NAND Gate

Logic gates are the electronic circuits that explain the logical relationship between input and outputs. Now the question arises what are the logic operations. We know that all types of digital equipment such as mobiles, computers, etc., understand the data in terms of binary bits i.e., either in terms of  0’s or 1’s, and also all types of digital equipment store the data in terms 0’s and 1’s. The mathematical operations with 0’s and 1’s are commonly known as logic operations. 

There are three basic gates according to logic operations, we have OR gate for addition, AND gate for multiplication, and NOT gate for inversion. The OR, AND, NOT are known as the basic gates. By making combinations of these basic gates we have two universal gates NAND and NOR. Here, we are focusing on understanding a NAND gate.

What Is a NAND Gate?

• A NAND gate is a two-input and single output device. The number of inputs can be two or more according to the need.

• A NAND gate means, it is a combinational logic circuit and a NAND gate is formed by combining an AND gate followed by a NOT gate. 

• If any of the one input is 0 then the output will be 1. In other words, the NAND gate will give output as high logic if any one of the inputs among the two is 0.

NAND Gate Symbol And NAND Gate Truth Table:

Now let us look at the logic symbol and the logic expression of the NAND gate circuit. The logic symbol of a NAND gate is shown below. A NAND gate consists of two basic gates AND and NOT. An AND gate is connected to NOT gate in series. The bubble at the output of the NAND gate is the symbol of NOT gate. A NOT gate is used for inverting the output results. Thus, A NAND gate is reciprocal of an AND gate.

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The logical expression or the Boolean expression for a NAND gate is given by:

\[\Rightarrow Y=\overline{A.B}\]

Where A and B are the inputs of the NAND gate and Y is the output.

For 2 inputs NAND truth table is given by:

In a NAND gate output will be high logic if any one of the one input is low. It is one of the most peculiar properties of a NAND gate. From the NAND gate truth table, we can see that it is just the reciprocal of an AND gate.

As in the case of a two-input NAND gate, the same analysis can be done for three input NAND gates. 

Therefore, the boolean expression and the truth table for a three-input NAND gate is given by:

The NAND gate expression for the three-input NAND gate is,

 \[\Rightarrow Y=\overline{A.B.C}\]

Where A, B, and C are the inputs of the NAND gate and Y is the output.

The Three Input NAND Truth Table:

NAND Gate Using Transistors:

Any logic gate can be constructed by using semiconductor diodes. An OR gate is constructed by two PN-junction diodes in forward bias, an AND gate is also constructed by diodes. Similarly, a simple NAND gate can be constructed by using transistors. The NAND gate circuit connection is as shown below. The inputs of the gates are the bases of the transistors.

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Example:

1. The Output(X) of the Following Circuit is:

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Sol: 

Let us begin by identifying the gates available in the given logic circuit. After analyzing the logic circuit we came to know that there is a NAND gate cascaded with an OR gate.

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Then, the boolean expression for the given circuit is,

\[\Rightarrow X=\overline{A.B}+C\]………(1)

Equation (1) gives the output(X) of the given circuit. Thus, the operation of the NAND gate is simple and easy. (For cross-checking, we can analyze the circuit by giving some numerical inputs.)

Did You Know:

From the truth table of the NAND gate, we notice that the last two inputs are resulting in opposite outputs just like a NOT operation. We can use a NAND gate as a NOT gate. This is so interesting because, though a NAND gate is a combinational circuit it can be used as a basic logic circuit.

Now the question is how can we convert a NAND gate into a NOT gate. This can be accomplished by combining two inputs of the NAND gate by making it as single input values as shown below:

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The logic expression will be,

\[\Rightarrow X=\overline{A.B}=\overline{I}\]

Then, the corresponding truth table is:

From the truth table, it is more evident to say that a NAND can be used as a NOT gate.