Implementation of AND Gate from NAND Gate

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As we know that the NAND Gate is a universal logic gate, therefore using the NAND gate, we can implement any logic gate or any other logical expression. Read this tutorial to understand how you can implement an AND gate using NAND gate. Let's start with a basic overview of AND and NAND gates.

What is an AND Gate?

An AND Gate is a basic logic gate. An AND gate may have two or more than two inputs, but gives only one output. The AND gate gives a LOW (Logic 0) output if any one of its inputs is in the LOW or Logic 0 state, otherwise, it gives a HIGH (Logic 1) state as output. Therefore, the output of the AND gate is HIGH or Logic 1 state, only if all its inputs are HIGH or Logic 1 state.

The AND gate is also known as an "all or nothing gate". The logic symbol of a two input AND gate is shown in Figure-1.

Output Equation of AND Gate

If A and B are the input variables and Y is the output variable for an AND gate, then the output equation of the AND gate is given by,

$$\mathrm{Y \: = \: A\cdot B}$$

Where, the "·" (dot) symbol represents the AND operation. It is read as Y is equal to A AND B.

Truth Table of AND Gate

The table that show the relationship between inputs and output of a logic gate is referred to as a truth table. The following is the truth table for the AND Gate −

What is a NAND Gate?

The NAND Gate is a type of universal logic gate. Where, a universal logic gate is one that can be used to realize any kind logical expression or any other type of logic gate.

A NAND gate is basically a combination of two basic logic gates namely AND gate and NOT gate, i.e.

$$\mathrm{NAND \: Logic \: = \: AND \: Logic \: + \: NOT \: Logic}$$

A NAND gate is the type of logic gate whose output is LOW (Logic 0) when all its inputs are high, and its output is HIGH (Logic 1), when any of its inputs is LOW (Logic 0). Therefore, the operation of the NAND gate is opposite that of the AND gate. The logic symbol of a two input NAND gate is shown in Figure-2.

Output Equation of NAND Gate

If A and B are the input variables and Y is the output variable of the NAND gate, then its output is given by,

$$\mathrm{Y | \: = \: \overline{A \: \cdot \: B} \: = \: (\arrowvert A \: \cdot \: B)'}$$

It is read as "Y is equal to A·B whole bar".

Truth Table of NAND Gate

The following is the truth table of the NAND gate −

Now, let us discuss the implementation of AND Gate from NAND Gate.

Implementation of AND Gate from NAND Gate

As discussed above that the NAND gate is a type of universal logic gate, because it can be used to implement any other logic gate. The implementation of an AND gate using NAND gate is shown in Figure-3.

From this circuit diagram, it is clear that the implementation of the AND gate from NAND gate is quite simple, as we just require two NAND gates.

Where, the first NAND gate produce a complement binary product of inputs A and B, while the second NAND gate again complement the output of first NAND gate to produce an AND output. Therefore, the logic circuit using NAND gates shown in figure-3 is equivalent to the AND gate.

Output Equation

The output produced by the first NAND gate is,

$$\mathrm{Y_{1} \: = \: \overline{A \: \cdot \: B}}$$

The output produced by the second NAND gate is,

$$\mathrm{Y \: = \: \overline{\overline{A \: \cdot \: B}} \: = \: A \: \cdot \: B}$$

This is the output equation of the AND gate.