Computer arithmetic design: Why is a carry look-ahead adder commonly preferred for binary addition in high-speed digital systems?
-
AIt costs less to implement
-
BIt is faster
-
CIt is more accurate
-
DIt uses fewer gates
-
EIt needs no propagation delay
Answer
Correct Answer: It is faster
Explanation
Introduction / Context:Adders are central to arithmetic logic units (ALUs). Ripple-carry adders are simple but slow because each bit's carry must wait for the previous one. Carry look-ahead adders (CLAs) improve speed by computing carries in parallel using generate/propagate logic.
Given Data / Assumptions:
- Comparing ripple-carry vs. carry look-ahead techniques.
- Metric of interest: addition speed (latency).
- Accuracy of addition is identical for correct implementations.
Concept / Approach:CLA forms carry generate (Gi = AiBi) and carry propagate (Pi = Ai + Bi) signals to compute all carries through combinational look-ahead networks. This removes the linear dependency of carry propagation and reduces critical path delay.
Step-by-Step Solution:
Define Gi = AiBi and Pi = Ai + Bi for every bit i.Compute carries: C1 = G0 + P0C0; C2 = G1 + P1G0 + P1P0C0; and so on.Because carries are produced in parallel (via logic trees), total delay scales logarithmically or by block rather than linearly with word length.Verification / Alternative check:In timing analysis, a CLA's worst-case delay is substantially less than an n-bit ripple adder (which is O(n)). Thus, CLAs are the industry standard for high-speed addition.
Why Other Options Are Wrong:
Cost / gate count: CLAs typically use more gates and wiring than ripple-carry.Accuracy: Not a differentiator—both produce correct sums.'Needs no propagation delay': impossible in real circuits.Common Pitfalls:
Assuming fewer gates always means faster; interconnect and carry logic dominate speed.Final Answer:
It is faster