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