As a simple example here's how we can define the XOR function using only NOR: Like NAND, we can use NOR to define any logical expression. In both electronics and logic the NOR gate has the same properties as the NAND gate (see the previous post ' Go Language: NAND Grammar'). And we can further illustrate this with a different exercise by using the built-in universal systems of GeneXproTools (the NAND, NOR, and MUX systems) to automatically convert NOT-AND-OR circuits into NAND, NOR, or MUX circuits.Īs an illustration let's use the minimal NOT-AND-OR circuit presented above with only 5 literals.Īnd now let's convert this circuit to NAND gates using the NAND Grammar of GeneXproTools:

This is of course just a simple exercise using a simple function and we are bound to get some variation with different functions, but overall the MUX System is considerably more compact than the NAND System and the NOR System. Y = gepMux(gepMux(d,d,d),d,d)Īs you can see, compared to the NAND and NOR circuits, the MUX circuit is very compact with only 5 literals (in this case, it's the same number of literals we got for the NOT-AND-OR circuit). So let's start by designing a minimal logic circuit for the 3-Majority function using just NOT, AND, and OR: In the remainder of this post I'll show you some simple examples to illustrate this claim.įor this exercise I had to choose a very simple function – the 3-Majority function – otherwise we would get huge circuits for some of the Universal Logical Systems I'll be using to make comparisons, namely, the NAND System and the NOR System.įurthermore, I also decided on a very simple architecture of only 1 gene so that we could make more meaningful comparisons between the logical systems. MUX circuits are very popular, and the reason for their popularity is their compactness.

This means that we can automatically convert all kinds of logic circuits to MUX circuits with this grammar.

The Go MUX Grammar of GeneXproTools defines not just the XOR function but all the 258 built-in logical functions in terms of MUX gates and NOT. As a simple example, here's a MUX circuit for the XOR function: And with these two types of building blocks we can design any kind of logic circuit. The building blocks of the MUX Universal System are 3-Multiplexer gates (MUX, for short) and NOT (inverters).

Nand x read bad block 258