**Understanding
Hex**

Mark
Mansur, http://www.tunerpro.net/

**Introduction**

Hexidecimal
seems to be a mystical topic to a good portion of beginners in the DIY-EFI
community. I hope to clear up the concept as simply as possible with this
short paper.

**Decimal
and Base-10**

If you can
read this paper theres a good chance you can also count. When we count in
our every-day world, we count in decimal. The "geek" term for decimal
is Base-10. What it means is that we use 10 different, unique, digits as building
blocks to form numbers (all numbers). For the sake of clarity, I'll list the
base-10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

**Hexidecimal
and Base-16**

So what exactly
is hexidecimal? Well, its base-16 (Hex means 6 and dec means 10. Look:
6 + 10 = 16)! And from what I told you about base-10, you sharper readers
may have deduced that it means we use 16 different, unique digits to form
numbers (all numbers). Again, for clarity, I'll list the base-16 digits: 0,
1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.

**What's
with the letters?**

In every-day
counting we are familiar with digits 0-9. But what if we wanted more numeric
"building blocks" with which we could create numbers? We would have
to invent 6 more digits. Having an alphabet at our disposal makes this easy.
We'll borrow letters!. A is the 10th digit, B is the 11th digit, etc, ending
with F as the 15th digit.

**Ones,
Tens, Hundreds, and Ones, Sixteens, and Two-Fifty-Sixes!**

When we count
from 0, what do we do when we run out of digits in the ones column? We increment
the number in the tens column and start again from zero in the ones column!
Example: counting from 9 to 10, or 19 to 20, or 29 to 30, etc. This is a familiar
concept to everyone reading this, I'm sure.

What happens
when count in *hex* from 0 and we run out of digits in the ones column?
Similar to decimal, we increment the number in the *sixteens* column
and start again from zero in the ones column! Example: counting from F to
10, 1F to 20, 2F to 30, etc. This may still seem a little strange. Read on.

**I
still don't understand. Explain it a different way. Please?**

Follow me
for a second. Lets say every month in the year had exactly 30 days, no more,
no less. We'll start on January 1st (1/1). Now we count to January 30th (1/30).
What day comes next? "Easy!" you say... February 1st (2/1)!

When we continue
to walk through the days and get to February 30th (remembering all of our
months have 30 days), what day comes next? March 1st (3/1)!

Guess what,
if you can follow that, you can count in base-30!

"What?"
you say? Well, before we incremented the month, we counted through all of
the days. When we ran out of days in the month, we incremented the month and
start the day count over again!

Hex is the
same conceptually, only we count in 16's instead of 30's. The only difference
is that we use letters A - F for 10th - 15th **digits**
(remember that digits are the building blocks for expressing numbers).
For the sake of clarity, I'll list the first 32 decimal numbers and their
corresponding hexidecimal digits for you. I'll highlight where we run out
of digits and therefore increment the next digit column for each:

Dec |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
31 |
32 |

Hex |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
A |
B |
C |
D |
E |
F |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
1A |
1B |
1C |
1D |
1E |
1F |
20 |

**Tools
for counting high**

I personally
use hex almost every day of my life. Even so, if you asked me, "Quick!
Using only your brain, what is the decimal number 13503 converted to its hex
equivelant?" I'd look at you and make a remark like, "if only was that smart, I could rule the world!"

I use the
Windows calculator for converting decimal values to their hex equivelant and
hex values to their decimal equivelant. Try it! Open the calculator (in the
start menu, programs, accessories - or some of you may have a shortcut on
your keyboard) and make sure "Scientific" is checked in the view
menu. While the "dec" radio button is selected, enter a decimal
number and then click the "hex" radio button. The hex equivelant
of the decimal number you entered will be displayed! Try it backwards - while
"hex" is selected, enter an arbitrary hex number (can't think of
one? Try: 1A) and then click the "dec" radio button. The decimal
equivelant is displayed (if you used my example, you'll get 26 as the decimal
equivelant ... look in the table above!).

**Does
this have something to do with $ and 0x?**

Ever wonder
why people always talk about money when discussing code? $32 this and $6E
that?! The $ symbol means the number is a hexidecimal number and not a decimal
number. Why use a symbol? Becuase if I wrote 32 all by itself you would have
no way of knowing whether I meant decimal 32 or hex 32 (hex 32 is 50 in
decimal - I know this because I used the windows calculator). In some computer
languages '0x' is placed in front of the number to signify hex: 0x32.

**Conclusion**

Hex is your
friend. Get to know it. It's worth it.