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Codiode/Problems/Combinational Logic

SOP to POS via Complementary Indexing

MediumLogic CircuitAnalyze

Hardware synthesis tools rely on set-theoretic properties of Boolean algebra to translate logic expressions without generating exhaustive truth tables. A three-variable Boolean function F over variables A, B, and C is defined in sum-of-minterms (SOP) form as F = Σm(1, 3, 5, 7).

Determine the equivalent product-of-maxterms (POS) expression for F using complementary indexing. Identify the exact mathematical relationship between the minterm indices of a function and its maxterm indices.

Constraints

  • The universal set of indices is determined by the number of input variables.
  • Variables are ordered A, B, C with A as the most significant bit.
  • Do not construct a truth table to solve these questions.

Topics

boolean-algebrasopmintermsposmaxterms

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