I stumbled on this trying to figure out how to do this, and I found out NONE OF THEM WORK! So I figured it out instead. Place a repeating redstone curcuit going into a command block, and type in the command block this:
/effect @p[r=(number)] 13 1 0
with a comparotor coming out of it.
Then, hook up whatever you want to the comparotor! Now, here's how to know what number to put: the number you put = how many blocks away a player has to be before the redstone comparotor turns on. Also, if you put "m" after r, so "rm" it will work only if the player has LEFT the number of blocks put.
Don't you use ANY () in your command! JUST []
The most resource efficient way I can come up with to power a horizontal line of droppers is this
with the redstone line on the left being connected to a clock. This works because the repeaters strongly power the dropper they are pointing into causing the droppers to the left and right to be indirectly powered.
The vertical line of droppers is powered as described in this Youtube video, with a comparator being used to send a (inverted by a redstone torch) signal to a vertical stack of redstone torches powering repeaters pointing into every 2nd vertical dropper.
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With regards to the specific situation you are in the most resource efficient way to get the mobs from the exit of the spawner to the 'home' area would be to bring them up high enough using a mob elevator (a 1x1 tube filled with alternating water blocks and signs will cause the mobs to swim themselves up to the top) to a point where they can be dropped down the required number of blocks.
The only pitfall with this type of system is ensuring that the mobs fall a consistent distance everytime. All that is required to do this is to ensure that the water stream at the top of the elevator is set up like this
XXXXXXXXXX
X X
X~~~~~S X
XSXXXXX X
(where ~ = water and S is a sign)
So that mobs get pushed into the drop shaft by other mobs pushing against them instead of directly by a water stream.
Best Answer
Comparators put against any container will output a signal at a strength equal to the percentage filled the container is - one notable combo is to use a cauldron filled with water, which is also able to move, and produces a signal with a strength of 15 when placed behind a comparator.
In terms of block updates, you could probably modify the normal BUD that uses a redstone block to instead use a cauldron-comparator combo, but it won't be particularly space efficient.
I've added some pictures of a proof of concept below. It basically takes the one wide tileable design from this page and replaces the redstone blocks and the redstone torch with filled cauldrons.