Learning by Doing: CISCO Certified Network ... - SCN Research

Hexadecimal Numbering
Objective:
To learn how to convert between Hexadecimal, Decimal, and Binary numbers.
Tools and Materials:
Pencil and Paper
Bit-bashing worksheet
Background:
In the previous lab you learned how to convert between a base 2 numbering system
(binary) and a base 10 numbering system (decimal). As Emeril says we will be “kicking
it up a notch” here by adding in base 16 numbering systems (hexadecimal). Just like our
decimal system used the numbers zero-one-two-three-four-five-six-seven-eight-nine to
represent the 10 places in a base 10 system we use zero-one-two-three-four-five-sixseven-eight-nine-ten-eleven-twelve-thirteen-fourteen-fifteen
to represent the 16 places in
a base 16 system. The only difference is since we cannot distinguish a one-four from a
fourteen we use letters for ten through fifteen. Therefore our base 16 system is coded:
0-9 0-9
10 A
11 B
12 C
13 D
14 E
15 F
It’s actually easy once you get used to it. Once again, just like our decimal and binary
system, each column would be represented as a power with base 16. If we look at the
“column headings” for five bits of hexadecimal numbers they become:
16 4 16 3 16 2 16 1 16 0
65536 4096 256 16 1
Let’s start with binary to hexadecimal conversions using octets…they are the easiest.
Since there is eight bits these are easy:
1. We just divide the octet into two groups of 4 bits
2. Make new column headings
3. Add them up.
4. Then, with those totals, we use our decimal to hexadecimal conversion chart
above to complete the conversion.
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