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For an NMOS transistor network described by a series-parallel expression in conducting inputs, replace series by parallel, parallel by series, and each device by a PMOS transistor driven by the same input. De Morgan's laws show recursively that the resulting pull-up network conducts exactly when the original pull-down network does not. This proves complementary rail connections for stable binary inputs in the ideal static model. Factoring a Boolean function before constructing its dual can remove duplicated devices: $ab\vee bc=b(a\vee c)$ needs three lower and three upper devices, instead of four of each. Physical switching transients, device sizing and delays are additional engineering questions.

The two lower conducting branches are the series pairs controlled by $a,b$ and by $c,d$. Their overall NMOS transistor conduction condition is $ab\vee cd$. Apply complementary CMOS network duality: the upper network has the parallel pair of PMOS transistors controlled by $a,b$, in series with the parallel pair controlled by $c,d$. Its first end connects to the high rail, its last end connects to $z$, and the junction between the two pairs is internal to the upper network.

The left panel gives that completion. Every upper transistor uses its correspondingly named input and conducts when that input is low. Its conducting condition is $(\neg a\vee \neg b)\wedge (\neg c\vee \neg d)$, exactly the complement of the lower condition. Thus the ideal static circuit connects the output to one supply rail for every stable binary input.

The lower network pulls the output low exactly when either series branch conducts. Therefore the Boolean function isThe inversion is important: $ab\vee cd$ describes connection to the low rail, not a high output. The pull-up network found in part a implements the complementary high condition.

A pull-up network connects a logic output to the high supply rail when its conducting condition holds. In static complementary CMOS, it is built from PMOS transistors and paired with a complementary pull-down network.