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:
- We compare an unsimplified vs simplified combinational circuit implementing the same Boolean function.
- Cost correlates with gate count, fan-in, and interconnect length.
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