One MUX makes logic tangible: a control bit chooses which source reaches the output.

Wire constants, variables, and inverted variables into that choice, then compose the choices into a graph. MUX Algebra develops the same rule through selector equations, a four-bit configuration, and all 16 two-input Boolean functions.

A Control Bit Chooses the Next Value

A two-input multiplexer accepts two candidate sources and one selector. The selector routes exactly one source to the output. That simple operation gives a circuit an explicit decision point.

Constants turn the selector into familiar logic. Select between 0 and an input to form AND-like behavior. Select between an input and its inverse to form XOR. Nest more selectors and the graph can express any Boolean table.

Formal systems such as the Calculus of Constructions show how far composition and generalization can reach. A MUX graph gives that compositional instinct a circuit-level form: each node names a choice, each route carries a value, and time determines when state captures the result.

The three returned values below provide the next lesson with a concrete input pattern for binary addition.

return [0, 1, 0];