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Codiode/Problems/Combinational Logic

Distributive Law: Both Directions

EasyLogic CircuitAnalyze

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

boolean-algebradistributive-lawsop-pos

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