Combining Boolean operators using AND, OR and NOT gates
Circuit components which take several inputs, compare the inputs with each other, and provide a single output based on logical functions such as AND, OR and NOT. can be combined to form more complex Data which is inserted into a system for processing and/or storage. and Data which is sent out of a system.. These combinations are known as logic circuits. AND, OR and NOT gates can be used in any combination to generate the desired output.
Combining two AND gates
Here, the output Q is 1 (TRUE) only if inputs C and D are 1 (TRUE). D is only 1 (TRUE) if inputs A and B are 1 (TRUE).
As a A table to list the output for all possible input combinations into a logic gate., this circuit is:
| A | B | C | D = A /\ B | Q |
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 | 0 |
| 1 | 1 | 0 | 1 | 0 |
| 1 | 1 | 1 | 1 | 1 |
| A | 0 |
|---|---|
| B | 0 |
| C | 0 |
| D = A /\ B | 0 |
| Q | 0 |
| A | 0 |
|---|---|
| B | 0 |
| C | 1 |
| D = A /\ B | 0 |
| Q | 0 |
| A | 0 |
|---|---|
| B | 1 |
| C | 0 |
| D = A /\ B | 0 |
| Q | 0 |
| A | 0 |
|---|---|
| B | 1 |
| C | 1 |
| D = A /\ B | 0 |
| Q | 0 |
| A | 1 |
|---|---|
| B | 0 |
| C | 0 |
| D = A /\ B | 0 |
| Q | 0 |
| A | 1 |
|---|---|
| B | 0 |
| C | 1 |
| D = A /\ B | 0 |
| Q | 0 |
| A | 1 |
|---|---|
| B | 1 |
| C | 0 |
| D = A /\ B | 1 |
| Q | 0 |
| A | 1 |
|---|---|
| B | 1 |
| C | 1 |
| D = A /\ B | 1 |
| Q | 1 |
In A form of algebra which works only with two values, TRUE or FALSE., this circuit is represented as one of:
- Q = (A AND B) AND C
- Q = (A/\B) /\ C
- Q = (A.B).C
Note - D is not strictly necessary in the table, but it helps in understanding Q.
Combining OR and NOT gates
Here, the output Q is 1 (TRUE) only if inputs A and B are both 0 (FALSE).
| A | B | C | Q |
| 0 | 0 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 1 | 0 |
| A | 0 |
|---|---|
| B | 0 |
| C | 0 |
| Q | 1 |
| A | 0 |
|---|---|
| B | 1 |
| C | 1 |
| Q | 0 |
| A | 1 |
|---|---|
| B | 0 |
| C | 1 |
| Q | 0 |
| A | 1 |
|---|---|
| B | 1 |
| C | 1 |
| Q | 0 |
In A form of algebra which works only with two values, TRUE or FALSE., this circuit is represented as one of:
- Q = NOT (A OR B)
- Q = ¬ (A \/ B)
- Q = NOT (A + B)
- Q = \(\overline{A+B}\)
Note - This is sometimes called the NOR gate, ie a NOT OR gate. In the same way, a NOT AND gate can be referred to as the NAND gate.
