Distributive Law: Both Directions
Logic synthesis tools optimize gate counts by aggressively factoring and expanding Boolean expressions before mapping to physical standard cells. The distributive law operates in two distinct directions: expanding a Product of Sums (POS) into a Sum of Products (SOP), and factoring an SOP into a POS. The expressions under analysis are F1 = A(B + C) and F2 = A + BC. The second expression represents the often-forgotten dual of the standard distributive law. Determine the equivalent expanded and factored forms for these expressions. Trace how the terms combine to verify logical equivalence across both representations.
Constraints
- Apply Boolean algebra rules strictly without altering the logical meaning of the expressions.
- Assume all variables represent standard single-bit binary values.
Topics
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