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In this paper, a new algorithm, called contention resolution algorithm for weight-two subexpressions (CRA-2), based on an ingenious graph synthesis approach has been developed for the common subexpression elimination of the multiplication block of digital filter structures. CRA-2 provides a leeway to break away from the local minimum and the flexibility of varying optimization options through a new admissibility graph. It manages two-bit common subexpressions and aims at achieving the minimal logic depth as the primary goal. The performances of our proposed algorithm are analyzed and evaluated based on benchmarked finite-impulse-response filters and randomly generated data. It is demonstrated that CRA-2 achieves the shortest logic depth with significant reduction in the number of logic operators compared with other reported algorithms.