Combining 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 A closed loop through which current moves - from a power source, through a series of components, and back into the power source.. The three types of gate can be used in any combination to generate the desired output.
Example - 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 AND 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 AND B | 0 |
| Q | 0 |
| A | 0 |
|---|---|
| B | 0 |
| C | 1 |
| D = A AND B | 0 |
| Q | 0 |
| A | 0 |
|---|---|
| B | 1 |
| C | 0 |
| D = A AND B | 0 |
| Q | 0 |
| A | 0 |
|---|---|
| B | 1 |
| C | 1 |
| D = A AND B | 0 |
| Q | 0 |
| A | 1 |
|---|---|
| B | 0 |
| C | 0 |
| D = A AND B | 0 |
| Q | 0 |
| A | 1 |
|---|---|
| B | 0 |
| C | 1 |
| D = A AND B | 0 |
| Q | 0 |
| A | 1 |
|---|---|
| B | 1 |
| C | 0 |
| D = A AND B | 1 |
| Q | 0 |
| A | 1 |
|---|---|
| B | 1 |
| C | 1 |
| D = A AND B | 1 |
| Q | 1 |
In A form of algebra which works only with two values, TRUE or FALSE., this circuit is represented by the logic The smallest element of a programming language which expresses an action to be carried out. Q = (A AND B) AND C.
Note - D is not strictly necessary in the table, but it helps in understanding Q.
Example - 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 Boolean algebra, this circuit is represented by the logic statement Q = NOT (A OR B).
Operator precedence
In mathematics, the acronym BODMAS (brackets, orders, division, multiplication, addition, subtraction) is used to help remember the order in which to carry out a mathematical calculation. Boolean algebra also has a particular order for carrying out calculations. It is brackets, NOT, AND, OR. You may need to know this to answer exam questions.
More guides on this topic
- Decomposition and abstraction - Edexcel
- Algorithms - Edexcel
- Further algorithms - Edexcel
- Binary and data representation - Edexcel
- Computers - Edexcel
- Programming languages - Edexcel
- Networks - Edexcel
- Network security and cybersecurity - Edexcel
- Encryption - Edexcel
- Environmental, ethical and legal concerns - Edexcel