August 7, 2024

# Binary number system

## Binary number system

The binary number system is a numerical system that uses only two digits, 0 and 1. It is the foundation of all modern digital computers because it aligns with the electronic nature of computer hardware, which can represent information in terms of binary states (on/off, high/low voltage, etc.).

In the binary system, each digit is called a “bit” (short for binary digit). A bit can represent one of two values: 0 or 1. The binary system follows a place value system, just like the decimal system we commonly use, but with powers of 2 instead of powers of 10.

Here’s an example to illustrate how binary numbers work:

Decimal: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 …
Binary: 0 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110 1111 …

In binary, each position represents a power of 2. Starting from the rightmost position, the powers of 2 increase as you move to the left. For example, in the binary number 1011, the rightmost digit (1) represents 2^0 (which is 1), the next digit (1) represents 2^1 (which is 2), the next digit (0) represents 2^2 (which is 4), and the leftmost digit (1) represents 2^3 (which is 8). Adding these values together, we get 8 + 0 + 2 + 1 = 11 in decimal.

In computers, binary is used to represent and manipulate data. The binary system maps well to electronic circuits because it can be easily implemented using two voltage levels (e.g., 0V and 5V). In computer memory, individual bits are grouped together to form larger units of data. For example, 8 bits make up a byte, which is the fundamental unit of storage in most computers. Binary arithmetic operations, logical operations, and data storage are all based on the binary number system.

To work with binary numbers, you can use various programming languages and computer systems that provide built-in support for binary operations or bitwise operations. These operations allow you to perform logical operations, shifting, masking, and other manipulations on binary data.