Consider a carry look ahead adder for adding two n-bit integers, built using gates of fan-in at most two. The time to perform addition using this adder is
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'B'. Can you explain this answer?

Computer Science Engineering (CSE) Question

Rachika Grewal answered Jul 05, 2018
 Look ahead carry generator gives output in constant time if fan-in = number of inputs.

For Example:

It will take O(1) to calculate 
c4 = g3 + p3g2 + p3p2g1 + p3p2p1g0 + p3p2p1p0c0c4 
   = g3 + p3g2 + p3p2g1 + p3p2p1g0 + p3p2p1p0c0, 
              if OR gate with 5 inputs is present.
And, if fan-in != number of inputs then we will have delay in each level, as given below.

If we have 8 inputs, and OR gate with 2 inputs, to build an OR gate with 8 inputs, we will need 4 gates in level-1, 2 in level-2 and 1 in level-3. Hence 3 gate delays, for each level.

Similarly an n-input gate constructed with 2-input gates, total delay will be O(log n).

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