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The hopper is a useful device for controlling/counting/sorting items.

Day counter

This is a very simple machine for counting days. Every time it becomes day, the dispenser is activated and shoots an item into the chest, but you have to be nearby for this to activate, making this fairly useless.

Item counter

A mechanism that outputs short redstone signal for every item that goes through the dropper. The mechanism slows down the items moving through the dropper and the hopper above to make the outputs comfortable to use for counting mechanisms.
The output of this counter can be used in any counting mechanism and can be counted using the scoreboard command in a command block.
It is possible to change the outputs timing by replacing the bottom comparator with repeater (to make it slower) or redstone dust (to make it faster).
Size: 1×4×5 blocks.
Item Counter
This mechanism made by Xbxp.

You can download this mechanism from: Planet Minecraft - Item Counter

Item sorter

Introduction

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Layout for one cell. The item channel runs through "I", and the output (usually a double chest) is at "O". The upper hopper contains the 22 items.

Most item sorters work using hoppers.

More specifically, a hopper with all five slots occupied by, for example, redstone, will only be able to collect redstone, because there is nowhere for any other items to go.

Connecting the hopper to a comparator will allow the sorter to measure the contents of the hopper. All five slots MUST remain occupied by the material you are sorting for, otherwise other items will be able to pass through. The easiest way to ensure this is to measure for a 2-strength signal from the comparator, which corresponds to 22 items inside - 18 inside the leftmost slot and 1 each in the other four slots (hoppers lose items in the leftmost slot first). You can also sacrifice an item that you will never sort for, like sticks, 18 inside the rightmost slot, 1 each in the other three slots, and the material that you are sorting for, in the leftmost slot. Alternatively, you can use an item that stacks to 16 (like snowballs). Place the item to be sorted in the first slot of the hopper. Then, place two snowballs in the second slot and one in each of the remaining slots.

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Overflow-proof sorter, layout for one cell.

If the output double chest fills up, though, the above design will break adjacent cells due to the signal from the hopper exceeding 2. This alternative design avoids that. The upper hopper here will contain 41 of the item being sorted in one slot, with the other four slots having one each of some item that stacks to 64 and will never go through the sorter (an arbitrary item renamed in an anvil may be used for this purpose).

Components

There are two components to an item sorter: the item channel and the sorting component(s). Here is an analogy to clarify this: the item channel is like a river, and the sorting components can be imagined as nets that only catch certain items. The river ends in a dump (the junk chest).

The item channel is simply a path that items travel through. It can be a horizontal chain of hoppers, or a water channel. Hoppers underneath the hopper chain or water channel act as the "net" and will extract items.

The sorting components are composed of hoppers. To enable deposition and extraction to be independently toggled, two hoppers must be used: one on top of the other, and the top one pointing sideways. The top hopper should be connected to the comparator, which will power the bottom hopper (which takes items out of the top hopper)

Auto Smelter/Cooker

Ores and cookable items can be automatically smelted while you're away. Sadly, I don't know how to use the grids correctly. So I will leave this for someone else to finish. Sorry.

Hopper Clock

Connect 4 hoppers in a circle (create one pointing at nothing, point a 2nd one at it while crouching, destroy the 1st and use the 2nd as the start of your circle since it's the 1st one pointing the right direction). Put any item that doesn't stack (a wooden axe for example) into any one of the hoppers. Attach a comparator to any one of the hoppers. It will give a signal every time the item goes through that hopper. If you want it to activate more often make a 2 hopper clock.

Slow Clock

Connect two hoppers (let's call them hopper A and B) with their outputs facing each other. Measure their outputs with comparators (comparator A and B). Connect the comparators' outputs to repeaters (repeater A and B), add repeaters perpendicularly to make them lockable (lock A and B). Connect the output of repeater A to hopper B and lock B and the output of repeater B to hopper A and lock A.

To start the clock, throw items into one of the hoppers. The speed of the clock will depend on the amount of items circulating in the system, with the longest duration being 128 seconds in case of 5 stacks of 64 items.

Silo

Sometimes we need a storage way larger than just a single large chest. What we need is a single output container which will be automatically filled up with contents of a large set of other containers preferably hidden behind a wall or a ceiling. We call such system a silo or a mass storage.

The basic form

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This is a basic form of silo with 4 large chests (216 slots) plus 5 hoppers (25 slots), total 270 slots. "I" and "O" denote input and output containers respectively.

This is a basic form of silo with 3 large chests. It is 3 blocks wide, 5 blocks high, and is tileable. The actual input of the system is the hopper below "I" so you can push items into it from the side not only from above. The bottommost hopper can obviously be replaced with a hopper facing any directions, feeding into another hoppers.

If you want to use a chest for the output container, it may be advisable to use a trapped chest rather than a normal one. This way item refilling gets suspended while you are accessing the chest so you can return items in case you took more items than you need.

Extended forms

Its true power comes from the extensibility. Here are some examples of extended forms. All of these are still tileable.

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Vertically extended evenly. The output hopper comes to the same side as the input.
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Vertically extended oddly. The output hopper comes to the opposite side.
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Horizontally stacked 2 units: 9 large chests (486 slots) plus 15 hoppers (75 slots), total 561 slots.
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Horizontally more stacked. Only the rightmost unit can have extra one large chest.
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