AND-OR-Invert

AND-OR-Invert (AOI) logic and AOI gates are two-level compound (or complex) logic functions constructed from the combination of one or more AND gates followed by a NOR gate. Construction of AOI cells is particularly efficient using CMOS technology where the total number of transistor gates can be compared to the same construction using NAND logic or NOR logic. The complement of AOI Logic is OR-AND-Invert (OAI) logic where the OR gates precede a NAND gate.

Logic operations

AOI gates perform one or more AND operations followed by an OR operation and then an inversion. For example, a 2-2 AOI gate can be represented by the boolean equation  and truth table:

${\displaystyle F={\overline {(A\wedge B)\vee (C\wedge D)}}}$

A 2-1 AOI gate can be represented by following the boolean equation and truth table:

{\displaystyle F={\overline {A\vee (B\wedge C)}}}

Larger AOI gates, such as 4-3 AOI or 3-3-3 AOI can also be used.