of Microprocessors

616 MUSICAL ApPLICATIONS OF MICROPROCESSORS
Each IC manufacturer has its own pet parallel multiplier line. One
approach to parallel multiplication divides the large logic array into a
number of identical blocks, which are then stacked horizontally and
vertically to form the whole array. One type (AM2505, Advanced Micro
Devices) uses a block that implements a complete 2 X 4 multiplication in a
24-pin Ie. These blocks are then interconnected using a column for each two
multiplier bits and row for each four multiplicand bits. Thus, the needed 10
X 10 multiplier would use three rows of five chips each for a total of 15 IC
packages.
A variety of complete parallel multipliers all on a single chip are also
available. One example, the MPY1616 from TRW, includes a 16 x 16-bit
multiplier array and a 35-bit adder/accumulator on the multiplier's output all
in a 64-pin IC package. The total multiply-add time is about 150 nsee. In
spite of the large (1 inch X 3 inch) ceramic package, the unit's 3-5 W power
dissipation requires that a heatsink be glued to its top surface, although it is
still substantially less than what 32 AM2505s would require. Other
organizations such as 12 X 12 and 8 X 8 are also available, and a couple of
recent units even use high-speed CMOS technology to reduce heat dissipation
to more manageable levels. Unfortunately, all parallel multiplier ICs
seem to be expensive ($50 to $100 or more), probably because usage volume
is quite low compared to other IC types. In any case, a parallel multiplier is
indicated for the Fourier series tone generator.
Before continuing, let's briefly investigate a method for eliminating the
amplitude multiplier. It is well known that if two sine waves of exactly the
same frequency and unity amplitude but of different phase are added, that
the amplitude and phase of the resultant depends on the phast ~ifference
according to:
PI-PZ
A=2 cos P
2
where A is the resultant amplitude, P is the resultant phase, and PI and pz
are the phases of the individual waves. Thus, the two parameters PI and
pz can be manipulated to give the effect ofA and P parameters. The advantage,
of course, is that multiplication by A and addition to the harmonic
accumulator is replaced by two additions to the accumulator. There are
disadvantages, however. One is that the throughput rate of the phase adder
and sine table is doubled; another is the highly nonlinear relation between
PIIPZ and A,P, which would probably require a translation table to overcome.
The most serious disadvantage, however, is that greatly increased
resolution in the sine table is necessary for good control at low-amplitude
levels where the two waves nearly cancel. This means both more words in the