”;
Before getting into implementing a NOT gate using NAND gate, let’s have a basic overview of NOT gates and NAND gates.
What is NOT Gate?
NOT gate is a basic logic gate used in digital electronic circuits. The NOT gate has a single input and a single output. The output of the NOT gate is the logical inversion of its input. For this reason, the NOT gate is also known as inverter.
The symbol of the standard NOT gate has a triangle pointing to the right with a circle at its right end as shown in figure-1. This circle is referred to as an inversion bubble. The NOT gate produces an output which is the complement or inversion of its input. For example, if we give a HIGH input single, then it provides a LOW output signal. Similarly, when we give a LOW input signal, then it provides a HIGH output signal.
Since, the NOT gate is a single input device, therefore, it is not used as a decision making component in the logic circuits.
Truth Table of NOT Gate
The following is the truth table of NOT gate −
| Input (A) | Output (Y = A’) |
|---|---|
| 0 | 1 |
| 1 | 0 |
Boolean Expression of NOT Gate
The following is the Boolean expression of the NOT gate −
$$\mathrm{Y \: = \: A”}$$
For a NOT gate, if A is 1 (HIGH / TRUE), then Y is 0 (LOW / FALSE), and vice-versa.
What is NAND Gate?
NAND is a universal logic gate. It is a digital logic gate having two or more input terminals and gives an output depending on the combination of the input signals. NAND represents NOT + AND, i.e. it produces an output which is the inversion or compliment of logic AND operation.
Since, NAND is a universal logic gate, therefore, it can be used to implement all kinds of logic operations like OR, AND, NOT. The symbol of the NAND gate is shown in Figure-2.
From the symbol, it is clear that it has a shape of standard AND gate with a circle. This circle is known as inversion bubble. The symbol gives the idea about the operation of the NAND gate, i.e. it takes inputs, performs AND operations, and at last takes the inversion of the result of AND operation to provide the final output of the NAND gate.
Truth Table of NAND Gate
The following is the truth table of the NAND gate −
| Inputs | Output | |
|---|---|---|
| A | B | Y = (AB)’ |
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
From the truth table of NAND gate, it is clear that the operation of the NAND gate is same as that of the AND gate followed by a NOT gate. For this reason, the symbol of the NAND is like as shown in the Figure-2.
Boolean Expression of NAND Gate
The following is the Boolean expression of the NAND gate −
$$\mathrm{Y \: = \: (AB)”}$$
Now, let us discuss the implementation of NOT gate using NAND gate.
Implementation of NOT Gate using NAND Gate
As we discussed in the above section that the NAND gate is a universal gate, thus we can use it to realize any basic logic gate. The realization of NOT gate using NAND gate is shown in Figure-3.
From Figure-3, it is clear that to realize the NOT gate using the NAND gate, we have to join the two input terminals of the NAND gate to form a single input terminal of the NOT gate, and the output of the NOT gate is taken from the output terminal of the NAND gate.
Truth Table of NOT Gate using NAND Gate
The following is the truth table of NOT gate using NAND gate −
| Inputs | Output | |
|---|---|---|
| A | B | Y = (AB)’ = A’ |
| 0 | 0 | 1 |
| 1 | 1 | 0 |
Hence, this is all about the implementation of NOT gate using NAND gate.
”;