I've had several people ask me what the true bandwidth of a T1 is. I usually respond that it is based upon how one defines bandwidth because it really isn't an easy question to answer otherwise. Of course, I could also give the short and sweet answer ("A T1 offers up to 1.536 megabits per second of data bandwidth..."), but understanding where the numbers come from and some of the variations that may change the figures might be more helpful. I'll explain how to understand the numbers behind a T1 circuit and then point you to a good resource on carrier transmissions.

To understand the T1 circuit - the foundation of digital circuits - you need to realize why it came into being. Prior to the digital T1, each telephone call made was carried over a pair of copper wires. Thus, for the carrier to serve 24 concurrent telephone conversations from one telco office to another, it would need to string 48 copper wires between offices. As telephone usage increases, the demand for copper increases, and, naturally, the cost of the infrastructure becomes astronomical. The T1 circuit was introduced as a method of reducing the amount of copper required to carry telephone calls. In fact, the T1 circuit can carry all 24 of those telephone calls on just two pairs of wires.

A couple of developments led to this ability to carry multiple telephone conversations on a just a few wires. The first was the Nyquist Theorem, which states that an analog signal can be accurately reproduced through sampling (periodically taking a sample of the analog form and quantizing it) if the sampling rate is at least twice the greatest frequency of the signal.

The human voice has a general frequency range from about 300 Hz (or 300 cycles per second) to around 3,500 Hz. Thus, for a medium to carry a telephone conversation, you would need to sample from 0 to 4,000 Hz, adding a bit of margin. According to the Nyquist Theorem, this would require that the analog signal be sampled 8,000 times each second (4,000 cycles per second, sampled twice per cycle).

Nyquist specifies only how often to sample the signal, but not how to quantize the sample - that is, how to represent the sampled information (e.g., the frequency). So the second significant development was pulse code modulation (PCM). Understanding PCM in depth is not necessary, other than to know that it is the method chosen to quantize the sampled signal, and that PCM specifies 256 distinct values, which can be represented by 8 bits (2^8 = 256).

That each of the 8,000 samples taken each second must be quantized and represented by 8 bits each. This works out to 64,000 bits per second for a single voice call to be transmitted accurately over a digital signal. Why do we care about all of this? Well, understanding these basic needs will let us understand the bandwidth of the more common carriers, such as T1.

T1 was designed to handle 24 individual voice calls. This is done using a technique called time division multiplexing (TDM), which breaks up the circuit into 24 distinct channels. In a way, they're like TV channels, but instead of each channel being carried on a different frequency, it's represented by a distinct "time slot" on the T1 circuit. Each time slot is simply a chunk of 8 bits taken from the wire. Thus, a T1 frame looks something like this:

Each of the 24 channels is composed of 8 bits, for a total of 192. Going back to the Nyquist rate, we know that we need to sample at 8,000 times per second to replicate the human voice. Therefore, to produce all 24 channels, the entire 192 bits must be transmitted 8,000 times each second, for a subtotal of 1,536,000 bits per second (1.536 Mbps).

Notice in the illustration, however, that a single framing bit is added between each 24-channel frame. Therefore, an additional 8,000 framing bits are sent each second, raising our total to 1,544,000 bits per second (1.544 Mbps). This number is the bit rate of the line itself, and the one you commonly see with reference to a T1 circuit. Because 8,000 of the bits sent each second are used for framing and not data, however, the maximum data you could theoretically put on the wire is the smaller number: 1.536 Mbps.
This discussion should shed some light on where these seemingly unusual numbers come from. There are some additional issues that can potentially decrease the available bandwidth. For instance, some framing variations (e.g., AMI) will "borrow" additional bits from data channels to send signaling information. Also, other carrier types, such as DS3 or E1/E3, have different framing requirements, so the calculations for the number of framing bits will again change.

One of the better resources I have found for descriptions of circuit framing is Cisco WAN Quick Start. This book provides the additional framing information you need to calculate available data bandwidth for most common circuit types.