<s>
A	O
digital	B-Device
differential	I-Device
analyzer	I-Device
(	O
DDA	O
)	O
,	O
also	O
sometimes	O
called	O
a	O
digital	B-Device
integrating	I-Device
computer	I-Device
,	O
is	O
a	O
digital	O
implementation	O
of	O
a	O
differential	B-Device
analyzer	I-Device
.	O
</s>
<s>
The	O
integrators	O
in	O
a	O
DDA	O
are	O
implemented	O
as	O
accumulators	B-General_Concept
,	O
with	O
the	O
numeric	O
result	O
converted	O
back	O
to	O
a	O
pulse	O
rate	O
by	O
the	O
overflow	O
of	O
the	O
accumulator	B-General_Concept
.	O
</s>
<s>
The	O
primary	O
advantages	O
of	O
a	O
DDA	O
over	O
the	O
conventional	O
analog	O
differential	B-Device
analyzer	I-Device
are	O
greater	O
precision	B-Architecture
of	O
the	O
results	O
and	O
the	O
lack	O
of	O
drift/noise/slip/lash	O
in	O
the	O
calculations	O
.	O
</s>
<s>
The	O
precision	B-Architecture
is	O
only	O
limited	O
by	O
register	O
size	O
and	O
the	O
resulting	O
accumulated	O
rounding/truncation	O
errors	O
of	O
repeated	O
addition	O
.	O
</s>
<s>
One	O
of	O
the	O
inspirations	O
for	O
ENIAC	B-Device
was	O
the	O
mechanical	O
analog	O
Bush	B-Device
differential	I-Device
analyzer	I-Device
.	O
</s>
<s>
However	O
,	O
although	O
ENIAC	B-Device
as	O
originally	O
configured	O
,	O
could	O
have	O
been	O
programmed	O
as	O
a	O
DDA	O
(	O
the	O
"	O
numerical	O
integrator	O
"	O
in	O
Electronic	B-Device
Numerical	I-Device
Integrator	I-Device
And	I-Device
Computer	I-Device
)	O
,	O
there	O
is	O
no	O
evidence	O
that	O
it	O
ever	O
actually	O
was	O
.	O
</s>
<s>
The	O
theory	O
of	O
DDAs	O
was	O
not	O
developed	O
until	O
1949	O
,	O
one	O
year	O
after	O
ENIAC	B-Device
had	O
been	O
reconfigured	O
as	O
a	O
stored	O
program	O
computer	O
.	O
</s>
<s>
The	O
first	O
DDA	O
built	O
was	O
the	O
Magnetic	B-Device
Drum	I-Device
Digital	I-Device
Differential	I-Device
Analyzer	I-Device
of	O
1950	O
.	O
</s>
<s>
The	O
basic	O
DDA	B-Device
integrator	I-Device
,	O
shown	O
in	O
the	O
figure	O
,	O
implements	O
numerical	O
rectangular	O
integration	O
via	O
the	O
following	O
equations	O
:	O
</s>
<s>
Where	O
Δx	O
causes	O
y	O
to	O
be	O
added	O
to	O
(	O
or	O
subtracted	O
from	O
)	O
S	O
,	O
Δy	O
causes	O
y	O
to	O
be	O
incremented	O
(	O
or	O
decremented	O
)	O
,	O
and	O
ΔS	O
is	O
caused	O
by	O
an	O
overflow	O
(	O
or	O
underflow	O
)	O
of	O
the	O
S	O
accumulator	B-General_Concept
.	O
</s>
<s>
Initial	B-Algorithm
conditions	I-Algorithm
for	O
the	O
problem	O
can	O
be	O
loaded	O
into	O
both	O
y	O
and	O
S	O
prior	O
to	O
beginning	O
integration	O
.	O
</s>
<s>
where	O
K	O
is	O
a	O
scaling	O
constant	O
determined	O
by	O
the	O
precision	B-Architecture
(	O
size	O
)	O
of	O
the	O
registers	O
as	O
follows	O
:	O
</s>
<s>
If	O
Δy	O
is	O
eliminated	O
,	O
making	O
y	O
a	O
constant	O
,	O
then	O
the	O
DDA	B-Device
integrator	I-Device
reduces	O
to	O
a	O
device	O
called	O
a	O
rate	B-Device
multiplier	I-Device
,	O
where	O
the	O
pulse	O
rate	O
ΔS	O
is	O
proportional	O
to	O
the	O
product	O
of	O
y	O
and	O
Δx	O
by	O
the	O
following	O
equation	O
:	O
</s>
<s>
Rounding/truncation	O
errors	O
due	O
to	O
the	O
limited	O
precision	B-Architecture
of	O
the	O
registers	O
.	O
</s>
<s>
However	O
,	O
as	O
this	O
reduces	O
the	O
scaling	O
constant	O
K	O
,	O
it	O
also	O
increases	O
problem	O
time	O
and	O
therefore	O
may	O
not	O
significantly	O
improve	O
accuracy	O
and	O
in	O
real	B-General_Concept
time	I-General_Concept
DDA	O
based	O
systems	O
may	O
be	O
unacceptable	O
.	O
</s>
<s>
The	O
effect	O
of	O
approximation	O
errors	O
can	O
be	O
reduced	O
by	O
using	O
a	O
more	O
accurate	O
numerical	O
integration	O
algorithm	O
than	O
rectangular	O
integration	O
(	O
e.g.	O
,	O
trapezoidal	O
integration	O
)	O
in	O
the	O
DDA	B-Device
integrators	I-Device
.	O
</s>
