Digital System Research

Archive for Mathematics

Algorithms

How does a new form of arithmetic processing affect algorithms? Does a change in arithmetic processing change or influence algorithm design? There may be more influence than expected. Researchers at DSR are defining the benefits of a new arithmetic paradigm, not by copying binary algorithms, but by replacing binary algorithms. At DSR, it is clear […]

Fractional Representations

Researchers at DSR develop new methods for representing and processing fractional quantities. We promise that everything is different with residues! For example, when performing general purpose calculations, we usually turn to fractional formats such as floating point numbers. If we have N binary bits dedicated to the fractional portion of a binary value, then we […]

Computational Complexity

Can the known order of arithmetic operations be smashed? Does an underlying number system affect the computational complexity of basic arithmetic operations? Indeed, this is true. Researchers at DSR are studying and analyzing newly discovered relationships. There are significant tradeoffs between performing calculations in the binary number system versus performing calculations in the residue number […]

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