A full-adder gives Boolean choice a numerical consequence: three input bits produce one sum bit and one carry bit.

MUX Algebra supplies the selector rule for inversion, XOR, AND, OR, and every other two-input Boolean function. Connect those functions around a carry path and one bit position can feed the next.

Let the Carry Bit Move the Number Forward

XOR computes the low bit of a two-input sum. AND detects the carry. A full-adder adds the incoming carry, combines the two carry conditions, and sends the result toward the next bit position.

A MUX graph can construct each of those Boolean choices. Repeating the graph across bit positions turns one local operation into an adder of any desired width.

The three-value sequence below keeps the lesson anchored to an executable input pattern before the course moves into a continuous bit stream.

return [0, 1, 0];