Hexadecimal numbers - conversion and purpose

1. Why Use Hexadecimal?

A computer, internally, can only handle binary numbers.

Such as 101001110 11011001010 110100101011 1010101 111001011 and so on.

However people find writing and reading binary numbers very awkward and error prone - we are just not built to handle long strings of 1s and 0s directly.

Therefore a more human-friendly system is used, namely the hexadecimal number system.

Denary numbers are base-10 because they use ten symbols, and binary is base-2 because it uses two symbols. Hexadecimal numbers are base-16 which uses sixteen symbols.

Hexadecimal is useful because it is much more readable to humans than binary but at the same time it still shares a lot of the qualities of binary. It is widely used in computing because it is a much shorter way of representing a byte of data (8 binary digits or bits).

If we were to represent a byte of data in binary, it would require 8 digits, e.g. 10100110.

However, that same byte of data could be represented in hexadecimal in just two digits e.g. "A6". This is much more compact and user friendly than a binary number.

Since a byte is 8 digits long it has a maximum value. In denary this is 255. The same number can be written as 11111111 in binary, or FF in hex.