What are Hexadecimal Numbers?
Hexadecimals are numbers that use the base 16 system of counting and expressing value. Instead of using just the numeric characters 0-9 like we're accustomed to, hexadecimals also use the letters A-F to represent the values 10-15.
Why are Hexadecimals Used?
Using the base 16 system of counting allows us to more succinctly express or communicate numeric values than other number systems that have fewer numeric characters to work with (decimal, octal, binary).
To illustrate, suppose you were a computer programmer, and you needed to write or communicate a binary number like 1101101101102 (the numbering system recognized by computers). The decimal equivalent of that binary number would be "3510" whereas the hexadecimal equivalent would simply be "DB6".
So as you can see, the primary reason we use hexadecimals instead of other number systems is simply that they are more compact and therefore more convenient to write and communicate.
How to Convert Hexadecimal to Decimal
If the hexadecimal number you are converting is less than 16, then you can simply use the following hex to decimal conversion chart:
| Base 16 : | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
| Base 10: | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
On the other hand, if the hexadecimal you are converting is greater than 15, then it helps to use a conversion method that identifies and sums place values -- a method you are already familiar with for identifying place values in the decimal number system.
So, to help you to understand how to convert hexadecimal to decimal, it may help to recall how we translate the value of a decimal number. Let's use the decimal number 1357 (135710, or one-thousand, three-hundred and fifty-seven) as an example:
| A | Power of 10: | 103 | 102 | 101 | 100 |
| B | Place value (A result): | 1000 | 100 | 10 | 1 |
| C | Entered decimal digit: | 1 | 3 | 5 | 7 |
| D | Product of B * C: | 1000 | 300 | 50 | 7 |
| E | Cumulative total of D: | 1000 | 1300 | 1350 | 1357 |
Multiplying the values in row B by their corresponding values in row C gives us the equation: 1(1000) + 3(100) + 5(10) + 7 -- which calculates out to 1357.
With the above base 10 translation in mind, here is how you would convert the base 16 number 12CA (12CA16 or one-two-C-A) into a base 10 number:
| A | Power of 16: | 163 | 162 | 161 | 160 |
| B | Place value (A result): | 4096 | 256 | 16 | 1 |
| C | Entered hex digit: | 1 | 2 | C | A |
| D | Product of B * C: | 4096 | 512 | 192 | 10 |
| E | Cumulative total of D: | 4096 | 4608 | 4800 | 4810 |
Adding the values of line D we get the base 10 number of 4810. In other words, the number 12CA16 coverts to the number 481010. Note that the above is how the hex to decimal converter shows its work.
As you can see, converting a hexadecimal number to a decimal number is a simple process of identifying the hexadecimal place value of each digit, multiplying each digit by its place value, and then adding up all of the products.