NOT gate
- A NOT gate has one input and will invert it to produce an opposite output. This is shown in the truth table below
- A is the input
- Z is the output
Input | Output |
| A | Z |
| 0 | 1 |
| 1 | 0 |
AND gate
- An AND gate has two inputs
Input | Output | |
| A | B | Z |
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
- The AND gate truth table shows the only combination of inputs which will result in a positive output is 1 and 1
OR gate
- An OR gate has two inputs
Input | Output | |
| A | B | Z |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
- The truth table shows an OR gate produces an output of 1 if any of the inputs are a 1
NOR gate
- A NOR gate has two inputs
Input | Output | |
| A | B | Z |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |
- The truth table shows a NOR gate works oppositely to an OR gate – the only input combination which results in a 1 is two 0s
NAND gate
- A NAND gate has two inputs
Input | Output | |
| A | B | Z |
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
- The truth table shows a NAND gate works in the opposite way to an AND gate – the only input combination which does not result in a 1 is two positive inputs (1 +1)
XOR gate
- An XOR gate has two inputs
Input | Output | |
| A | B | Z |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
- The truth table shows how an XOR gate works. It will only output a 1 if the two inputs are different to one another
Truth tables can also be used to help work out the possible outputs of a logic circuit containing more than one gate
- When creating a truth table for multiple inputs, begin by entering the possible input combinations into the leftmost columns
A truth table for a three input (A, B and C) logic gate
| A | B | C | Z | |
| 0 | 0 | 0 | ||
| 0 | 0 | 1 | ||
| 0 | 1 | 0 | ||
| 0 | 1 | 1 | ||
| 1 | 0 | 0 | ||
| 1 | 0 | 1 | ||
| 1 | 1 | 0 | ||
| 1 | 1 | 1 |
›
- The column on the right contains the final output of the logic circuit (Z)
- Column(s) in between the inputs and the final output can be used to help work out the final output by containing intermediary outputs
- Intermediary outputs are the output of gates found within the logic circuit
- In the logic circuit diagram below, D and E are intermediary outputs
- The fourth column labelled D represents the output of NOT A
| A | B | C | D (NOT A) | E | Z |
| 0 | 0 | 0 | 1 | ||
| 0 | 0 | 1 | 1 | ||
| 0 | 1 | 0 | 1 | ||
| 0 | 1 | 1 | 1 | ||
| 1 | 0 | 0 | 0 | ||
| 1 | 0 | 1 | 0 | ||
| 1 | 1 | 0 | 0 | ||
| 1 | 1 | 1 | 0 |
- The next intermediary output is E which is the equivalent of ((NOT A) AND B) this notation is called a logic expression
- The E intermediary output can be worked out by performing the AND logical operation on columns B and D
A | B | C | D (NOT A) | E ((NOT A) AND B) | Z |
| 0 | 0 | 0 | 1 | 0 | |
| 0 | 0 | 1 | 1 | 0 | |
| 0 | 1 | 0 | 1 | 1 | |
| 0 | 1 | 1 | 1 | 1 | |
| 1 | 0 | 0 | 0 | 0 | |
| 1 | 0 | 1 | 0 | 0 | |
| 1 | 1 | 0 | 0 | 0 | |
| 1 | 1 | 1 | 0 | 0 |
- The final output (Z) can be worked out by performing the OR logical operation on columns E and C
A | B | C | D (NOT A) | E ((NOT A) AND B) | Z (((NOT A) AND B) OR C) |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 | 1 |
| 0 | 1 | 0 | 1 | 1 | 1 |
| 0 | 1 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 | 0 | 1 |
| 1 | 1 | 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 0 | 0 | 1 |
