Combining logic gates
A single logic gate can only do one simple function. To create more complex decisions and control systems, such as how a robot moves or how a microwave starts when the door is closed and a timer is set, logic gates are combined.
NAND gate (NOT AND)
An example of a combined logic gate is the NAND gate. This is made from a AND gate followed by a NOT Gate. The NAND gate gives the opposite result of an AND gate. It outputs 1 unless both inputs are 1.
An AND gate followed by a NOT gate can be drawn as two gates or combined as a NAND gate, as shown below:
The Boolean expression can be written as: Q = NOT (A AND B)
The Used to assess possible results of a Boolean algebra statement. would look like this:
| A | B | A or B | Q = NAND |
| 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 0 |
| A | 0 |
|---|---|
| B | 0 |
| A or B | 0 |
| Q = NAND | 1 |
| A | 0 |
|---|---|
| B | 1 |
| A or B | 0 |
| Q = NAND | 1 |
| A | 1 |
|---|---|
| B | 0 |
| A or B | 0 |
| Q = NAND | 1 |
| A | 1 |
|---|---|
| B | 1 |
| A or B | 1 |
| Q = NAND | 0 |
NOR gate (NOT OR)
The NOR gate gives the opposite result of an OR gate. It outputs 1 only if both inputs are 0.
An OR gate and NOT gate can also be drawn as an OR gate with a small circle on its output, for example:
The Boolean expression can be written as: Q = NOT (A OR B)
The truth table would look like this:
| A | B | C = A + B | Q = NOR |
| 0 | 0 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 1 | 0 |
| A | 0 |
|---|---|
| B | 0 |
| C = A + B | 0 |
| Q = NOR | 1 |
| A | 0 |
|---|---|
| B | 1 |
| C = A + B | 1 |
| Q = NOR | 0 |
| A | 1 |
|---|---|
| B | 0 |
| C = A + B | 1 |
| Q = NOR | 0 |
| A | 1 |
|---|---|
| B | 1 |
| C = A + B | 1 |
| Q = NOR | 0 |
