How to obtained xor gate using nand gate

In this article we will discuss about How to obtained xor gate using nand gate, Truth table for XOR gate, Applications of XOR gate in digital electronics.

XOR gate is a fundamental building block in digital electronics that outputs a high (1) signal when the number of high (1) inputs is odd, and a low (0) signal when the number of high inputs is even.

Introduction

Brief explanation of XOR gate and its function

An XOR gate, also known as an exclusive OR gate, is a digital logic gate which gives high output i.e., 1 if either input A or input B but not both are high i.e., 1.

It may be noted that if both the inputs of the XOR gate are high, then the output is low (i.e., 0).

The XOR gate compares two inputs and outputs a high signal if the inputs are different and a low signal if the inputs are the same. The function of the XOR gate can be represented mathematically as A XOR B = (A + B)(A’ B’ ), where A and B are the inputs and A’ and B’ are the complement of inputs.

The truth table for a 2-input XOR gate is as follows:

Input AInput BOutput
000
011
101
110

From this table, we can see that when input A and input B are the same, the output is low (0). When input A and input B are different, the output is high (1).

XOR gates are widely used in digital electronics for various applications such as error detection and correction, parity generation and checking, encryption and decryption, and so on. Additionally, XOR gates are used to implement Boolean functions and Boolean algebra. They are also used as building blocks for other logic gates such as XNOR gate, NAND gate, and NOR gate.

The XOR gate can be obtained using the NOT gates, the AND gates and the OR gate.

The logic symbol for the XOR gate is shown in the figure below

 logic symbol for the XOR gate

Another way to construct an XOR gate is by using NAND gate, which are relatively simple and inexpensive to manufacture. In this article, we will discuss the construction of XOR gate using NAND gates, Advantages of XOR gate, and Applications of XOR gate.

Explanation of NAND gate and its function

A NAND gate is a digital logic gate that outputs a high signal (1) when one or more of its inputs are low (0). The name “NAND” is an acronym for NOT-AND, which describes the logic function of the gate. The NAND gate is essentially an AND gate with an inverter (NOT gate) connected to its output.

The function of a NAND gate can be described by its truth table, which shows the output of the gate for all possible combinations of input states. The truth table for a 2-input NAND gate is as follows:

Input AInput BOutput
001
011
101
110

As we can see from the truth table, the output of a NAND gate is high (1) when one or more of the inputs are low (0), and it’s low (0) when all of the inputs are high (1).

NAND gates are commonly used in digital electronics as they are versatile and can be used to construct other logic gates such as NOT, OR, and XOR.

They can also be cascaded to form more complex logic functions such as multiplexers, decoders, and flip-flops. Additionally, NAND gates are relatively simple and inexpensive to manufacture, making them a cost-effective option for digital circuits.

Construction of XOR gate using NAND gate

By connecting multiple NAND gates in a specific configuration, it is possible to create an XOR gate.

  • The input A and B are first passed through a NAND gate.
  • Then the output is passed through another NAND gate along with the input A.
  • Finally, the output of the second NAND gate is passed through a third NAND gate along with the input B.
  • The final output of the third NAND gate represents the XOR of input A and B.

The circuit diagram of XOR gate using NAND gate

circuit diagram of XOR gate using NAND gate

Truth table for XOR gate

InputInputOutput
ABY
000
011
101
110

Boolean Expression for the XOR gate

Boolean Expression for the XOR gate

Advantages of using NAND gate to implement XOR gate

  1. One of the main advantages of using NAND gates to implement an XOR gate is their cost-effectiveness.
  2. NAND gates are relatively simple and inexpensive to manufacture, making them a cost-effective option for digital circuits.
  3. Additionally, NAND gates are relatively easy to implement, making them a convenient option for many digital circuits.

Applications of XOR gate in digital electronics

The XOR (Exclusive OR) gate is a fundamental building block in digital electronics. It has many applications, including:

  1. Error detection and correction: XOR gates are often used to detect errors in digital data transmission and storage, and to correct errors in data that has been encoded using error-correcting codes.
  2. Data encryption: XOR gates are used in encryption algorithms such as the one-time pad and the stream cipher, which are used to encrypt data for secure communication.
  3. Logic gates: XOR gates can be used to build other logic gates such as AND, OR, and NOT gates.
  4. Digital circuits: XOR gates are used in digital circuits such as adders, comparators, and flip-flops, which are the building blocks of digital systems such as computers, smartphones, and other digital devices.
  5. Boolean Algebra: XOR is a basic logical operation in Boolean algebra, the mathematical foundation of digital logic.

Conclusion

In conclusion, an XOR gate can be constructed using NAND gates, and this method offers several advantages including cost-effectiveness and ease of implementation. Additionally, XOR gates have a wide range of applications in digital electronics, making them a fundamental component in many electronic devices. If you are looking to build a digital circuit, using NAND gates to construct XOR gates is a great alternative that can save you time and money.

FAQ’s on xor gate using nand gate

How do you make an XOR gate with NAND gates?

The input A and B are first passed through a NAND gate.
Then the output is passed through another NAND gate along with the input A.
Finally, the output of the second NAND gate is passed through a third NAND gate along with the input B.
The final output of the third NAND gate represents the XOR of input A and B.

What is the benefit of using NAND gates to implement logic circuits?

One advantage of using NAND gates to implement logic circuits is that NAND gates are relatively inexpensive and easy to manufacture compared to other types of gates. Additionally, NAND gates are less prone to errors caused by noise and other disturbances, since they have a high noise margin.

How can I test my XOR circuit using NAND gates?

You can test your XOR circuit using NAND gates by applying a set of input test vectors and comparing the output to the expected results. You can also use a logic analyzer or simulation software to verify the correct operation of your circuit.

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