[gilgoomesh]

> Why use splines or polynomials or haphazardly chosen basis functions if you can just fit (gradient descent) your data or wave functions to the proper computational EML tree?

Same reason all boolean logic isn't performed with combinations of NAND – it's computationally inefficient. Polynomials are (for their expressivity) very quick to compute.

[brucehoult]

The Cray 1 was built 100% from NOR gates and SRAM.

[IAmBroom]

50 years ago.

[brucehoult]

Correct. Your point being? Digital logic didn't change.

[Nevermark]

They are done with transistors though. Transistors form an efficient, single element, universal digital basis.

And are a much less arbitrary choice than NAND, vs. NOR, XOR, etc.

Using transistors as conceptual digital logic primitives, where power dissipation isn't a thing, Pass Logic is "The Way".

[samus]

Single transistors aren't yet logic gates by themselves; they are amplifiers with a very specific gain function that makes it possible to use them as switches. Logic gates usually consist of at least two transistors. See https://en.wikipedia.org/wiki/CMOS for an example of how it is done in CMOS technology.

[adrian_b]

That is correct.

Moreover, the amplifying function must exist at least in some gates, to restore the logic levels, but there is no need for it to exist in all gates.

For instance, any logic circuit can be implemented using AND gates and/or OR gates made with diodes, which have no gain, i.e. no amplifying function, together with 1-transistor inverters, which provide both the NOT function and the gain needed to restore the logic levels.

The logic functions such as NAND can be expressed in several way using simpler components, which correspond directly with the possible hardware implementations.

Nowadays, the most frequent method of logic implementation is by using parallel and series connections of switches, for which the MOS transistors are well suited.

Another way to express the logic functions is by using the minimum and maximum functions, which correspond directly with diode-based circuits.

All the logic functions can also be expressed using the 2 operations of the binary finite field, addition (a.k.a. XOR) and multiplication (a.k.a. AND).

This does not lead to simpler hardware implementations, but it can simplify some theoretical work, by using algebraic results. Actually this kind of expressing logic is the one that should have been properly named as Boolean logic, as the contribution of George Boole has been precisely replacing "false" and "true" with "0" and "1" and reinterpreting the classic logic operations as arithmetic operations. It is very weird to see in some programming languages a data type named Boolean, whose possible values are "false" and "true", instead of the historically correct Boolean values, "0" and "1", which can also be much more useful in programming than "false" and "true", by simplifying expressions, especially in array operations (which is why array-oriented languages like APL use "0" and "1", not "false" and "true").

[Nevermark]

"Pass transistors" are transistors being operated in pass/impedance switch mode.

Pass logic. Digital. [0]

This is extremely basic digital circuit design. You can create digital circuits as compositions of gates. But you can often implement the same logic, with fewer transistors, using pass logic.

Pass logic is also great for asynchronous digital design.

[0] https://en.wikipedia.org/wiki/Pass_transistor_logic

[throw-qqqqq]

> Transistors form an efficient, single element, universal digital basis

But transistors can be N or P-channel, so it’s not a single logical primitive, like e.g. NAND-gates.

[Nevermark]

True.

NAND also use both N and P-channel transistors, and have to use at least the same number, but frequently many more transistors for anything non-trivial.

But as you point out, as a computational basis, pass transistors have two variants.