How to convert NAND to XNOR?


Want to know How to convert NAND to XNOR? To convert Nand to XNOR, you need the four NOR gates that makes NAND gates to an XOR gate be converted to an XNOR gate by inverting the output or one of the inputs. A given example of converting Nand gates to XOR is by introducing a fifth NAND gate into the equation.

Exclusive-NOR gate or XNOR gate is formed by combining the Exclusive-OR gate (XOR gate) and the NOT gate. On analysing the XNOR truth table, we understand that the output is similar to the standard NOR gate except that the output of the XNOR gate is high when both inputs are high.
To understand this you need basic nowledge of how Nand gates work.
A NAND gate is a universal logic gate which performs the negated logical multiplication. A NOR gate is a universal logic gate which performs the negated logical addition. Implementation. NAND gate can be implemented by using an AND gate followed by a NOT gate.

To convert a NAND gate to an XNOR gate, we need to understand the logic behavior of both gates and then implement a circuit that mimics the XNOR gate behavior using NAND gates.

A NAND gate has the following truth table:

| A | B | Output |
|---|---|--------|
| 0 | 0 |   1    |
| 0 | 1 |   1    |
| 1 | 0 |   1    |
| 1 | 1 |   0    |

An XNOR gate has the following truth table:

| A | B | Output |
|---|---|--------|
| 0 | 0 |   1    |
| 0 | 1 |   0    |
| 1 | 0 |   0    |
| 1 | 1 |   1    |

To convert the NAND gate to an XNOR gate, we can use De Morgan’s theorem, which states that the complement of a NAND gate is equivalent to an OR gate. Similarly, the complement of an OR gate is equivalent to a NAND gate.

So, if we take the output of a NAND gate and apply it as an input to another NAND gate along with its original inputs, we can achieve the XNOR gate behavior.

Let’s go through the steps to convert a NAND gate to an XNOR gate:

Step 1: Start with a single NAND gate with inputs A and B and output Y.

      ____
A --|      |
    | NAND |---- Y
B --|______|

Step 2: Apply the output Y as an input to another NAND gate along with its original inputs A and B.

      ____          ____
A --|      |       |      |
    | NAND |----- Y| NAND |-- Y
B --|______|       |______|

Step 3: The output of the second NAND gate is the desired XNOR output.

The resulting circuit will look like this:

      ____          ____
A --|      |       |      |
    | NAND |----- Y| NAND |-- Y
B --|______|       |______|

This circuit will produce the correct output for an XNOR gate based on the inputs A and B.

Remember, if you need to implement XNOR gates using NAND gates, you can continue cascading NAND gates in a similar manner, connecting the output of one NAND gate as an input to the next NAND gate, until you achieve the desired number of input ports for the XNOR gate.

In summary,

The four NOR gates that turn NAND gates into XOR gates can be transformed into an XNOR gate by inverting either the output or one of the inputs. Incorporating a fifth NAND gate is a concrete illustration of how to transform a series of NAND gates into an XOR.

The XNOR gate, also known as the Exclusive-NOT gate, is created when the XOR gate and the NOT gate are combined. The truth table analysis of the XNOR gate reveals that its output is quite similar to that of the regular NOR gate, with the exception that it is high when both inputs are high.
You need to know the fundamentals of Nand gates in order to follow along.

It is the negated logical multiplication that a NAND gate is able to accomplish. The logical operation of a NOR gate is negated logical addition, and it is found in all types of logic gates. Implementation. You can create a NAND gate by chaining together two AND gates and two NOT gates.

Hope this explanation helps you understand how to convert a NAND gate to an XNOR gate using NAND gates themselves!

Eddie Mcfarren

Eddie Is no stranger to technical writing after spending years in Networking, IT Infrastructure management, and online content marketing. He is an avid researcher, Software and apps dev tester who spends hours solving problems behind the scenes. Get in touch with him via social media and you can email him via contact@gawkygeek.com

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