Bits, Baud and BPS: What They Really Mean

Mar 29, 2001

The Bottom Line The true measure of modem speed is the number of data bits transmitted per second. "Baud" refers to changes in state of a modem's signal. All are defined here ...

Do you know what “bits,” “baud” and “bps” really mean? Modem transmission speed is the source of no little 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 ... and just maybe make the whole matter of modem speed a little less intimidating.

Computer data format
Before we examine how fast data can be moved by modems, we should take a quick look at just what computer data is.
We perceive most computer data as letters, numerals, spaces, and other symbols (including graphic elements). These are referred to as characters or bytes. Your PC sees data as more than that, however. Within a computer, each character is handled as a group of what are called data bits. A data bits is literally the smallest discreet data unit, and data bits are the building blocks of all computer data. Your computer, the programs it runs, storage media, and data transmission devices like modems see each character or byte as a group of 7 or 8 bits.
The computer sees the data bits these as binary digits, represented by digital 0’s and 1’s. (The word “bit” is actually a contraction of “Binary digIT.”) Depending on the device, the 0 or 1 may be represented by an “off” or “on” state, a positive or negative electrical charge, etc. The important element here is that there are only two possible states for a bit, represented digitally by 0 or 1.
Thus, all characters or bytes are merely groupings of digital 1’s or 0’s. The number of possible groupings in 7- or 8-bit strings is exactly what’s required to represent all possible letters, numerals, spaces, and other symbols your PC uses. These groups are what your system’s software and your modem deal with--in different formats, but always representing bytes as groups of digital 1’s and 0’s. (The letter “T” at the beginning of this sentence, for example, is represented digitally by 110110.)
Given that the basic unit of data is the bit, and your system and modem handle data as bits, it should be no surprise that the true measure of modem speed is the number of bits transmitted per second.

Bits per second
Bits per second is a measure of the number of data bits transmitted each second by a modem. This is sometimes referred to as the "bit rate,” but more commonly referred to as bps (short for “bits per second”).
A given character (letter, number, space, symbol, or other character) is made up of
Individual characters (letters, numbers, etc.) are made up of 7 or 8 bits, and are called bytes. Thus, bits are the basic components, or building blocks, of data in your computer.
are composed of several bits.
While a modem’s bps rate is tied to its baud rate, the two are not the same, as explained below.

Baud rate
Modems transmit data by changing the signal in a communications link (a telephone line). Changes in the signal (in strength, frequency, or other elements) represent bits. The nature of the signal and how it changes aren’t important here; what does matter is the fact that the signal changes in some respect to represent each bit--one sort of signal change can be a digital 0, another can be a digital 1. Thus, a series of changes represents each byte (letter, numeral, etc.) transmitted. You don’t have to worry about how this is done; your modem and software take care of that.
Each change is referred to as a baud.
Baud rate is a measure of the number of times per second a signal in a communications link changes. 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, again, 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--nor are there any 2400-baud modems. 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 send only four bits per baud, with 300 bauds per second. So:

300 baud X 4 bits per baud = 1200 bps


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


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


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

Characters per second
Characters per second (cps) is a measure of the number of characters (letters, numerals, spaces, and symbols) transmitted over a communications link 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-rate or bps.
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 for each character. 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, 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:

9600 bps
----------------------- = 960 characters per second
10 bits per character

14,400 bps
----------------------- = 1,440 characters per second
10 bits per character

28,800 bps
----------------------- = 2,880 characters per second
10 bits per character

…and so on.

CPS and file-transmission times
Remember: The number of characters per second is the same as the number of bytes transmitted each second. So, you can use this information to estimate the amount of time required to send or receive a given file. If, for instance, you want to download a file that is 403,200 bytes in size at 14,400 bps, the download should take about 4-1/2 minutes.
Note that I should the download “should” take 4-1/2 minutes; in reality, it will take up to half again as much time. This is because of “overhead time” your system and the remote system require. Your system has to open the file, check incoming data, and write the file to your hard disk, while the remote system has to find, check, and transmit the data--and both systems carry on data-checking communications as the file is transmitted. So, the ideal time of 4-1/2 minutes is stretched to 6-1/2 minutes, on the average. This overhead time becomes less of a percentage of the total expected time the larger the file is, fortunately.
Not incidentally, you may on occasion find that a transmission is taking even longer than you expect, even allowing for the overhead time. When this is the case, it is usually caused by the fact that your modem and the remote system’s modem have reduced their communication speed due to poor telephone line conditions (or, in the case of a large download, too many errors during file transmission).
When the difference is enough to be noticeable, it is probably a good idea to log off and reconnect. Quite often, you can get a “bad” line and calling back solves the problem. If the problem is persistent, it is probably due to weather conditions somewhere along the modem link. In that case, all you can do is live with the slowdown, or wait a few hours and try again.

Adding it all up
Now you have a better idea of what modem speed is all about. Not to mention how your computer handles data, how data is transmitted, and how that transmission is measured. Armed with this knowledge, you should find the “techie” language of modem speed less intimidating--and feel more comfortable about what’s happening the next time you download a file.
--Copyright, 2001, Michael A. Banks

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