OR-AND-invert

OR-AND-invert gates or OAI-gates are logic gates comprising OR gates followed by a NAND gate. They can be efficiently implemented in logic families like CMOS and TTL. They are dual to AND-OR-invert gates.

Overview

OR-AND-invert gates implement the inverted product of sums. $n$ groups of $m_i$, $m_i\ge 1,i=1\dots n$ input signals combined with OR, and the results then combined with NAND.

Examples

2-1 OAI-gate

Symbol for an 2-1 OAI-gate. The OR gate has the inputs A and B.

A 2-1-OAI gate realizes the function

$Y=\overline{(A\vee B)\wedge C}$

with the truth table shown below.

Truth table 2-1 OAI
Input A   B   C			Output Y
Template:No2	Template:No2	Template:No2	Template:Yes2
Template:No2	Template:No2	Template:Yes2	Template:Yes2
Template:No2	Template:Yes2	Template:No2	Template:Yes2
Template:No2	Template:Yes2	Template:Yes2	Template:No2
Template:Yes2	Template:No2	Template:No2	Template:Yes2
Template:Yes2	Template:No2	Template:Yes2	Template:No2
Template:Yes2	Template:Yes2	Template:No2	Template:Yes2
Template:Yes2	Template:Yes2	Template:Yes2	Template:No2

2-2 OAI gate

A 2-2-OAI gate realizes the function

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

with the truth table shown below.

Truth table 2-2 OAI
INPUT A   B   C   D				OUTPUT Q
Template:No2	Template:No2	Template:No2	Template:No2	Template:Yes2
Template:No2	Template:No2	Template:No2	Template:Yes2	Template:Yes2
Template:No2	Template:No2	Template:Yes2	Template:No2	Template:Yes2
Template:No2	Template:No2	Template:Yes2	Template:Yes2	Template:Yes2
Template:No2	Template:Yes2	Template:No2	Template:No2	Template:Yes2
Template:No2	Template:Yes2	Template:No2	Template:Yes2	Template:No2
Template:No2	Template:Yes2	Template:Yes2	Template:No2	Template:No2
Template:No2	Template:Yes2	Template:Yes2	Template:Yes2	Template:No2
Template:Yes2	Template:No2	Template:No2	Template:No2	Template:Yes2
Template:Yes2	Template:No2	Template:No2	Template:Yes2	Template:No2
Template:Yes2	Template:No2	Template:Yes2	Template:No2	Template:No2
Template:Yes2	Template:No2	Template:Yes2	Template:Yes2	Template:No2
Template:Yes2	Template:Yes2	Template:No2	Template:No2	Template:Yes2
Template:Yes2	Template:Yes2	Template:No2	Template:Yes2	Template:No2
Template:Yes2	Template:Yes2	Template:Yes2	Template:No2	Template:No2
Template:Yes2	Template:Yes2	Template:Yes2	Template:Yes2	Template:No2

Realization

Implementation of a 3-1 OAI-gate in CMOS

OAI-gates can efficiently be implemented as complex gates. An example of a 3-1 OAI-gate is shown in the figure below.

Examples of use

One possibility of implementing an XOR gate is by using a 2-2-OAI-gate with non-inverted and inverted inputs.

Implementation of an XOR gate using a 2-2-OAI gate