A SIMPLE GRAY CODE TO LIST ALL MINIMAL SIGNED BINARY REPRESENTATIONS


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    		Views: (1004)   Date: (13-05-09)   Pages: ()

  • Author:  by J. Sawada  

  • 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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