# How should an AND-OR-INVERT gate look like?

I was asked to implement a logic expression (F = A'B' + C'D' + AC') with AND-OR-INVERT(AOI) gates. I made the circuit (Figure 1) below, but I looked it up on Wikipedia and found that AOI gates are made out of two AND gates and a single NOR gate. So I made the second circuit (Figure 2), but their outputs were different eventhough their inputs were the same. I would really appreciate it if someone could explain this to me, thanks.

## Figure 2

• Are you only allowed to use and-or-invert gates? Or are other gates permitted?
– jonk
Nov 15 '20 at 6:55
• Yes, but im not sure if and-or-inverter means and, or, not gates or and, nor gates. Nov 15 '20 at 9:07
• Well, if you put the same input value into all four inputs then the output will be the inverted input value. I'm curious what you are allowed. That's not clear to me, yet.
– jonk
Nov 15 '20 at 9:10
• We are only allowed to use AND-OR-INVERT gates. Nov 15 '20 at 10:51

Your first gate realization does indeed implement $$\F =A'B' +C'D' + AC' \$$
As far as I can see, your second circuit implements $$\F =(AB +CD)' + AC' =(AB)'(CD)'+AC'\$$