Networking: A Beginner's Guide
Decimal numbers should use commas as you were taught in school. So, the
number 10,100 should be read as ten thousand one hundred, whereas the
number 10100 should be read as the binary number for the quantity twenty.
Sometimes people put the letter b at the end of a binary number, although this
convention isn't widely followed.
Put all these things together, plus a little common sense, and you'll usually have no
doubt whether you're reading a binary or decimal value.
Other Important Numbering Systems
Two other important numbering systems that you encounter in the world of
networking are octal and hexadecimal. Hexadecimal is far more prevalent than octal,
but you should understand both.
The octal number system is also called the base-8 numbering system. In this scheme,
each position in a number can hold only the numerals 0 to 7. The number 010 in the octal
numbering system corresponds to 8 in the decimal numbering system. Octal numbers can
be indicated with a leading zero, a leading percent symbol (%), or a trailing capital letter O.
The hexadecimal numbering system is fairly common in networking, and is often
used to represent network addresses, memory addresses, and the like. The hexadecimal
system (also called the base-16 numbering system) can use 16 different symbols in each
of its positions. Since we have written numerals for only 0 to 9, the hexadecimal system
uses the letters A through F to represent the extra symbols.
How to Quickly Convert Hexadecimal, Decimal, Octal, and Binary Numbers
The Calculator application that comes with all versions of Windows allows you
to convert values quickly between hexadecimal, decimal, octal, and binary. With
the calculator open, place it into Scientific mode (open the View menu and choose
Scientific). This mode reveals a lot of advanced features in the calculator. In the
upper-left area of the calculator, you can now see four option buttons labeled
Hex, Dec, Oct, and Bin. These correspond to the hexadecimal, decimal, octal, and
binary numbering systems. Just choose which system you want to use to enter a
number, and then click any of the other options to convert the number instantly.
For instance, suppose that you click the Bin option button and enter the
number 110100100110111010. If you then click the Dec button, the calculator
reveals that the number you just entered is 215,482 in the decimal system. If you
click the Hex button, you find that the binary number that you entered is 349BA in
the hexadecimal numbering system. And if you click the Oct button, you discover
that the number is 644672 in the octal numbering system. You can also go in the
other direction: Click the Dec button, enter some number, and then click the other
option buttons to see how the number looks in those other numbering systems.