Adder performance and timing in digital design: In a 4-bit ripple-carry adder constructed from full-adder stages, how does carry propagation delay affect overall operation speed?

Introduction / Context:
Ripple-carry adders are built by cascading full-adder (FA) stages. Each stage must wait for the carry from the previous stage before it can finalize its own sum and carry results. This question examines how that carry propagation limits arithmetic speed.

Given Data / Assumptions:

• Implementation is a 4-bit ripple-carry adder made from discrete full-adder cells.
• Each full-adder has nonzero gate delays for carry generation and propagation.
• Sum output of a stage is valid only after its incoming carry has settled.

Concept / Approach:
In a ripple structure, the least-significant carry must propagate sequentially through every stage until it reaches the most significant stage. Total delay equals the per-stage carry delay multiplied by the number of stages, plus additional sum-path delay at the final stage.

Step-by-Step Solution:
Let t_carry be carry-out delay per FA stage.For an n-bit ripple adder, worst-case carry chain length is n stages.Worst-case delay ≈ n * t_carry + t_sum(msb).Therefore, delay grows with bit-width, directly limiting maximum clock rate.

Verification / Alternative check:
Designers often replace ripple adders with look-ahead or prefix adders (carry-look-ahead, carry-select, Kogge-Stone) precisely because ripple delay is cumulative and becomes the critical path.

Why Other Options Are Wrong:
“Not a consideration” is incorrect—adder delay is frequently the ALU critical path.“Decreases with number of stages” contradicts cascade timing.“Increases but not limiting” is false; it is limiting.“Remains constant” is not true for ripple structures.

Common Pitfalls:
Assuming nanosecond-scale delays are negligible; in modern high-speed designs even tens of picoseconds matter across many bits.

Final Answer:
is cumulative for each stage and limits the speed at which arithmetic operations are performed