MAC
addresses are 48 bits in length and are expressed as twelve
hexadecimal digits. The first six hexadecimal digits, which
are administered by the IEEE, identify the manufacturer or
vendor and thus comprise the Organizational Unique Identifier
(OUI). The remaining six hexadecimal digits comprise the interface
serial number, or another value administered by the specific
vendor. MAC addresses are sometimes referred to as burned-in
addresses (BIAs) because they are burned into read-only memory
(ROM) and are copied into random-access memory (RAM) when
the NIC initializes.
2.
Basic hexadecimal (hex) numbering
Hexadecimal is a Base 16 numbering system that is used to
represent MAC addresses. It is referred to as Base 16 because
it uses sixteen symbols; combinations of these symbols can
then represent all possible numbers. Since there are only
ten symbols that represent digits (0, 1, 2, 3, 4, 5, 6, 7,
8, 9), and the Base 16 requires six more symbols, the extra
symbols are the letters A, B, C, D, E, and F.
The position of each symbol, or digit, in a hex number represents
the base number 16 raised to a power, or exponent, based on
its position. Moving from right to left, the first position
represents 160, or 1; the second position represents 161,
or 16; the third position, 162, or 256; and so on.
Example:
4F6A = (4 x 163)+ (F[15] x 162)+ (6 x 161)+ (A[10] x 160)
= 20330 (decimal)
3.
Converting decimal numbers to hexadecimal numbers
As with binary numbers, converting from decimal to hex is
done with a system called the remainder method. In this method
we repeatedly divide the decimal number by the base number
(in this case 16). We then convert the remainder each time
into a hex number.
Example:
Convert the decimal number 24032 to hex.
24032/16 = 1502, with a remainder of 0
1502/16 = 93, with a remainder of 14 or E
93/16 = 5, with a remainder of 13 or D
5/16 = 0, with a remainder of 5
By
collecting all the remainders backward, you have the hex number
5DE0.
4.
Converting hexadecimal numbers to decimal numbers
Convert
hexadecimal numbers to decimal numbers by multiplying
the hex digits by the base number of the system (Base
16) raised to the exponent of the position.
Example:
Convert the hex number 3F4B to a decimal number. (Work
from right to left.)
3
x 163 = 12288
F(15) x 162 = 3840
4 x 161 = 64
B(11) x 160 = 11
_________________
12288+3840+64+11 = decimal equivalent
|
 |
5.
Methods for working with hexadecimal and binary numbers
There
are two methods of converting binary numbers to hex numbers.
The first is to convert binary to decimal, and then convert
decimal to hex, using the methods you have already learned.
The second method is to use a scientific calculator.
It is important that you know how to do decimal, binary,
and hexadecimal conversions without a calculator. In this
course, the largest decimal number you have to deal with
is 255; the longest binary number you have to deal with
is 8 bits (11111111); and the largest hexadecimal number
is 2 hex digits (FF). You must be able to do these calculations
quickly, and do them in your head, both for practical
purposes and for your exams.
|
Dec |
Bin |
Hex |
Dec |
Bin |
Hex |
0
1
2
3
4
5
6
7
8
9
|
00000000
00000001
00000010
00000011
00000100
00000101
00000110
00000111
00001000
00001001
|
00
01
02
03
04
05
06
07
08
09
|
10
11
12
13
14
15
16
32
64
128 |
00001010
00001011
00001100
00001101
00001110
00001111
00010000
00100000
01000000
11111111 |
0A
0B
0C
0D
0E
0F
10
20
40
80 |
Author
unknown
credit by Paul Mack Roy
e-mail : pi-em-are@yahoo.com
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