Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Digital systems, linear algebra, introduction to formal proof resit / 3 / d

The modified output isFor example, $(a,b,c,d)=(1,0,0,1)$ gives $z=1$ and $z^{\prime }=0$. Neither original series branch is complete, but the new connection supplies the cross-route through the transistors controlled by $a,d$. Interchanging those roles gives the other cross-route example. In fact $(a\vee c)(b\vee d)=ab\vee ad\vee bc\vee cd$, so the modified circuit has added exactly those two possible lower conduction routes.