Adding two n-bit integers problem


#1

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

Θ(1)
Θ(log(n)
Θ√Θ(n)
Θ(n)


#2

Answer: (B)

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)