De Morgan’s Theorem
De Morgan’s Theorem provides a powerful way to simplify digital logic by converting OR operations to AND operations (and vice-versa) using negation.
1. First Law (NOR Gate Equivalent)
The complement of a sum is equal to the product of the individual complements.
A + B = A ⋅ B
Logic: A NOR gate is equivalent to an AND gate with inverted inputs (Bubbled AND).
2. Second Law (NAND Gate Equivalent)
The complement of a product is equal to the sum of the individual complements.
A ⋅ B = A + B
Logic: A NAND gate is equivalent to an OR gate with inverted inputs (Bubbled OR).
* Note: The bar above the variables represents the NOT (inversion) operation.
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