What is the process of converting a hexadecimal number to binary?

The process of converting a hexadecimal number to binary involves translating each hexadecimal digit into its four-digit binary equivalent.

To start with, it's important to understand that hexadecimal is a base-16 number system, while binary is a base-2 system. This means that each digit in a hexadecimal number can represent 16 different values (0-9 and A-F), while each digit in a binary number can only represent two values (0 and 1).

To convert a hexadecimal number to binary, you simply need to replace each hexadecimal digit with its binary equivalent. This is straightforward because each hexadecimal digit corresponds exactly to a four-digit binary number. For example, the hexadecimal digit '1' corresponds to the binary number '0001', '2' corresponds to '0010', '3' to '0011', and so on up to 'F', which corresponds to '1111'.

Here's a step-by-step guide on how to do it:

1. Write down the hexadecimal number that you want to convert to binary.
2. Starting from the left, take each hexadecimal digit in turn.
3. Look up the binary equivalent of this digit (you can use a conversion table for this).
4. Write down the four-digit binary number that corresponds to the hexadecimal digit.
5. Repeat this process for each digit in the hexadecimal number.

For example, if you wanted to convert the hexadecimal number '2A3' to binary, you would first convert the '2' to binary ('0010'), then the 'A' ('1010'), and finally the '3' ('0011'). So, '2A3' in hexadecimal is '001010100011' in binary.

Remember, the key to this process is understanding the relationship between the hexadecimal and binary number systems. Once you've grasped that, converting between the two is a simple matter of translation.