Logic gates
In its most basic form, a computer is a collection of powered and unpowered A closed loop through which current moves - from a power source, through a series of components, and back into the power source. and Microscopic devices that open and close circuits to communicate electrical signals. CPUs contain millions of transistors.. A 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. is a series of transistors connected together to give one or more Data which is sent out of a system., each output being based on the Data which is inserted into a system for processing and/or storage. or combination of inputs supplied to it. There are four types of gate to consider:
- AND gate
- OR gate
- NOT gate
- XOR gate
Each type of gate can be represented either as a diagram, in algebraic form, or as a A table to list the output for all possible input combinations into a logic gate..
AND gates
An AND gate uses two inputs to generate one output. The output is 1 (TRUE) only if both of the inputs are 1 (TRUE).
AND gates are represented diagrammatically as:
A represents the first input. B represents the second input. Q represents the output.
A truth table shows, for each combination of inputs, what the output will be. Like logic gates, a 0 in the table represents FALSE, while 1 represents TRUE.
An AND gate is represented in the truth table below.
| A | B | Q |
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
| A | 0 |
|---|---|
| B | 0 |
| Q | 0 |
| A | 0 |
|---|---|
| B | 1 |
| Q | 0 |
| A | 1 |
|---|---|
| B | 0 |
| Q | 0 |
| A | 1 |
|---|---|
| B | 1 |
| Q | 1 |
OR gates
An OR gate uses two inputs to generate one output. The output is 1 (TRUE) only if either or both of the inputs are 1 (TRUE).
OR gates are represented diagrammatically as:
A represents the first input. B represents the second input. Q represents the output.
An OR gate is represented in the truth table as below.
| A | B | Q |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
| A | 0 |
|---|---|
| B | 0 |
| Q | 0 |
| A | 0 |
|---|---|
| B | 1 |
| Q | 1 |
| A | 1 |
|---|---|
| B | 0 |
| Q | 1 |
| A | 1 |
|---|---|
| B | 1 |
| Q | 1 |
NOT gates
A NOT gate uses just one input to generate one output. A NOT gate inverts the input - the output is 1 (TRUE) if the input is 0 (FALSE), and the output is 0 (FALSE) if the input is 1 (TRUE).
NOT gates are represented diagrammatically as:
The NOT gate has what appears to be a nose at the front. When using more complex gates, this nose is added to other gates to show they have been combined with the NOT gate.
A NOT gate is represented in the truth table below.
| A | Q |
| 0 | 1 |
| 1 | 0 |
| A | 0 |
|---|---|
| Q | 1 |
| A | 1 |
|---|---|
| Q | 0 |
XOR gates
The XOR gate is known as the exclusive OR gate. This gives the true meaning of the word OR. The XOR gate outputs 1 (TRUE) when any input is 1 (TRUE). But unlike the OR gate, when both input 1 (TRUE), the OUTPUT is 0 (FALSE).
An XOR gate is represented in the truth table below.
| A | B | Output |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
| A | 0 |
|---|---|
| B | 0 |
| Output | 0 |
| A | 0 |
|---|---|
| B | 1 |
| Output | 1 |
| A | 1 |
|---|---|
| B | 0 |
| Output | 1 |
| A | 1 |
|---|---|
| B | 1 |
| Output | 0 |
Boolean notation
Logical expressions can also be expressed using A data type in computing which only has two possible values, true or false. algebra notation. Instead of writing the words AND, OR, NOT or XOR it is often written using the following shorthand notation.
| Boolean expression | Shorthand notation |
| A AND B | A . B |
| A OR B | A + B |
| NOT A | A’ (can be also shown as Ā) |
| A XOR B | A ⊕ B |
| Boolean expression | A AND B |
|---|---|
| Shorthand notation | A . B |
| Boolean expression | A OR B |
|---|---|
| Shorthand notation | A + B |
| Boolean expression | NOT A |
|---|---|
| Shorthand notation | A’ (can be also shown as Ā) |
| Boolean expression | A XOR B |
|---|---|
| Shorthand notation | A ⊕ B |
More guides on this topic
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