Write the cardinal Product-of-Sum (POS) expression for the sum and carry of a full adder.

For a full adder with inputs A, B, Cin: $SUM = \pi(0,3,5,6) = (A+B+Cin)(A+B'+Cin')(A'+B+Cin')(A'+B'+Cin)$ $CARRY = \pi(0,1,2,4) = (A+B+Cin)(A+B+Cin')(A+B'+Cin)(A'+B+Cin)$