Dual of a Boolean Expression
Boolean algebra theorems govern the optimization of digital logic networks and always exist in complementary pairs due to the principle of duality. The principle of duality states that any valid Boolean equation remains valid if every AND is swapped with an OR, every OR is swapped with an AND, every 0 is replaced by 1, and every 1 is replaced by 0. Variables and their complements remain entirely unchanged. Consider De Morgan's theorem expressed as (AB)' = A' + B' and the absorption law expressed as x + xy = x. Determine the dual form of these expressions and evaluate their validity.
Constraints
- Duality does not involve complementing the individual variables.
- The dual of a valid theorem is always another valid theorem.
- Operations inside parentheses must be swapped just like operations outside.
Topics
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