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Editing User:Larix/Adder
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− | + | 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. | |
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O1-SPABC-O2 | O1-SPABC-O2 | ||
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* 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. | * 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. In this case, the logical conditions for a carry are (NOT-A AND B) OR (CARRY_IN AND (A NXOR B)): if the A-Line (Diminuend) input is off (zero) and the B-Line (Subtrahend) input on (one), the carry output is active, regardless of the status of the carry input (the possible results at the bit are 0-1-0 = -11 and 0-1-1 = -10, and the carry output only tracks whether the result is positive or negative; both possible results are negative, so the carry-in status simply doesn't matter). If the carry input is active and A and B have the same value, the carry is passed on (0-0-1 = -11 and 1-1-1 = -11). |
+ | Negative results can be displayed either in the standard computing convention of reserving the highest bit for the negative numbers, wrapping around from 11..11 = -1 to 00..00 = 0, or by sending an additional "minus one" signal to the circuit and reversing the logic of all sum calculators apart from the lowest-bit one by sending an extra signal to generate the binary complement. | ||
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+ | 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 459; when properly linked and operational, the theoretical maximum consumption is 379. This breaks down to 14 tiles and 24 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. | |
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