AND-OR-Invert logic and AOI gates are two-level compound (or complex) logic functions constructed from the combination of one or more AND gate

AND gate

The AND gate is a basic digital logic gate that implements logical conjunction - it behaves according to the truth table to the right. A HIGH output results only if both the inputs to the AND gate are HIGH . If neither or only one input to the AND gate is HIGH, a LOW output results...

s followed by a NOR gate

NOR gate

The NOR gate is a digital logic gate that implements logical NOR - it behaves according to the truth table to the right. A HIGH output results if both the inputs to the gate are LOW . If one or both input is HIGH , a LOW output results. NOR is the result of the negation of the OR operator...

. Construction of AOI cells is particularly efficient using CMOS

CMOS

Complementary metal–oxide–semiconductor is a technology for constructing integrated circuits. CMOS technology is used in microprocessors, microcontrollers, static RAM, and other digital logic circuits...

 technology where the total number of transistor gates can be compared to the same construction using NAND logic

NAND logic

NAND gates are one of the two basic logic gates from which any other logic gates can be built. Due to this property, NAND and NOR gates are sometimes called "universal gates". However, modern integrated circuits are not constructed exclusively from a single type of gate...

 or NOR logic

NOR logic

Like NAND gates, NOR gates are so-called "universal gates" that can be combined to form any other kind of logic gate. For example, the first embedded system, Apollo Guidance Computer, was built exclusively from NOR gates, about 5,600 in total for the later versions. Today, integrated circuits are...

. The complement of AOI Logic is OR-AND-Invert (OAI) logic where the OR gates precede an AND 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

Truth table

A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—to compute the functional values of logical expressions on each of their functional arguments, that is, on each combination of values taken by their...

:

2-2 AOI
INPUT A   B   C   D				OUTPUT F
0	X	X	0	1
X	0	X	0	1
0	X	0	X	1
X	0	0	X	1
1	1	X	X	0
X	X	1	1	0

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

2-1 AOI
INPUT A   B   C			OUTPUT F
0	0	0	1
0	0	1	1
0	1	0	1
0	1	1	0
1	0	0	0
1	0	1	0
1	1	0	0
1	1	1	0

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

Electronic implementation

AOI gates can be readily implemented in CMOS

CMOS

Complementary metal–oxide–semiconductor is a technology for constructing integrated circuits. CMOS technology is used in microprocessors, microcontrollers, static RAM, and other digital logic circuits...

circuitry. AOI gates are particularly advantaged in that the total number of transistors (or gates) is less than if the AND, NOT, and OR functions were implemented separately. This results in increased speed, reduced power, smaller area, and potentially lower fabrication cost. For example, a 2-1 AOI gate can be constructed with 6 transistors in CMOS compared to 10 transistors using a 2-input NAND gate (4 transistors), an inverter (2 transistors), and a 2-input NOR gate (4 transistors).