Logic gates are the building blocks of digital electronics. They are used to implement Boolean logic, which forms the basis for all digital systems. In this blog post, we will discuss the different types of logic gates and their corresponding truth tables.
First, let’s define what a truth table is. A truth table is a table that shows the output of a logic gate for all possible combinations of inputs. Each row in the truth table represents a different input combination, and the output column shows the corresponding output of the logic gate.
There are seven basic logic gates: AND, OR, NOT, NAND, NOR, XOR, and XNOR. Each of these basic gates has a unique truth table that determines its behavior.
Basic Gates in Digital Electronics with symbolic representation and truth table
1) AND Gate:
An AND gate is a digital logic gate that has two or more inputs and one output. The output is “1” only if all the inputs are “1”. In other words, the AND gate performs a logical “and” operation on the inputs.
The truth table for an AND gate with two inputs is a summary of all the possible input combinations and the corresponding output. The truth table for an AND gate with two inputs is as follows:
Truth Table for AND Gate
| Input 1 | Input 2 | Output |
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
As you can see from the truth table, the output is “1” only when both input A and input B are “1”. In all other cases, the output is “0”.
For example, if input A is connected to a switch that is turned on and input B is connected to a sensor that detects the presence of an object, the output of the AND gate will be “1” only when the switch is turned on and the sensor detects the presence of an object. In all other cases, the output will be “0”.
This is just one example of how AND gates can be used in digital electronics, but it demonstrates how AND gates are useful for creating more complex logical circuits by combining multiple input signals.
2) OR Gate:
An OR gate is a digital logic gate that has two or more inputs and one output. The output is “1” if any of the inputs is “1”. In other words, the OR gate performs a logical “or” operation on the inputs.
The truth table for an OR gate with two inputs is a summary of all the possible input combinations and the corresponding output. The truth table for an OR gate with two inputs is as follows:
Truth Table for OR Gate
| Input 1 | Input 2 | Output |
| Â 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
As you can see from the truth table, the output is “1” when at least one of the input A or input B is “1”. In the case when both inputs are “0”, the output is “0”.
For example, if input A is connected to a switch that is turned on and input B is connected to a sensor that detects the presence of an object, the output of the OR gate will be “1” when either the switch is turned on or the sensor detects the presence of an object. If neither the switch is turned on nor the sensor detects the presence of an object, the output will be “0”.
This is just one example of how OR gates can be used in digital electronics, but it demonstrates how OR gates are useful for creating more complex logical circuits by combining multiple input signals, and also how it allows multiple input signals to trigger a single output.
3) NOT Gate:
A NOT gate, also known as an inverter, is a digital logic gate that has one input and one output. The output is the inverse or complement of the input. In other words, if the input is “1”, the output is “0”, and if the input is “0”, the output is “1”. The NOT gate performs a logical “not” operation on the input.
The truth table for a NOT gate with one input is a summary of all the possible input values and the corresponding output. The truth table for a NOT gate with one input is as follows:
Truth Table for Inverter or NOT gate
| Input | Output |
| 1 | 0 |
| 0 | 1 |
As you can see from the truth table, the output is the inverse of the input, “1” if the input is “0” and “0” if the input is “1”.
For example, if input A is connected to a switch that is turned on, the output of the NOT gate will be “0” because the input is “1”. If the switch is turned off, the output of the NOT gate will be “1” because the input is “0”.
NOT gates are often used in digital electronics to invert a signal, such as to convert an active-high signal into an active-low signal. It’s also used in combination with other logic gates to form more complex logic circuits.
4) NAND Gate:
A NAND gate (NOT-AND gate) is a digital logic gate that has two or more inputs and one output. The output is the inverse or complement of the output of an AND gate with the same inputs. In other words, the NAND gate performs a logical “and” operation on the inputs and then inverts the output.
The truth table for a NAND gate with two inputs is a summary of all the possible input combinations and the corresponding output. The truth table for a NAND gate with two inputs is as follows:
Truth Table for NAND gate
| Input 1 | Input 2 | Output |
| 0Â | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0Â | 1 |
| 1 | 1 | 0 |
As you can see from the truth table, the output is “0” only when both inputs are “1”, otherwise the output is “1”.
For example, if input A is connected to a switch that is turned on and input B is connected to a sensor that detects the presence of an object, the output of the NAND gate will be “0” only when the switch is turned on and the sensor detects the presence of an object. If one or both of them is not the case, the output will be “1”.
NAND gates are often used in digital electronics as a Universal Gate because any other logic gate can be implemented using a combination of NAND gates. They are also used to implement logic functions that require negation of the inputs or outputs, such as in flip-flops, memory elements and counters.
5) NOR Gate:
A NOR gate (NOT-OR gate) is a digital logic gate that has two or more inputs and one output. The output is the inverse or complement of the output of an OR gate with the same inputs. In other words, the NOR gate performs a logical “or” operation on the inputs, and then inverts the output.
The truth table for a NOR gate with two inputs is a summary of all the possible input combinations and the corresponding output. The truth table for a NOR gate with two inputs is as follows:
Truth Table for NOR gate
| Input 1 | Input 2 | Output |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |
As you can see from the truth table, the output is “1” only when both inputs are “0”, otherwise the output is “0”.
For example, if input A is connected to a switch that is turned on and input B is connected to a sensor that detects the presence of an object, the output of the NOR gate will be “1” only when the switch is turned off and the sensor does not detect the presence of an object. If one or both of them is not the case, the output will be “0”.
NOR gates are often used in digital electronics as a universal gate because any other logic gate can be implemented using a combination of NOR gates. They are also used in digital logic circuits to represent logical “stop” or “disable” conditions.
6) XOR Gate:
An XOR gate (Exclusive OR gate) is a digital logic gate that has two inputs and one output. The output is “1” if the inputs are different (one is “1” and the other is “0”), and “0” if the inputs are the same (both “1” or both “0”). In other words, the XOR gate performs a logical “exclusive or” operation on the inputs.
The truth table for an XOR gate with two inputs is a summary of all the possible input combinations and the corresponding output. The truth table for an XOR gate with two inputs is as follows:
Truth Table for XOR Gate
| Input 1 | Input 2 | Output |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
As you can see from the truth table, the output is “1” only when the inputs are different and “0” when the inputs are the same.
For example, if input A is connected to a switch that is turned on and input B is connected to a sensor that detects the presence of an object, the output of the XOR gate will be “1” only when one of the input is “1” and the other is “0”.
XOR gates are often used in digital electronics for tasks such as parity checking and data encoding, as well as in other applications where it is necessary to determine whether or not two input signals are different.
7) XNOR Gate:
An XNOR gate (Exclusive-NOR gate) is a digital logic gate that has two or more inputs and one output. The output is the inverse or complement of the output of an XOR gate with the same inputs. In other words, the XNOR gate performs a logical “xor” operation on the inputs, and then inverts the output.
The truth table for an XNOR gate with two inputs is a summary of all the possible input combinations and the corresponding output. The truth table for an XNOR gate with two inputs is as follows:
XNOR gate
| Input 1 | Input 2 | Output |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
As you can see from the truth table, the output is “1” only when both inputs have the same value, otherwise the output is “0”.
For example, if input A is connected to a switch that is turned on and input B is connected to a sensor that detects the presence of an object, the output of the XNOR gate will be “1” only when the switch is turned on and the sensor detects the presence of an object, or the switch is turned off and the sensor does not detect the presence of an object.
XNOR gates are used in digital electronics to compare two signals for equality, and also used in combinational logic circuits where it’s necessary to detect if two or more inputs are at the same state.
Conclusion:
In conclusion, logic gates are the building blocks of digital electronics. They are used to perform basic logical operations on binary signals such as AND, OR, NOT, NAND, NOR, XOR and XNOR. Each of these logic gates have their own unique truth table, which summarizes all the possible input combinations and the corresponding output. Understanding the behavior and functionality of these logic gates is essential for designing and implementing digital circuits and systems.
In addition to the basic logic gates, more complex logic functions can be built by combining these gates in various ways. This allows for the creation of sophisticated digital systems such as computer processors, memory devices, and digital control systems.
Overall, logic gates play a vital role in the field of digital electronics and are essential for the functioning of modern technology. With the increasing use of digital systems in various fields such as communication, transportation, and healthcare, the understanding and knowledge of logic gates will continue to be important for engineers and researchers working in these areas.