Chapter Five: Digital Audio
2. Binary numbers, bits and bytes | 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. CD audio uses two bytes, or 16 bits to encode music. By finding the power of 2 for the number of bits being uses, 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, 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 |
Pulse Code Modulation
Computers and digital audio circuits can transmit binary data as a a series of fluctuations in electrical amplitude, often call pulse code modulation or PCM for short. To transmit a single stream of binary data, 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 a possible pcm scheme representing the binary value on the top (there are several schemes).
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 their next computer (a 2 gigahertz Pentium 4, for example). PCM was developed by the U.S. Army during WWII for transmitting secure speech transmission on very limited bandwidths using a system called SIGSALY (which also pioneered another technique used in digital signal timing called FSK, or frequency shift keying). Later PCM work at Bell Labs by John Pierce and others laid the groundwork for an explosion in digital signal transmission and computing.
By using multiple voltage values instead of just two, multiple signals can be encoded and decoded in a process called time-division multiplexing or TDM. Originally developed for telephony, it is now in use by Digidesign's Pro Tools systems to send multiple streams of data across their DSP cards as well as T1 and other computer network protocols.
