In a full adder, the boolean expressions for the sum (S) and carry_out (C_out) are as follows: 

1
S=A⊕B⊕Cin, Cout=AB+BC+CA
2
S=AB+BC, Cout = AB+BC+CA 
3
S=A⊕B⊕Cin, Cout = AB + BCin + ACin 
4
S=AB+BC+Cin, Cout =AB+BC+CA

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