Practice question · Multiple choice
A 64-bit ripple-carry adder is 64 gate delays deep and sits on the critical path of nearly every instruction. What does carry-lookahead buy, and what does it cost?
Hints
- Trace the worst case: adding 1 to all ones. How far must the carry travel?
- Ask whether a carry could be computed without waiting for the previous one.
Show the answer
A. Delay growing like log n instead of n, at the cost of many more gates
Why
The carry chain is the bottleneck, and lookahead breaks it by computing each carry directly from the inputs rather than from its predecessor, logarithmic depth for a lot more silicon. It is the area-versus-speed trade in its purest form, which is why real adders are hierarchical compromises rather than either extreme.
Practise Adders, Multiplexers, and Decoders
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