Define carry propagate, and carry generate of a binary adder as$,$

$P_i=A_i+B_i$

$G_i=A_i{B}_i$

Show that the output carry, and the output sum of a full adder in the binary adder

becomes

$C_{i+1}=(C_i^{\text{'}}{G}_i^{\text{'}}+P_i^{\text{'}}{)}^{\text{'}}$

$S_i=(P_i{G}_i^{\text{'}})o+C_i$