Logic Gates

A logic gate has two inputs, A and B and an output. Each gate is characterized by a truth table composed of distinctions, + and -. Each truth table relates four possible combinations of inputs for A and B (+ and -, – and +, – and – and + and +) to outputs (+ or -).  The truth tables form into a mirror pair of three each, depending on whether the inputs + and -, and – and + both afford + or both afford – (De Morgan’s laws). The truth tables on each side are separated according to what the inputs – and + and – and + on one side, or + and – ad + and – on the other side, afford.

The two sides of the dashboard for a chiralkine exchange correspond with the truth tables for an XOR gate and an XNOR gate.

Each of the four columns in the truth table for an XOR gate is a triplet of signs. Each triplet can be interpreted as a statement that + means different and – means same. Each of the four columns in the XNOR gate can be interpreted as a statement that – means different and + means same. Each statement has the same meaning whatever the order in which the three polarities are read. Any two polarities can be taken as the inputs to generate the output. They form triplets. No polarity stands alone: each stands in the context of two others.

Each truth table can be converted into each other truth table by shifting the columns of triplets relative to one another.

Each truth table for a logic gate has a mirror image that corresponds with all of their signs being flipped or all of triplets being shifted by three spaces.

XOR and XNOR can be converted respectively into NAND or OR and NOR or AND by a shift of one triplet.

The truth tables for the six logic gates can be ordered in cycles, each step of which corresponds with shifting one or more triplets. These shifts correspond with exchange interactions. Through the exchange interactions the four statements making up the truth table for an XOR gate and the four statements making up the truth table for an XNOR gate can be mixed up to form paired transition states (AND, NAND, OR, NOR) then separated out again so that they have swapped positions. XOR and XNOR are distinct, but connected through exchange interactions.