Hexadecimal number

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Hexadecimal number

A hexadecimal number is a numeral system that uses a base of 16 (0-9 and A-F), providing an efficient way to represent large binary values by grouping them into 4-bit segments. Hexadecimal numbers are commonly used in computer programming, digital hardware, and networking.

What does Hexadecimal Number mean?

A hexadecimal number is a representation of a numeric value using a base-16 system. Each digit in a hexadecimal number represents a value from 0 to 15, with the digits A through F representing the values 10 through 15. Hexadecimal numbers are commonly used in computer science and other fields to represent large numeric values in a concise and human-readable format.

To convert a hexadecimal number to a decimal number, each digit is multiplied by its corresponding power of 16 and the results are added together. For example, the hexadecimal number 1A can be converted to decimal as follows:

1 * 16^1 + 10 * 16^0 = 16 + 10 = 26

Similarly, to convert a decimal number to hexadecimal, the number is repeatedly divided by 16 and the remainders are used to create the hexadecimal digits. For example, the decimal number 26 can be converted to hexadecimal as follows:

26 ÷ 16 = 1 remainder 10 (A)
1 ÷ 16 = 0 remainder 1

Therefore, the hexadecimal representation of 26 is 1A.

Applications

Hexadecimal numbers are used in a variety of applications, including:

  • Computer programming: Hexadecimal numbers are commonly used in computer programming languages to represent large numeric values and memory addresses.
  • Web development: Hexadecimal numbers are used to represent colors in HTML and CSS.
  • Networking: Hexadecimal numbers are used to represent IP addresses and [MAC](https://amazingalgorithms.com/definitions/mac) addresses.
  • Electronics: Hexadecimal numbers are used to represent hexadecimal codes for electronic components and devices.

History

The hexadecimal number system was first developed by French mathematician Jacques Peletier du Mans in the 16th century. Peletier proposed using a base-16 system to simplify calculations, but his work was not widely adopted.

In the 20th century, hexadecimal numbers were revived by computer scientists and engineers as a convenient way to represent large numeric values in a concise format. Hexadecimal numbers were particularly useful in the early days of computing, when computer memory was limited and it was important to conserve space.

Today, hexadecimal numbers continue to be used in a variety of applications, particularly in computer science and electronics. They provide a convenient and human-readable way to represent large numeric values, and they are also easy to convert to and from binary and decimal numbers.