User:Larix/Adder

Using mechanical logic and applying the principles shown by Jong, an extremely compact full adder can be built which functions similarly to a carry look-ahead adder, but thanks to the immediate operation of mechanisms in Dwarf Fortress can calculate all carries of an arbitrary-size addition in a single tick.

O1-SPABC-O2
       X
       c

P = Power

A,B = gear assemblies connected to the A and B inputs, active when the signal is on

C = gear assembly generating the carry output for this bit. The gear is not linked to any inputs and presence of power on it serves as carry input for the next higher bit.

X = a single gear assembly, connected to both A and B inputs, pre-toggled. It transmits power if one and only one of the inputs is on (an XOR gate).

c = carry input from the next lower bit. Like the output, an unconnected gear, presence of power on the gear serves as carry input.

S = the sum calculation, consisting of a single gear, connected to the A and B inputs as well as a signal generated by the carry input, pre-toggled. It transmits power when exactly one or three of the inputs are on.

O1 = power-to-signal converter or other output device to generate the sum output

O2 = output generating a signal from the carry, required to calculate the next higher bit's sum.

A carry is generated at a bit only when both A-line and B-line input are on. An active carry will be passed to the next higher bit if one and only one of A and B inputs are on; if both A and B are on, the carry will simply be generated again, the "X" gear will be disengaged and will not transport power. This easily prevents higher-bit carries erroneously flowing down the bit chain. All carries are effectively generated by providing power links between the power sources and the carry gears, i.e. they're present the moment the connecting gears get switched, without any further processing required.

• This adder takes a mere five installed gear assemblies per bit - four for the carry calculation and one for the sum. Additional mechanisms and machinery are required for power supply, signal generation and linkage. Linking an extra lever to all inputs of the "A" line in the carry computation allows to use this adder for subtraction as well.

Forum post featuring this adder: http://www.bay12forums.com/smf/index.php?topic=15096.msg4600870#msg4600870

less economical "fully mechanical" version: http://www.bay12forums.com/smf/index.php?topic=15096.msg4602227#msg4602227

P.S.: Further optimisation is possible, to make it even more space- and power-economical. The carry gear can be replaced by a roller running a minecart-based power-to-signal converter, saving three points of power requirement and removing the need for a dedicated "output" machine - a single-tile roller transmits power in all four compass directions on the same z-level, which is all we need here. The power train can consist mostly or entirely of rollers and axles. The track for minecart power-to-signal converters can be carved/laid under gears and axles without hindrance, allowing to minimise space consumption. The smallest, least power-hungry construction i've managed to install can add and subtract 16-bit numbers and takes up 205 tiles of open floor, plus 32 for required surrounding walls which could be shared with neighbouring adders and has a nominally installed power pull (before establishing the actual links) of 477, when properly linked and operational, the theoretical maximum consumption is 397. This breaks down to 14 tiles and 25 power per bit in an optimal configuration. The adder is contained on a single z-level and all sum and carry signals are generated within the mentioned area.