Introduction to the Hexadecimal System

The need for another number system

We have the decimal system for our everyday counting, which is conveniently base-10 because of our ten fingers. We also have the base-2 binary system because of the high and low states a transistor in a computer can have. So why would we need another number system? Let’s see with an example.

The number $900$ in binary is $1110000100$.

Because 2 is a small base, it takes a large number of digits to represent a value, and the problem here is that it is hard for humans to accurately read and write a number in binary.

So we need a method better than a string of 1’s and 0’s to represent binary numbers. Let’s try something.

$0011$ $1000$ $0100$

We have only split the above number into groups of four, appending 0’s to the left to round out the digits. This makes the number much easier to remember, as we only need to remember the value of each group of four places or four bits. For example, in this case, we can remember the number by keeping track of $3$ $8$ $4$ (the corresponding decimal values of the three groups of binary digits) and then expanding out the full binary form. So in a way, we have come to a more compact representation using this division into groups of four bits. The hexadecimal system is nothing but a formalization of this idea.