
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.
The right to reproduce this article is granted on the condition 
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

   (Copyright, 1988, Michael A. Banks.  All rights reserved.)

     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 
per second, please read this article carefully; I guarantee to 
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
            Published by Brady Books/Simon & Schuster
                 ISBN # 0-13-586646-4    $19.95

     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, 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,
using, and troubleshooting computer communications hardware and 
software.  (And the book "supports" all major microcomputer 
brands.)
     For more information, contact:
                        Michael A. Banks
                          P.O. Box 312
                       Milford, OH  45150
