Weighted two-valued digit-set encodings: unifying efficient hardware representation schemes for redundant number systems

Redundant Multiple-Valued Number Systems

In a civilization, human labor of one type is exchanged for human labor of another type. For example, when one eats at a restaurant, one exchanges money earned from one’s own labor for the labor of people who cook, raise animals and vegetables, deliver goods, etc.. This exchange is made possible by a salary, which establishes a value for labor of different types. There are many ways to represen...

Developing Efficient Encodings for Weighted Expressions in Answer Set Programs

Stored-transfer representations with weighted digit-set encodings for ultrahigh-speed arithmetic

Redundant representations play an important role in high-speed computer arithmetic. One key reason is that such representations support carry-free addition, that is, addition in a small, constant time, independent of operand widths. The implications of stored-transfer representation of digit sets and the associated addition schemes, as an extension of the stored-carry concept to redundant numbe...

Efficient squaring circuit using canonical signed-digit number representation

Squaring and exponentiation of a number are fundamental arithmetic and widely used in the real-time applications such as image processing, digital filtering and cryptography. In this paper, we propose a squaring algorithm of an integer with canonical signed-digit (CSD) number representation. For an n-digit CSD number, our method generates n/4 CSD numbers of 2n-digit length as partial products. ...

An Efficient Universal Addition Scheme for All Hybrid-Redundant Representations with Weighted Bit-Set Encoding

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 var...