# Design of Basic Logic Gates using NAND Gate

There are mainly three types of logic gate named AND, OR and NOT gate. And every gate does its own different logic Gates NAND Gate. So with the help of these basic logic gates, we can get any logical functions or any Boolean or else any logical expression.

- Truth Tables of Basic Logic Gates:
- 1.NOT Gate:
- 2.AND Gate:
- 3.OR Gate:
- 4. NAND Gate:

- Transformation of NAND Gate into Other Basic Gates:
- 1. Construction of NOT Gate with NAND Gate:
- 2.Construction of AND Gate with NAND Gate:
- 3.Construction of OR Gate with NAND Gate:

## Truth Tables of Basic Logic Gates:

It is important to know the functioning of the each individual gate so to get familiar with the conversion.

## 1.NOT Gate:

The most basic sort of digital logical circuit is the logical gate. This gate only has two terminals, one for input and the other for output. The gate’s input is a binary number, meaning it can only be one or zero. The output of a logic gate is always the inverse of the input, therefore if we give 1 at the input, the output will be 0 and vice versa.

2a will be used to compute the number of stages that are possible (the number of input will be calculated with the help of “a”).

The NOT Gate Truth Table is displayed below –

## 2.AND Gate:

There are two input terminals and one output terminal on this logic gate. These gates work in such a way that we only get binary 1 at the output terminal if and only if both inputs are binary 1. If any of the inputs contains a binary zero, the output will also be binary 0.

The number of possible phases is 2n =22 = 4.

The AND gate truth table is illustrated below –

## 3.OR Gate:

Similarly to the AND gate, the OR gate is a basic logic gate with two input terminals and one output terminal. If any of the inputs are in the low stage, i.e. binary 0, the output will be in the high stage, i.e. binary 1. If only one of the inputs is binary low, the output will also be binary low.

The number of possible phases is 2n =22 = 4.

OR see the table below for a gate truth table –

## 4. NAND Gate:

The NAND gate is the result of combining the expressions NOT gate and AND gate. As a result, the NAND gate is made up of an AND gate and an inverter. These gates work in the following way: we get binary 1 at the gate’s output if and only if both inputs are in the binary low state, i.e. at 0. If any of the input terminals are in the binary high state, i.e. 1, the output will be in the binary low state, i.e. 0.

The NAND gate’s expression and truth table are provided below —

## Transformation of NAND Gate into Other Basic Gates:

**1. Construction of NOT Gate with NAND Gate:**

We only need one input terminal, thus we shorted both NAND gate input terminals, as seen in the diagram above. Due to a property of the NAND gate that can be observed in the truth table, when we give binary 1 at the input terminal, we will obtain 0 at the output. We used the IC7400, which is a Quad two-terminal input NAND gate.

**2.Construction of AND Gate with NAND Gate:**

**3.Construction of OR Gate with NAND Gate:**

One should be familiar with the DE Morgan’s theorem before getting familiar with these one- It says that the complement of a product is equal to the sum of the complements.

(AB)‾ = A‾ + B‾ —- EQ 1

Through the figure that shown above, Two NAND gates are used, and the input terminal of each gate is been short, so the output we get as = A‾B‾

This output is now given to another NAND gate and the output that we receive here is –

**Required Components:**

- IC
- CD7402 – 1
- R1 (1K) – 1
- LED – 1