Introduction

Binary numbers are a numerical system that uses only two digits, 0 and 1, to represent numbers. Binary numbers are commonly used in computer science and digital electronics to represent and manipulate information.

## Characteristics:

- Only two digits, 0 and 1, are used in binary numbers.
- Each digit in a binary number represents a power of 2, starting from 2^0 (which equals 1), then 2^1 (which equals 2), 2^2 (which equals 4), and so on.
- The position of each digit in a binary number determines its value, with the rightmost digit representing the least significant bit (LSB) and the leftmost digit representing the most significant bit (MSB).

### Mathematical Formation:

To construct a binary number, you start with the rightmost digit and assign a value of 1 if the bit is 1 or a value of 0 if the bit is 0. For example, the binary number 1011 would be constructed 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.

### Working:

In digital electronics, binary numbers are used to represent the presence or absence of an electrical signal, with 1 representing a high voltage and 0 representing a low voltage. Binary numbers can be manipulated using logical operations such as AND, OR, and NOT to perform tasks such as arithmetic operations, data storage, and control of electronic devices.

#### 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.