...you just don't know it yet. Allow me to explain.

Back in elementary school, teachers taught us about the *ones*, *tens*, *hundredths*, ... columns. So the number 894 has 8 in the hundredths column, 9 in the tens column, and 4 in the ones column.

More specifically...

```
894 = (8 * 100) + (9 * 10) + (4 * 1)
```

Do you see a pattern with the ones, tens, and hundredths columns? They are all powers of ten: 10^{0}, 10^{1}, and 10^{2}. This is the numbering system we learned in school: *base 10*. The valid numbers in a column are 0 - 9. That makes sense, because we can only have a single digit in a column.

Now in the hexadecimal number system, the base is 16. So the first three columns are the ones, sixteens, and two hundred fifty-sixths columns. In powers of sixteen, they are: 16^{0}, 16^{1}, and 16^{2}. So the number 894 in hexadecimal is:

894_{16} = (8 * 256) + (9 * 16) + (4 * 1) = 2196_{10}

Note that the subscript indicates the base. 894 is the hexadecimal number. 2196 is the base 10 equivalent. You can also represent hexadecimal numbers like this: 0x894. For the 2196 base 10 number, we typically omit the 10 subscript since it is assumed.

The hexadecimal story continues a bit more. If base 10 uses the numbers 0 - 9, then what does base 16 use? Base 16 must have 16 possible digits. Its range of digits start with the same digits 0 - 9. The remaining six digits are: A, B, C, D, E, and F. The letters stand for 10 - 15 respectively. So, counting in hexadecimal is like this:

```
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
```

I guess it would be too confusing in elementary school to combine numbers and letters in math. But it would've been fun trying.

For a final example, here is the conversion of hexadecimal F0A to base 10:

F0A_{16}= (F * 162) + (0 * 161) + (A * 160) = (15 * 162) + (0 * 161) + (10 * 160) = (15 * 256) + (0 * 16) + (10 * 1) = (3840) + (0) + (10) = 3850_{10}

So there you have it. Hexadecimal numbers made easy! You already know hexadecimal. Just change the base from 10 to 16. And have a cup of `0xC0FFEE`

while you're at it!

Thanks for reading. π

*Follow me on Twitter @realEdwinTorres for more programming tips and help.*

## Top comments (1)

Doesn't everybody learn that in school?