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U. Glaeser

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FIGURE 2.43 Monolithic PTL and multilevel PTL.<br />

FIGURE 2.44 Example of multilevel BDD and its construction method.<br />

shown in Fig. 2.43(b). MPL can be synthesized from a multilevel BDD shown in Fig. 2.44(a). The<br />

methods for building a multilevel BDD can be categorized into two types. One is based on conversion<br />

from a monolithic BDD described in the section on “Top-Down Design of Pass-Transistor Logic Based<br />

on BDD”. Figure 2.44(b) shows a representative method in this category [11]. In this method, subgraphs<br />

that cannot be shared because at least one of their edges is not equivalent are searched for. Then,<br />

the detected sub-graphs are extracted and replaced with new nodes. For these new nodes, new introduced<br />

variables are assigned. In Fig. 2.44(b), X and Y are the new introduced variables. These variables are<br />

connected to the output of a new BDD, which has the same diagram as the extracted sub-graph except<br />

that its 0-edge and 1-edge are terminated to “0” and “1” nodes, respectively. By this extraction, it is<br />

possible to convert the monolithic BDD into two or more sub-BDDs, which are multiply connected<br />

with one another and have the same logic function as the original. Finally, by replacing the nodes with<br />

pass-transistor selectors, as described in the section on “Top-Down Design of Pass-Transistor Logic<br />

Based on BDD,” the MPL is obtained. Here, in the MPL the outputs of the pass-transistor selectors can<br />

be connected to the control inputs of other pass-transistor selectors, so level-restoration buffers are<br />

required for these places.<br />

© 2002 by CRC Press LLC<br />

primary<br />

inputs<br />

(a) Monolithic PT L<br />

0<br />

Out1<br />

Out2<br />

same shape sub-graphs<br />

Out1 Out2<br />

A A<br />

B<br />

D E<br />

B<br />

C C<br />

1<br />

sub BDD<br />

0<br />

F<br />

G<br />

1<br />

primary<br />

inputs<br />

sub BDD<br />

Out1<br />

sub PT L<br />

extract & replace<br />

sub PT L<br />

Out2<br />

(a) Multilevel BDD<br />

0<br />

sub BDD<br />

Out1<br />

X<br />

Out1<br />

(b) MPL<br />

Out2<br />

Y<br />

Out2<br />

sub PT L<br />

D E B<br />

(b) Multilevel BDD construction method<br />

1<br />

0<br />

F<br />

G<br />

1<br />

0<br />

A<br />

C<br />

1

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