CH 03 : Logic Gates And Logic Circuits
Logic Gates
- ==Logic Gates==: They take binary inputs and give binary outputs in an electronic circuit.
- ==Truth Table:== A table used to check the outputs from a logic gate or logic circuit.
* All possible combinations of binary inputs are considered in a Truth Table. - The six different types of Logic Gates are as follows:
- ==NOT Gate==: Has only one input and output is 1 only if input is 0.
* Truth Table:
| Input | Output |
|---|---|
| A | X |
| 0 | 1 |
| 1 | 0 |
- ==AND Gate==: Two inputs. Output is 1 if both inputs are 1s.
* Truth Table:
| Input | Input | Output |
|---|---|---|
| A | B | X |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 0 | 0 | 0 |
| 1 | 1 | 1 |
- ^^Tip: Multiply the inputs.^^
- ==OR Gate==: Two inputs. Output is 1 when any of the inputs is 1.
* Truth Table:
| Input | Input | Output |
|---|---|---|
| A | B | X |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 0 | 0 | 0 |
| 1 | 1 | 1 |
- ^^Tip: Add the inputs.^^
- ==NAND (NOT AND) Gate==: Two Inputs. Output is 1 if both inputs are not 1.
* Truth Table:
| Input | Input | Output |
|---|---|---|
| A | B | X |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 0 | 0 | 1 |
| 1 | 1 | 0 |
- ^^Tip: Calculate for AND and write opposite output.^^
- ==NOR (NOT OR) Gate:== Two inputs. Output is 1 if neither input is 1
* Truth Table:
| Input | Input | Output |
|---|---|---|
| A | B | X |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 0 | 0 | 1 |
| 1 | 1 | 0 |
- ^^Tip: Calculate for OR and write opposite.^^
- ==XOR Gate==: Two inputs. Output is 1 if inputs are not same.
* Truth Table:
| Input | Input | Output |
|---|---|---|
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 0 | 0 | 0 |
| 1 | 1 | 0 |
Logic Circuits
- Multiple Logic gates make up a ==Logic Circuit.==
- Complex operations are performed through them.
- Truth tables are made to check outputs, and all inputs are considered.
- To make a truth table, it is easier to divide the circuit into parts and name all the outputs at each stage.Example:
| Input A | Input B | Input C | Output P | Output Q | Output R | Output X |
|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 | 1 | 1 |
| 0 | 0 | 1 | 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 | 0 | 0 | 1 |
| 1 | 1 | 0 | 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 | 0 | 1 | 0 |
- In order to make a Logic Circuit from a Logic statement, mark all the gates in the statement, and always mind the brackets.
- To make a logic circuit from Boolean or Logic statements, make different parts of the circuit and then join them using gates which connect the brackets.
- Some logic gates can make a whole logic circuit and any other logic gate. They are known as ==Building Blocks==. NAND gate, for example, can make an AND gate:
- Logic circuit can also be simplified. Just like the circuit above can be simplified to just one AND gate.
- Note: When one input branches into two before entering a gate, the two branched inputs will ^^always^^ be same. 1,1 or 0,0.