Recently, I came across an interesting article about unusual electronic components. One of the components that article talks about is the multifunction gate, which is a 6-pin integrated circuit which can act as one of several different 2-input logic gates depending on which input pins are connected to which incoming signal lines, and whether the ones that aren't connected are pulled high or low.
However, the gates mentioned by that article can't act as any 2-input logic gate, only some of them. The 74LVC1G97 can't act as NAND or NOR, the 74LVC1G98 can't act as AND or OR, and neither of the devices can act as XOR or XNOR. Their truth tables are as follows:
| Inputs | 74LVC1G97 | 74LVC1G98 |
| 0 0 0 | 0 | 1 |
| 0 0 1 | 0 | 1 |
| 0 1 0 | 1 | 0 |
| 0 1 1 | 1 | 0 |
| 1 0 0 | 0 | 1 |
| 1 0 1 | 1 | 0 |
| 1 1 0 | 0 | 1 |
| 1 1 1 | 1 | 0 |
That got me wondering if it's possible for such a 6-pin device to act as any 2-input logic gate. Such a 6-pin device is naturally equivalent to a single 3-input logic gate, since two of the pins are needed for power. There are only 256 (28) possible 3-input logic gates (since the truth table for a 3-input logic gate contains 23=8 bits of information). So it's a simple matter to just write a program that enumerates all the possible 3-input logic gates, tries all the possible ways of connecting them up, and sees what the results are equivalent to.
There are 16 possible 2-input logic gates: 0, 1, A, B, ~A, ~B, A&B, A|B, ~(A&B), ~(A|B), A~B, ~(A~B), A&(~B), (~A)&B, A|(~B) and (~A)|B. Discounting the trivial gates, the gates that ignore one of their inputs and treating two gates as identical if we can get one from the other by swapping the inputs, gives us 8 distinct gates: AND, OR, NAND, NOR, XOR, XNOR, AND-with-one-inverting-input and OR-with-one-inverting-input.
There are 4 possibilities for connecting up each of the three input pins: low, high, incoming signal line A and incoming signal line B. I originally thought that connecting the output pin to one of the input pins might also be useful, but it turns out that it isn't - either the value of the input pin makes no difference (in which case it might just as well be connected to one of the other four possibilities) or it does. If it does, then either the output is the same as the input pin that it's connected to (in which case it's underconstrained, and not a function of the other two input pins), or the opposite (in which case it's overconstrained, and also not a function of the other two input pins).
So we have 256 possible 3-input logic gates times four possibilities for each of the three input pins, times two possible states for each of the two incoming signal line - that's 65536 circuit evaluations to try, which a computer program can run through in a timespan that is indistinguishable from instantaneous by unaided human senses.
Running the program didn't find any 3-input gates which can be configured to act as any of the 16 2-input gates, but it find something quite interesting - a dozen 3-input gates which can be configured to make 14 of them. Since swapping the inputs around gives equivalent gates, there's actually just two different gates, which for the purposes of this essay I'll call Harut and Marut.
| Inputs | Harut | Marut |
| 0 0 0 | 0 | 1 |
| 0 0 1 | 0 | 1 |
| 0 1 0 | 1 | 0 |
| 0 1 1 | 1 | 0 |
| 1 0 0 | 1 | 0 |
| 1 0 1 | 0 | 1 |
| 1 1 0 | 0 | 1 |
| 1 1 1 | 1 | 0 |
Note that the truth tables for Harut and Marut are quite similar to 74LVC1G97 and 74LVC1G98 respectively, just with two of the rows swapped or inverted. I haven't been able to find Harut and Marut gates on Mouser - it would be interesting to know if anybody makes them. One possible downside is that the 3-input gate isn't as useful in its own right (the 3-input gates for 74LVC1G97 and 74LVC1G98 are just a 2-input multiplexer and same with inverted output respectively).
I think it should be possible to design a 6-pin device that can yield any 2-input gate by making the supply lines take part in the configuration as well. For example, if you have a Harut gate and a Marut gate which give high-impedence outputs when power is not applied, you could put diodes on their supply lines and connect them up in parallel with the supply lines interchanged. Then applying power in the normal way would yield a Harut gate and reversing the polarity would yield a Marut gate. There's probably better ways to do it.