Understanding Hexadecimal Numbers

Hexadecimal is a positional numeral system with a base of 16.
It uses sixteen distinct symbols to represent values from 0 to 15.
The symbols used are 0–9 to represent values zero to nine and A–F to represent values ten to fifteen.

Hexadecimal and Binary

Hexadecimal is used in computing as a more human-friendly way of representing binary data.
Each hexadecimal digit represents four binary digits, also known as a nibble, which is half a byte (or 4 bits).
For example, the binary number 1010 is equal to the hexadecimal number A.

To convert a hexadecimal number to a decimal number, each hexadecimal digit in the number needs to be multiplied by 16 to the power of its position (counting from 0).
For example, to convert 2D (hexadecimal) to decimal, we would perform the calculation: (2 * 16^1) + (13 * 16^0) = 45.

To convert a decimal number to a hexadecimal number, divide the decimal number by 16 and record the remainder. The quotient is divided by 16 again repeating this process until the quotient is zero. The hexadecimal number is the concatenation of all remainders starting from the last to the first.
For example, to convert the decimal number 70 to hexadecimal, we would perform the following calculations:
- 70 / 16 = 4 remainder 6. For us in hexadecimal 6 is 6.
- 4 / 16 = 0 remainder 4. For us in hexadecimal 4 is 4.
So, 70 in decimal is equal to 46 in hexadecimal.

Hexadecimal is used in computing for a variety of reasons. It drastically reduces the number of digits when representing large binary numbers.
It is used frequently in debugging and programming as it can provide a human-friendly view of binary data.
Memory addresses are often represented in hexadecimal, and also in styling web pages – hexadecimal codes are used to represent colours.

An understanding of hexadecimal is not just for programmers and computer scientists - it is important for anyone using a computer.
Hexadecimal, binary, and other numeral systems are all key to understanding the underlying processes going on inside a computer. Familiarity with these systems is beneficial when solving technical problems or when trying to understand errors or issues that may arise.