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This article is about NAND Logic in the sense of building other logic gates using just NAND gates. For information on 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 (along with NOR gates) from which any other logic gates can be built. Due to this property, NAND and NOR gates are sometimes called "universal gates". However, contrary to popular belief, 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).
This is a NAND gate; trivially, just a NAND gate is used to realise it:
| Desired Gate |
NAND Construction |
 |
|
Truth Table
| Input A |
Input B |
|
Output Q |
| 0 |
0 |
|
1 |
| 0 |
1 |
|
1 |
| 1 |
0 |
|
1 |
| 1 |
1 |
|
0 |
|
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 |
|
An AND gate is made by following a NAND gate by 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 |
|
If the truth table for a NAND gate is examined, 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 |
|
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 |
|
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 N) NAND (B NAND N) where N = 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 |
|
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 |
|
[edit] See also
- NOR logic. Like NAND gates, NOR gates are also universal gates.
