thin-lens equation. The modified equation, which models the laser light as Gaussian beams, is appropriate for many single-mode and fiber-coupled laser sources. In addtion, the equation can be adapted for use when the laser light does not have a perfect Gaussian intensity profile. [1]

The modified thin-lens equation also includes either the input Rayleigh range (zR ) or the output Rayleigh range ( zR '). The Rayleigh range (Rayleigh length) is measured starting at the beam waist, along the propagation direction, to the point where the beam radius is larger by a factor of √2. Highly divergent beams have short Rayleigh ranges.

Comparator C++

Comparator Java

For example: if the signal strength is 6 at the left input, 7 at the right input and 4 at the rear, the output signal has a strength of max(4 − max(6, 7), 0) = max(4−7, 0) = max(−3, 0) = 0.

In another case, the conventional thin-lens equation predicts the image can be infinitely distant. But, if the beam is Gaussian with a nonzero Rayleigh range, the beam waist cannot be imaged to infinity. Instead, the maximum image beam waist distance,

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Figure 1: A thin lens, with focal length f , is shown inserted in a Gaussian beam. In the modified thin-lens equation, the object is the input beam's waist, located a distance s  from the input side of the lens. The input beam's radius (W ) is Wo at its waist and maintains a similar radius over the Rayleigh range (±zR ). The image is the output beam's waist, located a distance s ' from the lens' output side. The output beam's radius (W ') is Wo' at its waist and remains nearly Wo ' over its Rayleigh range (±zR').

The Minimum items for container signal strength table (right) shows the minimum full-stack-equivalent (FSE) to produce different signal strengths from common containers. A full-stack-equivalent quantifies how many normal 64-stackable items are needed to output a corresponding signal strength. The 's' is a constant 64, with the additional amount needed following after.

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Figure 2: Key to the model are the relationships between the input and output beams at the lens. There, the beams have equal radii, and the beams' wavefront curvatures are related by the focal length of the lens. The wavefront' radius of curvature is flat (thick vertical line) at the waist and gradually becomes more spherical with increasing distance from the waist.

Objects, and Images, and Laser BeamsThe conventional thin-lens equation (table, top) is based on the ray optics model and uses the focal length (f ) of the lens to relate the distance (s ) between the lens and the object to the distance (s ') between the lens and the image.

Comparator IC

Figure 3: Gaussian beam parameters such as the radius, W(z), and the wavefront's radius of curvature, R(z), are calculated using a distance, z, referenced to the beam's waist. The waist is always located at the origin.

A redstone comparator is a block that can produce a redstone signal from its front by reading chests, lecterns, beehives and similar blocks, or repeat a signal without changing its strength. It can also be set to either stop outputting a signal while its side input is receiving a stronger one (front torch off), or subtract its side input's signal strength from its output (front torch on).

A redstone comparator treats certain blocks behind it as power sources and outputs a signal strength proportional to the block's state. The comparator may be separated from the measured block by an opaque block. The comparator disregards the power level of the opaque block in this configuration, except that in Java Edition, if the opaque block is powered to signal strength 15, then the comparator outputs 15 no matter the fullness of the container.[1]

The redstone comparator can take a signal strength input from its rear as well as from both sides. Side inputs are accepted only from redstone dust, block of redstone‌[Java Edition only], redstone repeaters, other comparators, and observers in specific scenarios. The redstone comparator's front is its output.

If the signal strength is 9 at the rear, 2 at the right input and 5 at the left input, the output signal has a strength of max(9 − max(2, 5), 0) = max(9−5, 0) = 4.

A redstone comparator can output a signal indicating how full a container is. (0 for empty, 15 for full, etc.) The table on the right is described more in detail, later in this section.

It takes 1 redstone tick (2 game ticks, or 0.1 seconds barring lag) for signals to move through a redstone comparator, either from the rear or from the sides. This applies to changing signal strengths as well as simply to turning on and off.

The redstone comparator has a front and a back — the arrow on the top of the comparator points to the front. When placed, the comparator faces away from the player. The comparator has two miniature redstone torches at the back and one at the front. The back torches turn on when the comparator's output is greater than zero (the arrow on top also turns red). The front torch has two states that can be toggled by using the comparator:

Note that the beam radius (W ) and wavefront's radius of curvature (R ) are calculated using the relative distance (z ) from the waist (Figure 3). There are two modifed thin-lens equations (table, bottom), since the form of the equation differs depending on whether the input beam parameters (zR and s ) or the output beam parameters (zR ' and s ') are known.