In many digital signal processing algorithms, e.g., linear transforms and digital filters, the multiplier coefficients are constant. Hence, it is possible to implement the multiplier using shifts, adders, and subtracters. In this work two approaches to realize constant coefficient multiplication with few adders and subtracters are presented. The first yields optimal results, i.e., a minimum number of adders and subtracters, but requires an exhaustive search. Compared with previous optimal approaches, redundancies in the exhaustive search cause the search time to be drastically decreased. The second is a heuristic approach based on signed-digit representation and subexpression sharing. The results for the heuristic are worse in only approximately 1% of all coefficients up to 19 bits. However, the optimal approach results in several different optimal realizations, from which it is possible to pick the best one based on other criteria. Relations between the number of adders, possible coefficients, and number of cascaded adders are presented, as well as exact equations for the number of required full and half adder cells. The results show that the number of adders and subtracters decreases on average 25% for 19-bit coefficients compared with the canonic signed-digit representation.

Multiple constant multiplication (MCM) has been an active research area for the last decade. Most work so far have only considered the number of additions to realize a number of constant multiplications with the same input. In this work we consider the number of full and half adder cells required to realize those additions and a novel complexity measure is proposed. The proposed complexity measure can be utilized for all types of constant operations based on shifts, additions and subtractions. Based on the proposed complexity measure a novel MCM algorithm is presented. Simulations show that compared with previous algorithms, the proposed MCM algorithm have a similar number of additions while the number of full adder cells are significantly reduced.

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In this work we propose a switching activity model for single adder multipliers. This correspond to the case where a signal is added to a shifted version of itself, which is a common part in multiple constant multiplication (MCM). Hence, the proposed model is suitable to be used in power consumption aware MCM algorithms. The model is shown to agree well with simulations, and for the studied test cases a maximum error of 0.26% is obtained.

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