Full-adder chains and performance: What is true about carry propagation delay in cascaded full-adder (FA) stages?

Introduction / Context:
Ripple-carry adders are built by cascading full adders, with each stage waiting for the previous carry. This architecture is simple but introduces carry propagation delay, a key metric that determines how fast multi-bit addition can be completed.

Given Data / Assumptions:

• Adder type: ripple-carry (cascaded FAs).
• Carry out of stage i must settle before stage i+1 can settle.
• Each FA has a finite gate delay.

Concept / Approach:
Propagation delay through each full adder adds to the total delay because carry must ripple through all stages from least to most significant bit. Thus total delay roughly scales with the number of bits, directly impacting maximum clock or throughput.

Step-by-Step Solution:
Let t_FA be the worst-case carry delay of one full adder.For N bits in ripple form, worst-case delay ≈ N * t_FA (carry must traverse all stages).Therefore, the carry propagation delay is cumulative and limits speed.

Verification / Alternative check:
Compare with look-ahead adders: they reduce dependency chain length by computing carries in parallel, achieving much lower effective delay than N * t_FA. This contrast supports that ripple carry delay is indeed limiting.

Why Other Options Are Wrong:
Negligible: Not for wide adders; it dominates speed.Decreases with stages: Opposite of reality.Increases but not limiting: In practice it is often the limiting factor.Eliminated by sum-only logic: Sums still depend on carries.

Common Pitfalls:
Ignoring worst-case paths, or assuming average delay sets the clock limit; synchronous systems must accommodate worst case.

Final Answer:
It is cumulative per stage and limits arithmetic speed.