Operating
Instructions—7A42
5.
The
following
two
expressions,
known
as
DeMorgan's Theorem,
shows
the
relationship
of
the
AND,
OR
and
NOT
(invert)
logic
functions
to
one another.
With
the
use
of
the
invert function,
the
AND
function
can
be
expressed
in
terms
of
OR
function,
and
vise
versa.
X
•
Y=
/(/
X+
/
Y)
X+Y=/(/X
•/
Y)
6.
AND functions
and
OR functions
can
be
combined
together
in
one
of
two
equivalent
notations, called
sum
of
products and
product
of
sums.
The
7A42
trigger
function
uses
the
sum
of
products
notation,
that
is,
the
OR
of two
AND
functions.
DeMorgan
s Theorem
can
be used
to convert
from
one notation
to
another.
An
example
of
the sum
of
products
notation as
it
relates
to
the
7A42
is:
(CH1«CH2)+(CH3«CH4)
where
CH1
,
CH2, CH3,
and
CH4
are
the
Boolean
variables, the
two
quantities
in
parantheses
(AND
functions)
are
called
products,
and the
two
products
are
“
ORed”
together
to
form
a
sum.
Each
7A42
trigger
function can
consist
of
up
to
two
products
of
the
four
input
channels
summed
together.
The
products
may
be
formed
in
any
combination
from
one
or
all of
the
input channels.
The
analog
channel
input
signals
become
Boolean
variables
when
they
are
compared
to
a
threshold
voltage.
If
the signal
is
higher than
the
threshold,
it
is
true;
if
lower,
it
is
false. The
Boolean
variables
may
be
programmed
into the
trigger
function
in
either
their
non-inverted
(high)
or
inverted
(low)
form.
A
channel
input
which
is
not
part
of
the
trigger
function
is
considered
a
“don't
care”.
Figure
2-3
shows
two examples
of
a
user
programmed
trigger
function.
In each
example,
the
trigger
function
is
comprised
of
a
logical
contribution of
input
channels
1
through
4.
NOTE
Logic
symbols used in the following functional tables are of the
positive
logic convention
and are defined as follows:
H = high level (true or logic
"1")
L = low
level (false or logic
"0")
I
=
transition from low
to
high level
I
=
transition
from
high
to low
level
X
= irrelevant (any input, including transitions)
TL
- one high-level
pulse
2-
4