.
).
The NAND gate is drawn as follows
The three basic logic gates can be combined to provide more complex logical functions. Four important logical functions are described here, namely NAND, NOR, XOR and XNOR. In each case a summary is given including the logic symbol for that function, the corresponding truth table and the Boolean expression.
The NAND gate has two or more inputs.
The output from the NAND gate is 0 if
and only if all of the inputs are 1 otherwise the output is 1.
Therefore the output from the NAND gate is the NOT of
A AND B (also known as the complement or inversion of
.).
The NAND gate is drawn as follows
where the small circle immediately to the right of the gate on the output line is known as an invert bubble.
The output from the NAND gate is written as 
(the same rules apply regarding the placement and appearance of the dot
as for the AND gate - see the section on
basic logic gates). The Boolean expression
reads as "A NAND B".
The truth table for a two-input NAND gate looks like
|
| |
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
The NOR gate has two or more inputs. The output from the NOR gate is 1 if and only if all of the inputs are 0, otherwise the output is 0. This output behaviour is the NOT of A OR B. The NOR gate is drawn as follows
The output from the NOR gate is written as
which reads "A NOR B".
The truth table for a two-input NOR gate looks like
|
| |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |
The exclusive-OR or XOR gate has two or more inputs. For a two-input XOR the output is similar to that from the OR gate except it is 0 when both inputs are 1. This cannot be extended to XOR gates comprising 3 or more inputs however.
In general, an XOR gate gives an output value of 1 when there are an odd number of 1's on the inputs to the gate. The truth table for a 3-input XOR gate below illustrates this point.
The XOR gate is drawn as
The output from the XOR gate is written as
which reads "A XOR B".
The truth table for a two-input XOR gate looks like
| |
|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
For a 3-input XOR gate with inputs ,
and 
the truth table is given by
| |
|  |
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 1 |
The exclusive-NOR or XNOR gate has two or more inputs. The output is equivalent to inverting the output from the exclusive-OR gate described above. Therefore an equivalent circuit would comprise an XOR gate, the output of which feeds into the input of a NOT gate.
In general, an XNOR gate gives an output value of 1 when there are an even number of 1's on the inputs to the gate. The truth table for a 3-input XNOR gate below illustrates this point.
The XNOR gate is drawn using the same symbol as the XOR gate with an invert bubble on the output line as is illustrated below
The output from the XNOR gate is written as
which reads "A XNOR B".
The truth table for a two-input XNOR gate looks like
| |
|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
For a 3-input XNOR gate with inputs ,
and the truth table is given by
| |
|  |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 0 |