NAND gate

NAND gate

The Negated AND, NO AND or NAND gate is the opposite of the digital AND gate, and behaves in a manner that corresponds to the opposite of AND gate, as shown in the truth table on the right. A LOW output results only if both the inputs to the gate are HIGH...

s are one of the two basic logic gates (the other being 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...

) from which any other logic gates can be built. Due to this property, NAND and 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...

s are sometimes called "universal gates". However, modern integrated circuit

Integrated circuit

An integrated circuit or monolithic integrated circuit is an electronic circuit manufactured by the patterned diffusion of trace elements into the surface of a thin substrate of semiconductor material...

s are not constructed exclusively from a single type of gate. Instead, EDA

Electronic design automation

Electronic design automation is a category of software tools for designing electronic systems such as printed circuit boards and integrated circuits...

 tools are used to convert the description of a logical circuit to a netlist

Netlist

The word netlist can be used in several different contexts, but perhaps the most popular is in the field of electronic design. In this context, a "netlist" describes the connectivity of an electronic design....

 of complex gates (standard cell

Standard cell

In semiconductor design, standard cell methodology is a method of designing application-specific integrated circuits with mostly digital-logic features. Standard cell methodology is an example of design abstraction, whereby a low-level very-large-scale integration layout is encapsulated into an...

s) or transistors (full custom

Full custom

Full-custom design is a methodology for designing integrated circuits by specifying the layout of each individual transistor and the interconnections between them...

 approach).

NOT

A NOT gate is made by joining the inputs of a NAND gate. Since a NAND gate is equivalent to an AND gate followed by a NOT gate, joining the inputs of a NAND gate leaves only the NOT part.

Desired Gate	|NAND Construction
EWLINE Truth Table Input A Output Q 0 1 1 0

AND

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...

An AND gate is made by following a NAND gate with a NOT gate as shown below. This gives a NOT NAND, i.e. AND.

Desired Gate	|NAND Construction
EWLINE Truth Table Input A Input B Output Q 0 0 0 0 1 0 1 0 0 1 1 1

OR

OR gate

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

If the truth table for a NAND gate is examined or by applying De Morgan's Laws, it can be seen that if any of the inputs are 0, then the output will be 1. However to be an OR gate, if any input is 1, the output must also be 1. Therefore, if the inputs are inverted, any high input will trigger a high output.

Desired Gate	|NAND Construction
EWLINE Truth Table Input A Input B Output Q 0 0 0 0 1 1 1 0 1 1 1 1

NOR

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...

A NOR gate is simply an OR gate with an inverted output:

Desired Gate	|NAND Construction
EWLINE Truth Table Input A Input B Output Q 0 0 1 0 1 0 1 0 0 1 1 0

XOR

An XOR gate is constructed similarly to an OR gate, except with an additional NAND gate inserted such that if both inputs are high, the inputs to the final NAND gate will also be high, and the output will be low. This effectively represents the formula: "(A NAND (A NAND B)) NAND (B NAND (A NAND B))".

Desired Gate	|NAND Construction
EWLINE Truth Table Input A Input B Output Q 0 0 0 0 1 1 1 0 1 1 1 0

XNOR

An XNOR gate is simply an XOR gate with an inverted output:

Desired Gate	|NAND Construction
EWLINE Truth Table Input A Input B Output Q 0 0 1 0 1 0 1 0 0 1 1 1

External links

• Using Logic Gates

See also

• 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...
  
  . Like NAND gates, NOR gates are also universal gates.