Adder performance: A carry look-ahead (CLA) adder uses extra logic to compute carries in parallel and is generally faster than a ripple-carry adder. Evaluate the claim that a look-ahead-carry adder is slower because it requires additional logic.

Difficulty: Easy

Correct Answer: Incorrect

Explanation:


Introduction / Context:
Adder architectures trade off complexity and speed. Ripple-carry adders propagate carry serially through each bit, while carry look-ahead (CLA) adders compute carry signals in parallel using generate/propagate logic to reduce delay.


Given Data / Assumptions:

  • Ripple adders have O(n) carry-chain delay for n bits.
  • CLA adds extra logic (generate/propagate) to shorten the critical path.
  • We compare speed, not just gate count.


Concept / Approach:
CLA adds logic to compute carries simultaneously across groups, transforming linear carry delay into a shorter, usually logarithmic or block-based delay. Although hardware cost rises, the net effect is faster addition for moderate and wide bit-widths compared to ripple schemes.


Step-by-Step Solution:

Define G = A * B (generate), P = A ⊕ B (propagate).Use CLA equations to compute C1, C2, ... in parallel from Cin and the G/P terms.Observe reduced dependency chain vs. bit-by-bit ripple.Conclude CLA is faster despite additional logic.


Verification / Alternative check:
ASIC/FPGA timing models consistently show CLA outperforming ripple for nontrivial widths; further enhancements (carry-select, carry-skip, parallel-prefix) push speed even higher.


Why Other Options Are Wrong:

  • Correct: Misinterprets added logic as a speed penalty; it is a speed optimization.
  • Ambiguous / Cannot be determined: The architectural comparison is well-established.


Common Pitfalls:
Equating gate count with speed; in arithmetic circuits, structured parallelism often improves timing at the cost of area.


Final Answer:
Incorrect

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