OR-AND-invert gates, or OAI-gates, are

logic gates A logic gate is a device that performs a Boolean function, a logical operation performed on one or more Binary number, binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic gate, one ...

comprising

OR gate The OR gate is a digital logic gate that implements logical disjunction. The OR gate outputs "true" if any of its inputs is "true"; otherwise it outputs "false". The input and output states are normally represented by different voltage levels. ...

s followed by a

NAND gate In digital electronics, a NAND (NOT AND) gate is a logic gate which produces an output which is false only if all its inputs are true; thus its output is complement to that of an AND gate. A LOW (0) output results only if all the inputs to the ...

. They can be efficiently implemented in logic families like

CMOS Complementary metal–oxide–semiconductor (CMOS, pronounced "sea-moss ", , ) is a type of MOSFET, metal–oxide–semiconductor field-effect transistor (MOSFET) semiconductor device fabrication, fabrication process that uses complementary an ...

and TTL. They are dual to

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 (equivalent to an OR gate through an Inverter gate, which is the "OI" part ...

gates.

Overview

OR-AND-invert gates implement the inverted

product of sums In Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form ( CDNF), minterm canonical form, or Sum of Products (SoP or SOP) as a disjunction (OR) of minterms. The De Morgan dual is the canonical conjuncti ...

n

groups of

m_i

m_i \ge 1, i=1\ldots n

input signals combined with OR, and the results then combined with NAND.

Examples

2-1 OAI-gate

A 2-1-OAI gate realizes the following function: :

Y = \overline

2-2 OAI gate

A 2-2-OAI gate realizes the following function: :

Y = \overline

Realization

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 XOR gate (sometimes EOR, or EXOR and pronounced as Exclusive OR) is a digital logic gate that gives a true (1 or HIGH) output when the number of true inputs is odd. An XOR gate implements an exclusive disjunction, exclusive or (\nleftrightarrow) ...

is by using a 2-2-OAI-gate with non-inverted and inverted inputs. XOR gate based on 2-2 AOI gate

References

{{Logic-stub Logic gates