Computer Organization and Design MIPS Edition, 6th Edition

Note the repeated appearance of (ai · bi) and (ai + bi) in the formula above. These two important factors are traditionally called generate (gi) and propagate (pi):

$\begin{array}{c}\text{g}i=\text{a}i·\text{b}i\\ \text{p}i=\text{a}i+\text{b}i\end{array}$

Using them to define ci + 1, we get

$\text{c}i+1=\text{g}i+\text{p}i·\text{c}i$

To see where the signals get their names, suppose gi is 1. Then

$\text{c}i+1=\text{g}i+\text{p}i·\text{c}i=1+\text{p}i·\text{c}i=1$

That is, the adder