NAND logic

This article is about NAND Logic in the sense of building other logic gates using just NAND gates. For NAND Gates, see NAND gate. For NAND in the purely logical sense, see Logical NAND. For logic gates generally, see Logic gate.

NAND gates are one of the two basic logic gates (the other being NOR logic) 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. Instead, EDA tools are used to convert the description of a logical circuit to a netlist of complex gates (standard cells) or transistors (full custom 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
Truth Table Input A Output Q 0 1 1 0

AND

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
Truth Table Input A Input B Output Q 0 0 0 0 1 0 1 0 0 1 1 1

OR

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
Truth Table Input A Input B Output Q 0 0 0 0 1 1 1 0 1 1 1 1

NOR

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

Desired Gate	NAND Construction
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
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
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. Like NAND gates, NOR gates are also universal gates.