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Codiode/Problems/Combinational Logic

Consensus Theorem: Removing a Redundant Term

HardLogic CircuitAnalyze

Static hazards in digital circuits are eliminated by adding redundant logic gates that bridge transitions between prime implicants. The Boolean expression Y = AB + A'C + BC represents a three-variable logic function in sum-of-products form.

Evaluate the algebraic necessity of the term BC. Expand the expression algebraically to determine if BC alters the final logic output. Compare the truth table of Y against the reduced expression Z = AB + A'C across all possible input states.

Constraints

  • Boolean algebra rules must be applied strictly to prove equivalence.
  • The variables A, B, and C represent standard binary logic levels.

Topics

Boolean AlgebraConsensus TheoremLogic MinimizationHazards

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