Pin-Constrained Chip Design - Digital Microfluidic Biochips - page 75

X 0 1 0

E 1 E 2 E 3 E 4

Figure 3.31
Illustration of a “don't-care” in electrode activation.

E 1 E 2 E 3

E 8

E 4

E 7 E 6 E 5

(a)

Electrode 12345678
Activation
Sequence

0
1
0
0
X
X
X
X

1
0
0
X
X
X
X
0

0
0
X
X
X
X
0
1

0
X
X
X
X
0
1
0

X
X
X
X
0
1
0
0

X
X
X
0
1
0
0
X

X
X
0
1
0
0
X
X

X
0
1
0
0
X
X
X

(b)

Figure 3.32
Example of activation sequence calculation: (a) routing and layout information; (b) calculated
activation sequences.

We use the three values “1,” “0,” and “x” to represent the electrode-activation
sequences for a bioassay. An example is shown in Figure 3.32. A droplet is
routed anticlockwise, one electrode per step, along the loop consisting of
eight electrodes. Suppose that at time instant (clock cycle) t 0 , the droplet rests
on electrode E 2 . The activation sequence for each electrode is now calculated
and listed in Figure 3.32b.
In Figure 3.32b, each sequence contains several don't-care terms, which
can be replaced by “1” or “0.” By carefully replacing these don't-care terms,
the two activation sequences corresponding to E 1 and E 4 can be made identi-
cal. For example, we can map the four don't-cares in the activation sequence
for E 1 with “0010” and the four don't-cares in the activation sequence for E 4
with “0100.” We refer to such sequences as compatible sequences . Compatible