Abstract:An algebraic number β ∈ C with no conjugate of modulus 1 can serve as the base of a numeration system (β, A) with parallel addition, i.e., the sum of two operands represented in base β with digits from A is calculated in constant time, irrespective of the length of the operands. In order to allow parallel addition, sufficient level of redundancy must be given to the alphabet A. The complexity of parallel addition algorithm depends heavily on the size #A of the alphabet: the bigger alphabet is considered, the l… Show more
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