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In fact, both NAND and NOR gates are so-called "universal gates" and any logical function can be constructed from either NAND logic or NOR logic alone. If the four NOR gates are replaced by NAND gates, this results in an XOR gate, which can be converted to an XNOR gate by inverting the output or one of the inputs (e.g. with a fifth NAND gate).
An XNOR gate is made by considering the disjunctive normal form + ¯ ¯, noting from de Morgan's law that a NAND gate is an inverted-input OR gate. This construction entails a propagation delay three times that of a single NAND gate and uses five gates.
A single NOR gate. A NOR gate or a NOT OR gate is a logic gate which gives a positive output only when both inputs are negative.. Like NAND gates, NOR gates are so-called "universal gates" that can be combined to form any other kind of logic gate.
Each of the singleton sets { NAND} and { NOR} is functionally complete. However, the set { AND, OR} is incomplete, due to its inability to express NOT. A gate (or set of gates) that is functionally complete can also be called a universal gate (or a universal set of gates).
An entire processor can be created using NOR gates alone. The original Apollo Guidance Computer used 4,100 integrated circuits (IC), each one containing only two 3-input NOR gates. [3] As NAND gates are also functionally complete, if no specific NOR gates are available, one can be made from NAND gates using NAND logic. [2]
A logic circuit diagram for a 4-bit carry lookahead binary adder design using only the AND, OR, and XOR logic gates.. A logic gate is a device that performs a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output.
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This explains why "EQ" is often called "XNOR" in the combinational logic of circuit engineers, since it is the negation of the XOR operation; "NXOR" is a less commonly used alternative. [1] Another rationalization of the admittedly circuitous name "XNOR" is that one begins with the "both false" operator NOR and then adds the eXception "or both ...