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- W2130333067 abstract "Redundant and hybrid-redundant number representations are used extensively to speed up arithmetic operations within general-purpose and special-purpose digital systems, with the latter (containing both redundant and nonredundant digits) offering cost advantages over fully redundant systems. We use weighted bit-set (WBS) encoding as a paradigm for uniform treatment of five previously studied variants of hybrid-redundant systems. We then extend the class of hybrid-redundant numbers to coincide with the entire set of canonical WBS numbers by allowing an arbitrary nonredundant position, heretofore restricted to ordinary bits (posibits), to hold a negatively weighted bit (negabit). This flexibility leads to interesting and useful symmetric variants of hybrid-redundant representations. We provide a high-level circuit design, based solely on binary full-adders, for a constant-time universal hybrid-redundant adder capable of producing a canonical WBS-encoded sum of two canonical WBS (or extended hybrid) numbers. This is made possible by the use of conventional binary full-adders for reducing any collection of three posibits and negabits, where negabits use an inverted encoding. We compare our adder to previous designs, showing advantages in speed, cost, and regularity. Furthermore we explore representationally closed addition schemes, holding the benefit of greater regularity and reusability, and provide high-level representationally closed designs for all the previously studied variants of hybrid redundancy and for the new symmetric variants introduced here. Finally, we present a new functionality for a conventional (4; 2) compressor in combining any collection of five equally weighted negabits and posibits, and show its utility in the design of multipliers for extended hybrid-redundant numbers." @default.
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- W2130333067 date "2006-02-01" @default.
- W2130333067 modified "2023-09-25" @default.
- W2130333067 title "An Efficient Universal Addition Scheme for All Hybrid-Redundant Representations with Weighted Bit-Set Encoding" @default.
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- W2130333067 doi "https://doi.org/10.1007/s11265-005-4177-6" @default.
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