Difficulty: Easy
Correct Answer: using Boolean algebra
Explanation:
Introduction / Context:
Designing efficient digital circuits requires reducing complexity without changing functionality. Boolean algebra provides a mathematical framework to manipulate logic expressions, enabling smaller, faster, and less power-hungry hardware implementations.
Given Data / Assumptions:
Concept / Approach:
Boolean algebra supplies identities such as commutative, associative, distributive, idempotent, absorption, and De Morgan’s laws. These rules let us rewrite expressions systematically to minimize terms and literals, or to transform between SOP and POS forms.
Step-by-Step Solution:
Verification / Alternative check:
A truth table or Karnaugh map can confirm the simplified result matches the original function; however, the algebra itself is the method of systematic reduction. Karnaugh maps provide a graphical route; Boolean algebra is the formal symbolic method.
Why Other Options Are Wrong:
Common Pitfalls:
Applying rules incorrectly (e.g., confusing absorption with idempotence); forgetting to verify equivalence after reduction; optimizing a subexpression without considering shared terms and fan-in limits in the final hardware.
Final Answer:
using Boolean algebra
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