Logic circuits
Combining gates
A circuit can connect gates so one gate's output becomes another gate's input. Evaluate from the inputs towards the output, using brackets to show the order. The circuit below means: first calculate A AND B, then OR that result with NOT C.
| A | B | C | A AND B | NOT C | Q |
|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 | 1 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 1 | 1 |
| 1 | 0 | 1 | 0 | 0 | 0 |
| 1 | 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 0 | 1 |
The final column is the circuit output, labelled Q.
Key terms
Writing an expression from a problem
Translate each condition into a Boolean expression, then combine them in the stated order. For example, a warning light comes on when the door is open (A = 1) or the temperature is high (B = 1):
If a light should come on only when a switch is on (A = 1) and a sensor is not triggered (B = 0), write:
Read the question carefully: AND means both conditions must be true; OR means either or both can be true. Brackets make a more complex expression unambiguous.