In a digital recording system, sound is stored and manipulated as a stream of discrete numbers, each number representing the air pressure at a particular time. The numbers are generated by a microphone connected to a circuit called an ANALOG TO DIGITAL CONVERTER, or ADC. Each number is called a SAMPLE, and the number of samples taken per second is the SAMPLE RATE. Ultimately, the numbers will be converted back into sound by a DIGITAL TO ANALOG CONVERTER or DAC, connected to a loudspeaker.

**Fig. 1 The digital signal chain**

Figure 1 shows the components of a digital system. Notice that the output of the ADC and the input of the DAC consists of a bundle of wires. These wires carry the numbers that are the result of the analog to digital conversion. The numbers are in the binary number system in which only two characters are used, 1 and 0. (The circuitry is actually built around switches which are either on or off.) The value of a character depends on its place in the number, just as in the familiar decimal system. Here are a few equivalents:

BINARY DECIMAL 0=0 1=1 10=2 11=3 100=4 1111=15 15

Each digit in a number is called a BIT, so that last number is sixteen bits long in its binary form. If we wrote the second number as 000001, it would be sixteen bits long and have a value of 1.

### Word Size

The number of bits in the number has a direct bearing on the fidelity of the signal. Figure 2 illustrates how this works. The number of possible voltage levels at the output is simply the number of values that may be represented by the largest possible number (no "in between" values are allowed). If there were only one bit in the number, the ultimate output would be a pulse wave with a fixed amplitude and more or less the frequency of the input signal. If there are more bits in the number the waveform is more accurately traced, because each added bit doubles the number of possible values. The distortion is roughly the percentage that the least significant bit represents out of the average value. Distortion in digital systems increases as signal levels decrease, which is the opposite of the behavior of analog systems.

**Fig. 2 Effect of word size**

The number of bits in the number also determines the dynamic range. Moving a binary number one space to the left multiplies the value by two (just as moving a decimal number one space to the left multiplies the value by ten), so each bit doubles the voltage that may be represented. Doubling the voltage increases the power available by 6 dB, so we can see the dynamic range available is about the number of bits times 6 dB.