We can also design the adder using the Truth table and generate the SOPs

SOP for Result:  

!A!BCin + !AB!Cin + A!B!Cin + ABCin  

Cin(!A!B + AB) + !Cin(!AB + A!B)    (Distribution law) 

Cin (A XOR B) + !Cin(A XOR B) 

Cin XOR (A XOR B) 

SOP for Carry Out:  

!ABCin + AB!Cin + AB!Cin + ABCin 

AB + BCin + ACin