Ripple-carry adder limitation: What is a primary disadvantage of the ripple-carry adder architecture when compared with faster adder structures?
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AThe interconnections are more complex.
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BMore stages are required to a full adder.
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CIt is slow due to propagation time.
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DAll of the above.
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EIt cannot be cascaded beyond 4 bits.
Answer
Correct Answer: It is slow due to propagation time.
Explanation
Introduction / Context:Adder design strongly influences CPU cycle time. The ripple-carry adder (RCA) is simple and area-efficient but suffers from worst-case delay proportional to bit-width. This question identifies the chief drawback.
Given Data / Assumptions:
- Adder built by cascading full-adder stages.
- Each stage must wait for the carry from the previous stage.
- No special carry acceleration is present.
Concept / Approach:Because each carry must ripple through all preceding stages, the overall delay grows linearly with the number of bits. This makes RCAs slow compared with carry-look-ahead or prefix adders.
Step-by-Step Solution:Model delay: T_total ≈ n * t_carry + t_sum(msb).As n increases, T_total increases linearly.Hence, the principal disadvantage is speed (propagation delay), not interconnect complexity.
Verification / Alternative check:Performance-optimized designs employ carry-look-ahead, carry-select, or parallel-prefix adders to reduce the carry chain depth.
Why Other Options Are Wrong:Interconnections are simpler, not more complex, than advanced adders.The number of stages equals the bit-width; it is not “more stages to a full adder.”“All of the above” is false because only the speed disadvantage is correct.RCAs can be cascaded to arbitrary widths; they just become slower.
Common Pitfalls:Confusing simplicity (an RCA is easy to wire) with performance advantages; they are often opposites.
Final Answer:It is slow due to propagation time.