# Heres an excerpt from The Modem Reference, written by Michael A. Banks and recommended by

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Here's an excerpt from The Modem Reference, written by Michael A.
Banks and recommended by Jerry Pournelle in Byte, The Smithsonian
Magazine, et al.
that all text, including this notice and the notice at the end of
the article, remain unchanged, and that no text is added to the
body of the article.
Thanks!  --MB

BITS, BAUD RATE, AND BPS
Taking the Mystery Out of Modem Speeds
by Michael A. Banks

Modem transmission speed is the source of a lot of
confusion, even among otherwise informed computer and modem
users.  The root of the problem is the fact that the terms "baud"
and "bits per second" are used interchangeably and
indiscriminately.  I strongly suspect this is a result of the
fact that it's easier to say "baud" than "bits per second,"
though misinformation has a hand in it, too.
If you've ever found yourself confused by the relationship
between bits and baud rate, or if you think that a modem's baud
rate is the same as the number of bits or characters it transmits
clear up the confusion and disabuse you of any false concepts ...

Bits per second (bps)
Bits per second is a measure of the number of data bits
(digital 0's and 1's) transmitted each second in a communications
channel.  This is sometimes referred to as "bit rate."
Individual characters (letters, numbers, etc.), also
referred to as bytes, are composed of several bits.
While a modem's bit rate is tied to its baud rate, the two
are not the same, as explained below.

Baud rate
Baud rate is a measure of the number of times per second a
signal in a communications channel varies, or makes a transition
between states (states being frequencies, voltage levels, or
phase angles).  One baud is one such change.  Thus, a 300-baud
modem's signal changes state 300 times each second, while a 600-
baud modem's signal changes state 600 times per second.  This
does not necessarily mean that a 300-baud and a 600-baud modem
transmit 300 and 600 bits per second, as you'll learn in a few
lines.

Determining bits per second
Depending on the modulation technique used, a modem can
transmit one bit--or more or less than one bit--with each baud,
or change in state.  Or, to put it another way, one change of
state can transmit one bit--or more or less than one bit.
As I mentioned earlier, the number of bits a modem transmits
per second is directly related to the number of bauds that occur
each second, but the numbers are not necessarily the same.
To illustrate this, first consider a modem with a baud rate
of 300, using a transmission technique called FSK (Frequency
Shift Keying, in which four different frequencies are turned on
and off to represent digital 0 and 1 signals from both modems).
When FSK is used, each baud (which is, a gain, a change in state)
transmits one bit; only one change in state is required to send a
bit.  Thus, the modem's bps rate is also 300:

300 bauds per second X 1 bit per baud  =  300 bps

Similarly, if a modem operating at 1200 baud were to use one
change in state to send each bit, that modem's bps rate would be
1200.  (There are no 1200 baud modems, by the way; remember that.
This is only a demonstrative and hypothetical example.)
Now, consider a hypothetical 300-baud modem using a
modulation technique that requires two changes in state to send
one bit, which can also be viewed as 1/2 bit per baud.  Such a
modem's bps rate would be 150 bps:

300 bauds per second X 1/2 baud per bit  =  150 bps

To look at it another way, bits per second can also be
obtained by dividing the modem's baud rate by the number of
changes in state, or bauds, required to send one bit:

300 baud
---------------  =  150 bps
2 bauds per bit

Now let's move away from the hypothetical and into reality,
as it exists in the world of modulation.
First, lest you be misled into thinking that "any 1200 baud
modem" should be able to operate at 2400 bps with a two-bits-per-
baud modulation technique, remember that I said there are no 1200
baud modems.  Medium- and high-speed modems use baud rates that
are lower than their bps rates.  Along with this, however, they
use multiple-state modulation to send more than one bit per baud.
For example, 1200 bps modems that conform to the Bell 212A
standard (which includes most 1200 bps modems used in the U.S.)
operate at 300 baud and use a modulation technique called phase
modulation that transmits four bits per baud.  Such modems are
capable of 1200 bps operation, but not 2400 bps because they are
not 1200 baud modems; they use a baud rate of 300.  So:

300 baud X 4 bits per baud  =  1200 bps

or

300 baud
------------------  =  1200 bps
1/4 baud per bit

Similarly, 2400 bps modems that conform to the CCITT V.22
recommendation (virtually all of them) actually use a baud rate
of 600 when they operate at 2400 bps.  However, they also use a
modulation technique that transmits four bits per baud:

600 baud X 4 bits per baud  =  2400 bps

or

600 baud
------------------  = 2400 bps
1/4 baud per bit

Thus, a 1200-bps modem is not a 1200-baud modem, nor is a
2400-bps modem a 2400-baud modem.
Now let's take a look at 9600-bps modems.  Most of these
operate at 2400 baud, but (again) use a modulation technique that
yields four bits per baud.  Thus:

2400 baud X 4 bits per baud  =  9600 bps

or

2400 baud
------------------  =  9600 bps
1/4 baud per bit

Characters per second (cps)
Characters per second is the number of characters (letters,
numbers, spaces, and symbols) transmitted over a communications
channel in one second.  Cps is often the bottom line in rating
data transmission speed, and a more convenient way of thinking
about data transfer than baud- or bit-rate.
Determining the number of characters transmitted per second
is easy: simply divide the bps rate by the number of bits per
character.  You must of course take into account the fact that
more than just the bits that make up the binary digit
representing a character are transmitted when a character is sent
from one system to another.  In fact, up to 10 bits may be
transmitted for each character during ASCII transfer, whether 7
or 8 data bits are used.  This is because what are called start-
and stop-bits are added to characters by a sending system to
enable the receiving system to determine which groups of bits
make up a character.  In addition, a system usually adds a parity
bit during 7-bit ASCII transmission.  (The computer's serial port
handles the addition of the extra bits, and all extra bits are
stripped out at the receiving end.)
So, in asynchronous data communication, the number of bits
per character is usually 10 (either 7 data bits, plus a parity
bit, plus a start bit and a stop bit, or 8 data bits plus a start
bit and a stop bit).  Thus:

300 bps
-----------------------  =  30 characters per second
10 bits per character

1200 bps
-----------------------  =  120 characters per second
10 bits per character

2400 bps
-----------------------  =  240 characters per second
10 bits per character

Common speeds
The most commonly-used communications rates for dial-up
systems (BBSs and online services like CompuServe, DELPHI, and
GEnie) are 300, 1200, and 2400 bps.  A few older systems--
especially Telex systems--communicate at 110 bps, but these are
gradually going the way of the dinosaur.  4800 and 9600 bps
modems are generally available, but few online services or BBSs
accommodate them.  This will be changing in the near future,
however, with the cost of high-speed modem technology decreasing
as the demand for it increases.
Modems with even higher bps rates are manufactured (19,200
and up) but these are not used with dial-up systems; the upper
limit on asynchronous data transmission via voice-grade telephone
lines appears to be 9600 bps.  The use of higher transmission
rates requires special dedicated lines that are "conditioned"
(i.e., shielded from outside interference) as well as expensive
modulation and transmission equipment.
#
If you found this article useful, you may want to pick up a
copy of the book from which it was excerpted:
THE MODEM REFERENCE
by Michael A. Banks
In addition to explaining the technical aspects of modem
operation, communications software, data links, and other
elements of computer communications, the book provides detailed,
illustrated "tours" of major online services such as UNISON,
CompuServe, DELPHI, BIX, Dow Jones News/Retrieval, MCI Mail, the
PRODIGY service, and others.  It also contains information on
using packet switching networks and BBSs, as well as dial-up
numbers for various networks and BBSs.
You'll also find hands-on guides to buying, setting up,
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Other books by Michael A. Banks
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