Basics

# Design of Basic Logic Gates using NAND Gate

Three primary types of logic gates are the AND gate, the OR gate, and the NOT gate. Each of these gates performs distinct logical operations, and there is also the NAND gate, which is a combination of these basic logic gates. With the aid of these fundamental logic gates, it is possible to derive various logical functions, Boolean expressions, or any other logical expressions.

### Outline

• 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 fundamental type of digital logical circuit is the logic gate, which possesses two terminals: one for input and the other for output. These gates accept binary input, which means it can only be either one (1) or zero (0). The output produced by a logic gate is always the opposite of the input; hence, if a 1 is provided at the input, the output will be 0, and vice versa.

The calculation of the number of stages possible (based on the value of “a”) will involve the use of 2^a to determine the number of inputs.

The NOT Gate Truth Table is displayed below –

## 2. AND Gate:

This logic gate features two input terminals and a single output terminal. Its operation is such that it only produces a binary 1 at the output when both input terminals are set to binary 1. If either of the inputs is at binary 0, 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:

Much like the AND gate, the OR gate is a fundamental logic gate equipped with two input terminals and one output terminal. If any of the inputs is in the low state (binary 0), the output will be in the high state (binary 1). When just one of the inputs is at a low state, the output will also be at a low state.

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 an amalgamation of the NOT gate and the AND gate. Consequently, it comprises an AND gate and an inverter. The operation of these gates functions as follows: a binary 1 is produced at the gate’s output exclusively when both inputs are in the binary low state, i.e., 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 —

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

A single input terminal suffices, so we’ve connected both input terminals of the NAND gate together, as depicted in the diagram above. Exploiting a characteristic of the NAND gate evident in the truth table, we can discern that supplying a binary 1 at the input terminal will yield a 0 at the output. We employed the IC7400, a Quad two-input NAND gate, for this purpose.

## 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 –

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

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