De Morgan's laws move inversion across AND and OR: NOT(AB) = NOT A + NOT B, and NOT(A + B) = (NOT A)(NOT B). Duality exchanges AND with OR and zero with one throughout a valid Boolean identity, producing another valid identity.
Worked example
To simplify NOT(A + BC), first invert the outer OR: (NOT A) AND NOT(BC). Then invert the inner AND: (NOT A) AND ((NOT B) OR (NOT C)). Each time inversion passes through a gate operation, that operation changes.
What to watch for
Invert every operand inside the affected group. Changing AND to OR while leaving one input uninverted gives the wrong function.
Try it yourself
Write the dual of A + 0 = A.
Answer: Exchange OR with AND and zero with one: A × 1 = A. The variable A itself stays unchanged.
How to study this topic
Read one operation at a time and use parentheses generously. Check a simplification with every truth-table row, not just a convenient example. A useful simpler expression must preserve the complete specified function.
Explore related programmes
These recorded programmes are upcoming. This article is general educational content, not a syllabus or course sample.
Digital Electronics