How they are manufactured is not of interest.
Ok, so if I can manufacture a NAND gate using the OP's gate, I am justified in calling that NAND gate "universal", but the one type of gate which is used to make the NAND gate is not?
How they are manufactured is not of interest.
There are only 16 possible boolean functions of 2 onputs and 1 output. FPGAs implement all of them, so this is a gate that is a basic gate in some implenentations.
Bob
Ok, so if I can manufacture a NAND gate using the OP's gate, I am justified in calling that NAND gate "universal", but the one type of gate which is used to make the NAND gate is not?
What nonsense. Apparenty, You can have an inverted outout, but not an inverted input. A NAND gate is basic, but if I remove the inverter on the output and put inverters on the two inputs it is no longer a single gate even though it implements the same function with the same circuit and all you have changed is the symbol. Or do you have another secret rule that covers this one as well?
Bob
So what is excluded? Any 2-input gate has 4 possible input combinations and 2 possible outputs for each input combination. But the gate function is determined by selecting just one of the possible outputs for each of the 4 possible input combinations; therefore, the gate's function can be represented by a 4-digit binary number. So there are 16 possible gate functions.I see no reason to exclude any of the 16 possible two input, one output gates
There are 7 basic gates as described in this link. Look at the top of the first page. Only two (NAND and NOR) are universal gates.
But not all possible gate functions are described in that link, and only two of those described are universal. Note that to be a universal gate function the gate does not necessarily need to be commercially available nor even especially useful - just that it can (theoretically) be used to generate all other gate functions.
There are basic gates, there are universal gates, and a few which are basic and universal. Don't be confused.
An interesting universal gate is the two input mux. It can't implement nand or nor on its own, but it can implement xor, or, and, and not, so with 2 of them you can implement nand and nor.
Incidentally, it implements xor faster than using conventional logic gates.
And it can implement the logic function in question in this thread with a single 2 input mux.
As I said above, I don't think a MUX or its relatives like PLA's should be considered as a single gate.
True, but it is based on the observation that creating a complex gate out of two or more basic gates, and calling it a new single gate, is cheating a bit on the definition of a single gate.That sounds like opinion.
Yes, but you also make a distinction between a gate with an inverter added at the output and a gate with an inverter added at one input. There seems to be no logical distinction other that perhaps some appeal to symmetry.
As @BobK points out, there is a simple list comparing all possible functions of a 2 input gate. This ignores the implementation of the gate, and can then be used to exhaustively determine all the possible universal gates. It turns out that all you need is a gate which has one output state that can only be achieved with a single set of input states.
As an example, consider a transmission gate with a down on the output. It implements one of the 16 functions and one that is universal. The function is NAND.
Change that pull down to a pull up and look at the logic function. It's not NOR.
The only reason why NAND and NOR (and AND and OR) exist while these odd gates don't is that they may be easier to imagine, and can be more simply expressed in Boolean algebra. However, that's a failure of our thinking and of the available Boolean operators. The XOR function is not one of those "simple" gates (and neither is it universal) but it has it's own symbol in Boolean algebra. Dear Morgan's law is different for XOR, why can't there be a gate with different Associative, Commutative, and/or Distributive laws? When handling XOR we often break it down into an equivalent using AND, OR, and inversion, the same could apply to some other new gate type symbol for the new gate type "left inverted OR" or perhaps LOR?
Once we have this, then we find that LOR is simpler than OR in silicon, and can be manipulated just like AND and OR in Boolean algebra, and can be used in its own to implement any other logic function.
How does it now differ from NAND or NOR (other than being ugly)?
Where is the definition of basic gate that you are using?
Bob