A SIMPLE GRAY CODE TO LIST ALL MINIMAL SIGNED BINARY REPRESENTATIONS
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Author: by J. Sawada
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Abstract: Abstract. A signed binary representation (SBR) of an integer N is a string ab ???a2a1a0 over the alphabet {-1, 0, 1} such that N = ?b i=0 ai2i. An SBR of an integer N is said to be minimal if the number of nonzero digits is minimum. In this paper, we describe a simple 3-close Gray code for listing all minimal SBRs of an integer N. The algorithm is implemented to run in constant amortized time. In addition, we identify the values for N that have the maximum number of minimal SBRs given the length of the binary representation of N. Key words. Signed binary representations, Gray code
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