Boolean algebra and Karnaugh maps

Từ vựng

English	Ý nghĩa
de morgan's theorem/də ˈmɔːɡənz ˈθɪərəm/	Breaking a complement bar changes AND to OR and vice versa: (A·B)' = A' + B'.
karnaugh map/ˈkɑːnɔː mæp/	A truth table laid out in Gray-code order so adjacent cells differ in exactly one variable.

English

Boolean and Karnaugh: adjacency is simplification

Absorption A + AB = A and De Morgan's theorem (AB)' = A' + B' do the shortening; Karnaugh map groups of $2^k$ cells eliminate k literals; don't-cares only ENLARGE groups.
Every answer checks by exhaustive evaluation — 8 rows is nothing.

Example

$\sum m(1,3,5,7)$ (the odd rows) is just C: all four minterms share only C, and the 8-row check confirms.