Quine’s method (with McCluskey) mechanised something people did by eye: take a messy truth table and find its smallest logical expression. Adjacent 1-cells that differ in one bit merge; keep merging and you get the prime implicants. Slide through boolean functions and watch the minimal form fall out — then be checked against all eight rows.
For 3 variables a,b,c the instrument builds the truth table from a set of minterms, then runs Quine’s merge: two implicants that differ in exactly one position combine, the changed bit becoming a dash. Iterating gives the prime implicants; a cover is chosen. A fail-loud self-check throws unless the minimised sum-of-products evaluates identically to the original truth table on all 2³=8 input rows — the exact equivalence a minimiser must never break.
Eight illustrative functions are cycled; the MINIMISATION and the 8-row equivalence proof are exact for each. Quine–McCluskey (1952–56) is exponential in general — fine at n=3, not a claim about scaling.