Half Adder circuit :
Full Adder circuit :
i.e, we can construct one full adder with 2 half adders and 1 OR gate.
For example if we add two 4-bit numbers A(a3,a2,a1,a0), B(b3,b2,b1,b0), we require 1 half adder(a0+b0) and 3 full adders(a1+b1+carry0, a2+b2+carry1,a3+b3+carry2).
Each full adder take 2 half adders and 1 OR gate.
i.e, 3 full adders take = 3*2 half adders + 3*1 OR gate.
Total for 4 bit addition it will take 7(6+1) half adders + 3 OR gates.
Generalization for n-bits addition:
It will take 1 half adder and (n-1) full adders .
These (n-1) full adders we can represent with (n-1)*2 half adders + (n-1)*1 OR gate.
So,total for n-bits addition it will take 2n-1(2n-2+1) half adders and (n-1) OR gates.