How do you convert a hexadecimal number to binary?

To convert a hexadecimal number to binary, each hexadecimal digit is replaced by its binary equivalent of four bits.

Hexadecimal is a base-16 number system, while binary is a base-2 system. This means that each digit in hexadecimal can represent 16 different values (0-15), while each digit in binary can represent 2 values (0-1). Because of this, each hexadecimal digit can be represented by exactly four binary digits.

To convert a hexadecimal number to binary, you simply replace each hexadecimal digit with its binary equivalent. For example, the hexadecimal digit 'A' represents the decimal number 10, which is '1010' in binary. So, if you have the hexadecimal number 'A3', you would replace 'A' with '1010' and '3' with '0011' to get the binary number '10100011'.

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

1. Write down the hexadecimal number you want to convert.
2. Look up the binary equivalent for each hexadecimal digit. You can use a conversion table for this. Here's a simple one:

Hexadecimal: 0 1 2 3 4 5 6 7 8 9 A B C D E F
Binary: 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111

3. Replace each hexadecimal digit with its binary equivalent. Write the binary digits in the same order as the hexadecimal digits.

4. The result is the binary equivalent of the hexadecimal number.

Remember, when converting from hexadecimal to binary, you're not changing the value of the number, just how it's represented. It's like translating a sentence from English to French - the meaning stays the same, but the words used to express it change.