Difficulty: Easy
Correct Answer: Incorrect
Explanation:
Introduction: Logic simplification aims to reduce the number of gates, inputs per gate, and interconnections while preserving function. Cost in digital hardware is closely tied to device count, input fan-in, and wiring complexity. This question tests whether simplification increases or decreases cost.Given Data / Assumptions:
Concept / Approach: Using Boolean algebra or Karnaugh maps, simplification typically reduces literals and product/sum terms, which maps to fewer gates or gates with lower fan-in. Fewer resources normally imply lower silicon area and lower cost, not higher.Step-by-Step Solution:
Step 1: Express function in canonical form (e.g., SOP or POS).Step 2: Apply Boolean algebra or K-map grouping to eliminate redundant literals.Step 3: Implement the minimized expression with fewer gates or smaller fan-in.Verification / Alternative check:
Practical synthesis tools target reduced area and delay, confirming that simplification reduces hardware resources on average.Why Other Options Are Wrong:
Correct: Contradicts the typical outcome; simplification reduces cost.Depends on technology only: While technology matters, simplification almost always helps across families.Insufficient information: Standard cost models are adequate to judge the direction.Common Pitfalls:
Assuming more complex algebra means more hardware; the opposite is typical.Ignoring fan-in reduction benefits on delay and power.Final Answer:
Incorrect
Discussion & Comments