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Difference between revisions of "User:Larix/Adder"
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O2 = output generating a signal from the carry, required to calculate the next higher bit's sum. | 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. | * 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. | ||
Revision as of 10:59, 8 November 2013
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