Issue No.01 - January (1992 vol.41)

pp: 109-112

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.123386

ABSTRACT

<p>In a standard binary search, the binary representation of the index of an element in an ordered linear array is recovered serially bit by bit. For an array of N elements, the index of an element is recovered, in principle, by assigning to each element one value out of log/sub 2/ N possibilities. It is shown here that by arranging 2/sup n/-1 elements in a circular array, the bits of the binary representation of the index of an element are all recovered simultaneously based n assigning to each element one value out of two possibilities. The main theoretical result shows that the parity of an integer X is trivially recovered from the parity of the Hamming weight of the binary representation of X, X+1, X+2, and X+3, whereas, on the other hand, the parity of the Hamming weight of the binary representation of an integer is consistent with modular arithmetic considerations.</p>

INDEX TERMS

circular binary search; binary representation; ordered linear array; circular array; parity; Hamming weight; modular arithmetic; codes; digital arithmetic; search problems.

CITATION

B. Arazi, "A Circular Binary Search",

*IEEE Transactions on Computers*, vol.41, no. 1, pp. 109-112, January 1992, doi:10.1109/12.123386