Karnaugh 1953: Map Adjacency, Covering, and Hardware Cost
Karnaugh's map turns Boolean-cube adjacency into geometry, including wrapped edges and don't-cares, while explicitly separating minimum two-stage forms from broader relay and circuit costs.
Maurice Karnaugh's 1953 article occupies printed pages 593–598, with its published discussion continuing on page 599 before another article begins. All seven physical pages were read and visually inspected.
Geometry as a Boolean cube #
Printed pages 593–594 arrange cells so adjacent entries differ in one coordinate and explain the identification of opposite edges. The familiar rectangular groups are therefore subcubes of the Boolean input cube; wraparound is part of the represented adjacency rather than a drawing convenience.
Printed pages 595–596 extend the method to incompletely specified functions. Indeterminate cells may enlarge or combine groups, but they do not create an obligation to cover a row whose output was left unspecified. The resulting implementation chooses one legal completion of the partial function.
Optimization boundary #
The minimal two-stage discussion on printed page 595 includes an explicit covering argument and warns that a set of specially marked cells can require more groups than a naive count suggests. It does not license “choose the largest groups first” as a proof of global optimality.
The article also distinguishes two-stage expression objectives from factored forms, bridge networks, relay contacts, and spring costs. A smallest map cover is not automatically the smallest, fastest, or cheapest physical circuit. Modern use should preserve that cost contract and verify the mapped implementation separately.