No. of Half Adders

Question

How many half adders are required to realize the following $4$ functions?
$f_1=A\oplus B\oplus C$
$f_2=\overline{A}BC+A\overline{B}C$
$f_3=AB\overline{C}+(\overline{A}+\overline{B})C$
$f_4=ABC$

Comments

how to solve f2,f3,f4???

---

3 half adders are required

Answer 1

all the above functions f1,f2,f3,f4 can be realized using 2 H.A circuit.

Answer 2

f2 : can be realized using 2 HA.

               s= A XOR B                                                              S = s XOR C => A XOR B XOR C

               carry = AB                                                                  carry = s.C => (A XOR B) .C = AB'C + A'BC

f3 and f4 : Both can be realized using 3 HA.

F is f3 and G is f4.

Note : All can be realized using 2 Half adders also .

for f3 and f4 :  just consider 1st and 2nd HA , pass the carry of 1st HA as input to 2nd HA.

Ref : http://www.exploreroots.com/dc41.html