NOR Gate
The NOR gate gives true output in case of all low inputs. In all other combinations, the NOR gate would maintain false output. The NOR gate follows the inverse logic of the OR gate due to the presence of the NOT gate.
2-Input NOR Gate Boolean Expression
The Boolean expression for above NOR gate is represented as:
The complement of the addition of two inputs A & B provides the output O.
The above boolean expression implies that: If both A and B are NOT true, then O is true
2-Input NOR Gate Truth Table
A NOR gate maintains a false output at all combinations, except when all inputs get low. A truth table showing all four combinations of inputs and output is tabulated below:
| A | B | Output |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |
3-Input NOR Gate Boolean Expression
The Boolean expression for the above NOR gate is represented as:
The complement of the addition of two inputs A & B provides the output O.
The above boolean expression implies that: If all of three inputs A, B & C are NOT true, then O is true.
3-Input NOR Gate Truth Table
A NOR gate maintains a false output at all combinations, except when all inputs get low. A truth table showing all four combinations of inputs and output is tabulated below:
| A | B | C | Output |
|---|---|---|---|
| 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 0 |
Transistors-Based 2-Input NOR Gate
NOR gates can also be designed through two transistors with two resistors at the base inputs. The emitter of both transistors is commonly grounded, while the collector of both transistors is commonly connected to Vcc=+5V.
The circuit follows the boolean expression and truth table logic of the NOR gate. The output shall appear only true when none of the transistors operate. In case any of the inputs to the transistor is true, the input signal will follow the ground path and will not reach the output, resulting in false or low states at every other combination of inputs.
NOR Logic Gate Operation
The operation logic of NOR gate can be easily verified when its two inputs are presented with two switches in parallel combination along with the parallel output as shown below:
We can now verify the operation logic of the NOR gate by choosing four different combinations of the two switch states one by one.
Case 1
When both of the inputs are low or off:
| Switch A | Switch B | Bulb (State) |
|---|---|---|
| Open | Open | On |
The lamp will glow in this case as there is a single path of current passage, which is through the lamp.
Case 2
When the first input is low or off and the second input is high or on:
| Switch A | Switch B | Bulb (State) |
|---|---|---|
| Open | Close | Off |
The lamp will not glow in this case, as current will follow the path of least resistance through closed switch B.
Case 3
When the first input is high or on and the second input is low or off.
| Switch A | Switch B | Bulb (State) |
|---|---|---|
| close | open | Off |
The lamp will not glow in this case, as the current will follow the path of least resistance through closed switch A.
Case 4
When the first and the second input both are high or on.
| Switch A | Switch B | Bulb (State) |
|---|---|---|
| close | close | Off |
The fluorescent bulb will not glow in this case as current will divide between two paths of two closed switches A & B offering the least resistance.
Conclusion
A NOR gate can only provide high/true output when all of its inputs are low/false. The inverted operation logic of the NOR gate is quite useful in a variety of digital electronics circuits where the inverted inputs are required from the gate circuits.
