# Construction of Basic Logic Gates using NOR Gate

Logic gates essentially consist of three fundamental logic gates known as the NOT, AND, and OR gates. All of the basic logic gates employ NOR logic functions. Through the utilization of these gates in various combinations, we can derive any Boolean or logical function.

### Outline

- Truth Tables of Basic Logic Gates:
- 1. NOT Gate:
- 2. AND Gate:
- 3. OR Gate:
- 4. NOR Gate:

- Transformation of NOR Gate into Basic Logic Gates:
- 1. Construction of NOT Gate using NOR Gate:
- 2. Construction of OR Gate using NOR Gate:
- 3. Construction of AND Gate using NOR Gate:

## Truth Tables of Basic Logic Gates:

We first need to get aware with the working of each and every gate before knowing the conversion.

## 1. NOT Gate:

The simplest form of a digital logical circuit is the NOT gate. It comprises two terminals: one for input and the other for output. The input for the NOT gate is limited to binary values, specifically 0 or 1. The NOT gate’s output is always the complement of the input, meaning that if a logic 1 is applied at the input, the output will be a logic 0, and vice versa. To calculate the potential number of stages, you can use the formula 2^n, where ‘n’ represents the number of inputs. In cases where there is only one input, the number of achievable stages is either 0 or 1 (2^1).

Truth table of NOT gate is shown below-

## 2. AND Gate:

The AND gate is a three-terminal component featuring two input terminals and one output terminal. This logic gate functions in a manner where the output is set to binary 1 only when both inputs are binary 1. If any of the inputs are in the binary 0 state, the output will also be binary 0. Below, you can find a truth table illustrating the gate’s behavior.

The maximum number of possible stages that can be achieved is given by 2^n, where ‘n’ represents the number of input terminals.

So, 2^{n }= 2^{2} = 4.

## 3. OR Gate:

Similar to the AND gate, the OR gate is a basic logic gate comprising two inputs and one output. Its functionality is such that if any of the inputs is in the binary low state, the output will be binary 1. Only when both inputs are low will we receive a logic zero at the output. The truth table for the OR gate is outlined below:

Number of possible stages = 2n =22 = 4.

## 4. NOR Gate:

The NOR gate is essentially a combination of the NOT and OR gates. Consequently, a NOR gate comprises an OR gate followed by an inverter. When all inputs are at the binary low state (0), the output is at the binary high state (1), and if any of the inputs are at the binary high state, the output becomes binary low.

The NOR’s phrase as well as truth table are presented below –

## Transformation of NOR Gate into Basic Logic Gates:

**1. Construction of NOT Gate using NOR Gate:**

Since the NOT gate has only one input, both input terminals have been connected together, as shown in the diagram above. When we provide a binary high signal, such as 1, at the input, the output will be binary low, such as 0, as indicated in the truth table for the NOR gate. We employed the IC 7402, which is a quad two-input NOR gate.

**2. Construction of OR Gate using NOR Gate:**

**3. Construction of AND Gate using NOR Gate:**

or getting familiar with these it is important that one should have knowledge about the De Morgan’s theorem – According to the theorem the sum of the complement is equal to the product of the complement.

(A+B)‾ = A‾ . B‾ – EQ 1

From the figure shown above, Two NOR gate is been used by us and we short the input terminal of each gate so the output we will obtain as

= A‾ + B‾

Now these output is again given as an input of the another NOR gate and the output which we will get as

= (A‾ + B‾)‾

=A‾ ‾ + B‾ ‾

= A.B

**Required Components:**

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