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Codiode/Problems/Combinational Logic

Absorption Law: Both Forms

EasyLogic CircuitAnalyze

Hardware synthesis tools rely heavily on algebraic reduction to minimize transistor count before layout. The Absorption Law is the most frequently applied theorem during this optimization phase because it eliminates redundant variables without altering the logic function.

Two primitive logic networks implement the expressions X + XY and X(X + Y).

Determine the minimal form for both expressions using only Boolean algebra axioms. Identify the intermediate forms and the specific theorems applied at each step. Prove the reduction algebraically rather than relying on a truth table.

Constraints

  • Simplification must be demonstrated through algebraic manipulation.
  • Truth table proofs are invalid for this analysis.
  • All intermediate logic states must follow standard Boolean postulates.

Topics

boolean-algebrasimplificationabsorption-law

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