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A new method of formulating constant integer multiplication is presented. It requires fewer adders in general than a canonic signed-digit (CSD) representation. Graphs are used to illustrate multiplier implementation. A general suboptimal algorithm for the design of multipliers of any wordlength is presented. For 32-bit words, it achieves an average improvement of 26.6% over CSD. Rules for the generation of graphs with the minimum number of adders and subtracters are presented. An exhaustive search algorithm using these rules is described, and applied for word-lengths up to 12 bits. For 12-bit words, it was found that an average improvement of 16% over CSD is achievable.
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Dempster et al. (1994) studied this question.
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