## Introduction

Binary to decimal conversion is the process of converting a binary number to its equivalent decimal representation.

Binary numbers use only two digits (0 and 1) to represent numbers, while decimal numbers use ten digits (0-9). Binary to decimal conversion is a basic operation used in digital electronics, computer science, and telecommunications.

### Characteristics:

- Binary numbers use only two digits (0 and 1) to represent numbers.
- Decimal numbers use ten digits (0-9) to represent numbers.
- Each digit in a binary number represents a power of 2.
- Each digit in a decimal number represents a power of 10.

### Construction

To convert a binary number to a decimal number, you start with the rightmost digit of the binary number and assign a value of 1 if the digit is 1 or a value of 0 if the digit is 0. Then, you move to the left and multiply the next digit by 2 and add it to the total. You repeat this process until you have multiplied all the digits by their respective powers of 2 and added them together to get the decimal equivalent.

### Working

Binary to decimal conversion is performed by multiplying each digit of the binary number by the corresponding power of 2 and adding the results. For example, the binary number 1011 can be converted to decimal as follows:

1 * 2^0 = 1 1 * 2^1 = 2 0 * 2^2 = 0 1 * 2^3 = 8

So the decimal value of the binary number 1011 would be 1 + 2 + 8 = 11.

### Procedure

- Write the binary number
- Starting from the rightmost digit, write down the powers of 2 in order (1, 2, 4, 8, 16, etc.)
- Multiply each digit of the binary number by its corresponding power of 2
- Add the results of each multiplication to get the decimal equivalent.

### Rules:

- Each digit of the binary number can only be 0 or 1.
- The rightmost digit represents 2^0, the next digit represents 2^1, the next represents 2^2, and so on.
- The decimal equivalent is the sum of the products of each binary digit with its corresponding power of 2.

### Need

Binary to decimal conversion is necessary for performing arithmetic operations and storing and manipulating data in digital electronics and computer science. It is also used in telecommunications for data transmission and encoding.

#### Applications:

- Computer science and programming
- Digital electronics and telecommunications
- Information technology and data processing
- Cryptography and security systems
- Image and audio processing
- Control systems and automation
- Finance and trading algorithms.