Cisco Certification  The Joy Of Hex
By Chris Bryant
Cisco certification candidates, particularly CCNA candidates, must master binary
math. This includes basic conversions, such as binarytodecimal and decimalto
binary, as well as more advanced scenarios involving subnetting and VLSM.
There's another conversion that might rear its ugly head on your Cisco exam,
though, and that involves hexadecimal numbering.
Newcomers to hexadecimal numbering are often confused as to how a letter of the
alphabet can possibly represent a number. Worse, they may be intimidated – after
all, there must be some incredibly complicated formula involved with representing
the decimal 11 with the letter "b", right?
Wrong.
The numbering system we use every day, decimal, concerns itself with units of
ten. Although we rarely stop to think of it this way, if you read a decimal
number from right to left, the number indicates how many units of one, ten, and
one hundred we have. That is, the number "15" is five units of one and one unit
of ten. The number "289" is nine units of one, eight units of ten, and two units
of one hundred. Simple enough!
Hex numbers are read much the same way, except the units here are units of 16.
The number "15" in hex is read as having five units of one and one unit of
sixteen. The number "289" in hex is nine units of one, eight units of sixteen,
and two units of 256 (16 x 16).
Since hex uses units of sixteen, how can we possibly represent a value of 10,
11, 12, 13, 14, or 15? We do so with letters. The decimal "10" is represented in
hex with the letter "a"; the decimal 11 with "b"; the decimal "12" with "c",
"13" with "d", "14" with "e", and finally, "15" with "f". (CCNA candidates will
remember that a MAC address of "ffff.ffff.ffff" is a Layer 2 broadcast.)
Practice Your Conversions For Exam Success
Now that you know where the letters fall into place in the hexadecimal numbering
world, you'll have little trouble converting hex to decimal and decimal to hex –
if you practice.
How would you convert the decimal 27 to hex? You can see that there is one unit
of 16 in this decimal; that leaves 11 units of one. This is represented in hex
with "1b" – one unit of sixteen, 11 units of one.
Converting the decimal 322 to hex is no problem. There is one unit of 256; that
leaves 66. There are four units of 16 in 66; that leaves 2, or two units of one.
The hex equivalent of the decimal 322 is the hex figure 142 – one unit of 256,
four units of 32, and 2 units of 2.
Hextodecimal conversions are even simpler. Given the hex number 144, what is
the decimal equivalent? We have one unit of 256, four units of 16, and four
units of 4. This gives us the decimal figure 324.
