symbol rate is related to gross bit rate expressed in bit/s. The term baud has sometimes incorrectly been used to mean bit rate, since these rates are the same in old modems as well as in the simplest digital communication links using only one bit per symbol, such that binary digit "0" is represented by one symbol, and binary digit "1" by another symbol. In more advanced modems and data transmission techniques, a symbol may have more than two states, so it may represent more than one bit. A bit (binary digit) always represents one of two states. If bits are conveyed per symbol, and the gross bit rate is , inclusive of channel coding overhead, the symbol rate can be calculated as By taking information per pulse N in bit/pulse to be the base-2-logarithm of the number of distinct messages M that could be sent, Hartley constructed a measure of the gross bit rate R as where Here, the denotes the ceiling function of . Where is taken to be any real number greater than zero, then the ceiling function rounds up to the nearest natural number (e.g. ). In that case, different symbols are used. In a modem, these may be time-limited sinewave tones with unique combinations of amplitude, phase and/or frequency. For example, in a 64QAM modem, , and so the bit rate is times the baud rate. In a line code, these may be M different voltage levels. The ratio is not necessarily even an integer; in 4B3T coding, the bit rate is of the baud rate. (A typical basic rate interface with a 160 kbit/s raw data rate operates at 120 kBd.) Codes with many symbols, and thus a bit rate higher than the symbol rate, are most useful on channels such as telephone lines with a limited bandwidth but a high signal-to-noise ratio within that bandwidth. In other applications, the bit rate is less than the symbol rate. Eight-to-fourteen modulation as used on audio CDs has bit rate of the baud rate. See also References External links Data transmission Units of frequency