of Microprocessors

646 MUSICAL ApPLICATIONS OF MICROPROCESSORS
Even when floating-point hardware or subroutines are available, rheir speed is
likely to be substantially less. The techniques of fixed-point computation are
rapidly becoming an obscure art, however. In the next few pages these will be
described to the depth necessary for use in digital signal-processing
applications. Reasonable familiarity with the binary number system will be
assumed. If the reader lacks such knowledge, introductory chapters of nearly
any book on microprocessor programming can provide the background.
Adequately illustrating such a discussion requires an example microprocessor.
Although Chapter 5 strongly suggested that the 68000 or other
16-bit machine should be used for direct synthesis applications, we will be
using the 6502 microprocessor here for illustration. Such a choice can be
rationalized in a couple of ways. First, programming just about any other
choice would be easier, since the 6502 does not have hardware multiply or
divide or even double byte add and subtract. Thus, understanding the given
examples implemented on a 6502 will make similar implementation on a
better machine seem simple in comparison. Another reason is that the 6502
is the basis of a great number of very inexpensive microcomputer systems.
Later, the FFT subroutine presented in BASIC in Chapter 13 will be
translated into 68000 assembly language to illustrate how integer arithmetic
can be used in that type ofalgorithm on a processor that has better arithmetic
capability.
The examples would not be very interesting unless actual synthesis and
analysis experiments can be performed. A-to-D and D-to-A boards are
available for most microcomputers, although they are seldom optimized for
audio applications. Micro Technology Unlimited, however, has audio DAC
and ADC systems at both the 8- and 16-bit levels that can be easily interfaced
to most computers. The 8-bit units are designed for 8-1O-ks/s sample rates
and already have the necessary filters included. While these are definitely not
hi-fi, they are indeed capable of illustrating all of the synthesis, modification,
and analysis techniques described in previous chapters. Most experimentation
will require a large memory buffer to hold a few seconds of
sampled sound, although some real-time operations are possible. A 32K
memory, for example, will hold 3-4 sec of sound at the sample rate for which
these boards were designed. The 16-bit units, however, are truly hi-fi and
include their own 32K sample buffer to simplify I/O programming as well as
stereo and plug-in filter features. Of course, any of the circuits given in
Chapters 7 and 12 can be used to build an audio DAC or ADC at considerable
savings over commercial units.
Properties ofBinary Arithmetic
Before plunging into programming examples, it is wise to review the
characteristics of binary ari thmetic that are important to signal processing.
We will be dealing with two fundamentally different kinds of numbers,