Every computer is built from just two values — true and false, 1 and 0 — and three operations: AND, OR, NOT. George Boole worked this out in 1847, before there were computers to run it on. Wire an XOR and an AND together and you get a HALF-ADDER: the circuit that adds two bits. From here, everything. Toggle the two inputs and watch the gates decide.
Boolean algebra operates on {0,1} with AND (∧), OR (∨), NOT (¬). Key laws: De Morgan — ¬(A∧B) = ¬A ∨ ¬B and ¬(A∨B) = ¬A ∧ ¬B — let any circuit be rebuilt from NAND (or NOR) alone (functional completeness). A HALF-ADDER computes the sum bit as A XOR B and the carry as A AND B; chaining full-adders builds arithmetic. This is the logical bedrock of every digital machine. A fail-loud self-check throws unless De Morgan holds and the half-adder gives 1+1 = sum 0, carry 1. ◆ real digital logic, node-verified.
The two-input half-adder and the named laws are exact; a real ALU chains many full-adders with carry logic. ‘Everything from two values’ is literally true for digital logic — the abstraction, not a metaphor.