Introduction to Computer Music: Volume One

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 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, 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 in T1 and other computer network protocols.

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