de Morgan’s theorem
(X + Y)' = X' • Y' NOR is equivalent to AND with inputs complemented
(X • Y)' = X' + Y' NAND is equivalent to OR with inputs complemented
X Y X' Y' (X + Y)' X' • Y' 0 0 1 1 1 1 0 1 1 0 0 0 1 0 0 1 0 0
X Y X' Y' (X • Y)' X' + Y' 0 0 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 1
Example: Find the complement of Z = A'B'C + A'BC + AB'C + ABC'
Z' = (A'B'C + A'BC + AB'C + ABC')'
= (A'B'C)' • (A'BC)' • (AB'C)' • (ABC')'
= (A+B+C') • (A+B'+C') • (A'+B+C') • (A'+B'+C)