Majority Logic Synthesis Based on Nauty Algorithm - Field-Coupled Nanocomputing: Paradigms, Progress, and Perspectives - page 121

i.e., the vector adds ''1'' 65536 times and overflows back to the null vector.
This resulted in 222 standard functions. The majority expressions for these standard
functions are obtained using the method introduced in Sect. 3.2 .
Notice, only standard functions with fewer than eight minterms need to be con-
sidered because functions with nine to sixteen minterms are just the complementary
form of functions comprising of seven to zero minterms. So, this method filters out all
vectors that have more than eight ''1''s.

4 Proposed method

4.1 Synthesis Method Overview

An overview of proposed synthesis method is shown in Fig. 16 . The input to the
algorithm is an arbitrary network of Boolean functions and the output is an optimized
majority expression network. The input network must be preprocessed and decom-
posed to a four-feasible network. This step is done with the SIS tool [ 22 ]. For each
node in the resulting decomposed network, the standard functions will be applied to
find its optimal majority expression. Then all redundancies are removed from the
preliminary majority expression network to obtain the final solution.

Fig. 16. An overview of proposed method