Carry-generation techniques: The look-ahead carry (carry lookahead) method is designed to reduce, not incur, long ripple propagation delays. Judge the accuracy of the claim that it “suffers from propagation delays.”
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AIncorrect
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BCorrect
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COnly true for 1-bit adders
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DOnly true at very low Vcc
Answer
Correct Answer: Incorrect
Explanation
Introduction / Context: Ripple-carry adders suffer from cumulative carry propagation delay, which scales with bit-width. Carry lookahead (CLA) logic addresses this by computing carry signals using generate/propagate terms in parallel, drastically shortening the critical path compared to ripple structures.Given Data / Assumptions:
- Ripple-carry: carry-out of each stage waits on the previous stage.
- CLA: uses G (generate) and P (propagate) to precompute carries.
- All digital logic still has finite gate delays; the question targets the concept of “suffering from” ripple-like delays.
Concept / Approach: CLA replaces serial carry dependency with parallel equations such as c1 = G0 + P0c0, c2 = G1 + P1G0 + P1P0c0, etc. While there is nonzero combinational delay in CLA networks, they specifically mitigate the linear propagation characteristic that plagues ripple adders.Step-by-Step Solution:
Define Gk = Ak*Bk and Pk = Ak + Bk (for a bit k).Compute carries using sums of products rather than waiting stage-by-stage.Observe reduced depth vs. ripple; hierarchical CLAs further minimize fan-in/fan-out issues.Hence the claim that CLA “suffers from propagation delays” (as ripple does) is inaccurate.Verification / Alternative check:
Compare timing: ripple delay ~ O(n); CLA delay ~ O(log n) or bounded by gate levels with hierarchy.Why Other Options Are Wrong:
Correct / Only true for 1-bit / low Vcc: None reflect the fundamental timing advantage of CLA over ripple.Common Pitfalls:
Equating “nonzero delay” with “suffers from propagation delay” in the ripple sense.Ignoring fan-in limitations and practical buffering, which are engineering details but do not negate CLA’s purpose.Final Answer:
Incorrect