Chapter Five: Digital Audio
2. Binary Numbers | Page 2
Bits and Bytes
Computers use a standardized number of bits in most circuits. These, by convention, are usually 8-bit values or multiples of 8-bit values. These 8-bit groups are called bytes. And two sequential bytes, used as a single value is often called a word, though more than two bytes can form double, triple words, etc.. CD audio uses two bytes, or 16 bits to encode music, but most studio work is now done in 24-bit words or higher. By finding the power of 2 for the number of bits being used, you can find the maximum number of values available, as indicated in the chart below.
| word size | power of 2 | # of values |
|---|---|---|
| 8-bit (1 byte) | 28 | 256 |
| 16-bit (2 bytes) | 216 | 65,536 |
| 24-bit (3 bytes) | 224 | 16,777,216 |
| 32-bit (4 bytes) | 232 | 4,294,967,296 |
When dealing with large numbers of bytes, the abbreviations below are used. Notice, however, that a kilobyte is somewhat more than a thousand bytes, a megabyte more than a million, etc.
| name | abbr. | power of 2 | # of bytes |
|---|---|---|---|
| Kilobyte | KB | 210 | 1,024 |
| Megabyte | MB | 220 | 1,048,576 |
| Gigabyte | GB | 230 | 1,073,741,824 |
| Terabyte | TB | 240 | 1,099,511,627,776 |
| Petabyte | PB | 250 | 1,125,899,906,842,624 |
Digital Encoding for Pulse Code Modulation
Computers and digital audio circuits can transmit binary data as a a series of fluctuations in electrical amplitude. To transmit a single stream of binary data with only two voltage values, an electrical value for 0 and a second for 1 is chosen. The data stream is then timed to a clock so that sequences of the 0's or 1's can be determined. The illustration below indicates one possible binary transmission scheme representing the binary value on the bottom (there are several three-voltage schemes, called duobinary; hover to see one).
We will be discussing various clock rates later on in this chapter, but most consumers are aware of clock speeds when they go to buy a computer (with a 5-gigahertz Intel or AMD processor, for example).
The use of binary code for transmission of audio data also goes back to 1903, with the transmission of voice for telephony at clock rates of around 4,000 Hz. But today's form of pulse code modulation, or (PCM for short) for audio was developed by the U.S. Army during WWII for transmitting secure speech transmission on very limited bandwidths using a system called SIGSALY (the same project pioneered another technique used in digital signal timing called FSK, or frequency shift keying, also used for drum machine and sequencer synchronization at one time in electronic studios prior to MIDI Time Code). Later PCM work at Bell Labs by John Pierce and others laid the groundwork for an explosion in digital signal transmission, computing and digital audio.
By using multiple voltage values instead of just two, multiple concurrent signals can be encoded and decoded in a process called time-division multiplexing or TDM. Originally developed for telephony as early as 1853, it was used by Digidesign's Pro Tools systems to send multiple streams of data across their DSP cards, as well as in T1 and other computer network protocols.
