Anyone who can count to ten and recite the alphabet already knows how to
count in hexadecimal. Of course, there is a certain amount of magic involved. .
Keep reading. Soon, you’ll know the same spell.
Hexadecimal is a base 16 number system. Remember that word “base” while your
reading the rest of this (no, not the same as Baseband!). The “base” of
hexadecimal is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0A, 0B, 0C, 0D, 0E, 0F, 10. Sixteen
digits, total, from which to create all the numbers you’ll ever need. And did
you see it, that magic in the last digit. Well, that’s nothing compared to the
digit that follows: 11.
Start with a more familiar number system: base 10, or decimal. The “base” of
the base 10 number system is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. From these digits
come all other digits in the base 10 system. Now look at those digits again.
They stop at 10. The next digit is, of course, 11. Remember that. When you pass
the end of the first number set in any base number, the next digit is always 11.
The pattern continues at the end of each number set. Even 20 is followed by 21,
30 by 31 and so on.
Once you’ve mastered decimal, it’s helpful to study an even simpler number
system: binary. In binary, you get two digits, 0 and 1. So there’s 00, 01 . . .
Pow, you’ve reached the end of the first base set. Guess what the next number
is:
11
Of course, the way your average network administrator will see the first
three digits in binary is:
0000 0000
0000 0001
0000 0011
Now, we’ll do it in hex. It does get a little trickier because letters enter
the mix. No choice, there just aren’t enough equivalent digits in decimal to
cover hex. So characters (A – F) are used to complete the base sets. Here,
again, is the first set in hex:
0
1
2
3
4
5
6
7
8
9
0A ---Remember, this is hex. So this number isn’t 10.
0B
0C
0D
0E
0F
10 ----This number, in hex, is 10.
Now, get ready for the magic. Guess what the next number in hex will be:
11
Now you’ve entered the second hex number set. You’ll think it’s familiar but
don’t be fooled.
12
13
14
15
16
17
18
19 ----- After this, the familiarity ends.
1A
1B
1C
1D
1E
1F
20 ----- Becomes familiar again. For a little while.
21
22
23
24
25
26
27
28
29
2A
2B
2C
2D
2E
2F
30
Now look at decimal, hexadecimal and binary side by side:
|
Decimal |
Hexadecimal |
Binary |
|
0 |
00 |
0000 0000 |
|
1 |
01 |
0000 0001 |
|
2 |
02 |
0000 0010 |
|
3 |
03 |
0000 0011 |
|
4 |
04 |
0000 0100 |
|
5 |
05 |
0000 0101 |
|
6 |
06 |
0000 0110 |
|
7 |
07 |
0000 0111 |
|
8 |
08 |
0000 1000 |
|
9 |
09 |
0000 1001 |
|
10 |
0A |
0000 1010 |
|
11 |
0B |
0000 1011 |
|
12 |
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