There exist several equivalent sets of primitive operations. While the sets containing only NAND or only NOR, or both AND and NOT or both OR and NOT are more notorious, these logical operations are more abstract and they do not indicate precisely a hardware implementation, i.e. there are many distinct hardware methods to make such logical gates.

Other sets of primitive operations map directly to hardware devices, e.g. the sets of primitive operations composed of maximum and complement or of minimum and complement map directly to a hardware implementation using rectifier diodes and inverting amplifiers (which can be made with either semiconductor devices or with vacuum tubes, or also with pneumatic or hydraulic devices).

Other sets of primitive operations are obtained by replacing the maximum or minimum circuits with series or parallel connections of switches, like in the CMOS logic that is nowadays dominant.

The alternative IF expression corresponds in hardware to a 2-way multiplexer, which, together with the 2 constant functions "0" and "1" (a.k.a. "false" and "true" or "low voltage" and "high voltage"), is sufficient for a complete set of computational primitives.

Besides those mentioned above, the main remaining variant for a complete set of computational primitives consists of an analog (possibly weighted) adder and an analog comparator, which had been used in the so-called RTL circuits (resistor-transistor logic) and which also corresponds to perceptrons. RTL had been used in some early integrated circuits, before being replaced by DTL and TTL circuits (which are based on minimum and complement functions).

In hardware, e.g. in RTL circuits, a combined analog adder+comparator can be made with a single high-gain amplifying device, together with a set of weighting resistors and a bias resistor. RTL circuits can implement complex logic with fewer devices (e.g. they can implement a neural network in the analog domain), but they were replaced during the sixties of the past century with DTL, then TTL, because those were faster (in RTL, the resistors limit the charging currents for input capacitors and parasitic capacitors, which slows down the logical transitions) and the fact that they needed more devices was not important, due to the quick increase in circuit density.