look ahead carry generator

In a look-ahead carry generator, the carry generate function Gi and the carry propagate function Pi for inputs Ai and Bi are given by:

Pi = Ai ⨁ Bi and Gi = AiBi 

The expressions for the sum bit Si and the carry bit Ci+1 of the look-ahead carry adder are given by:

Si = Pi ⨁ Ci and Ci+1 = Gi + PiCi , where C0 is the input carry. 

Consider a two-level logic implementation of the look-ahead carry generator. Assume that all Piand Gi are available for the carry generator circuit and that the AND and OR gates can have any number of inputs. The number of AND gates and OR gates needed to implement the look-ahead carry generator for a 4-bit adder with S3, S2, S1, S0 and C4 as its outputs are respectively:

 

ans:10,4 can sum1 explain this plz

1Comment
Shraddha @shraddhagami
16 Jan 2017 02:42 am
c1 = g0 + p0c0 = 1 AND, 1 OR
c2 = g1 + p1g0 + p1p0c0
= 2 AND, 1 OR

c3 = g2 + p2g1 + p2p1go + p2p1p0c0
= 3 AND, 1 OR
c4 = g3 + p3g2 + p3p2g1 + p3p2p1g0 + p3p2p1p0c0
= 4 AND, 1 OR
Total AND gates =1+2+3+4 = 10
Total OR gates = 1+1+1+1 = 4

Look ahead carry is only responsible for generate carry. Sum part is handled by adder part.