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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.