Istituto di Scienza e Tecnologie dell'Informazione     
Barsi F. Residue arithmetic in binary systems. Progetto finalizzato materiali e dispositivi per l'elettronica a stato solido. Internal note IEI-B4-37, 1988.
A natural approach to the problem of performing mod m computations in a binary system is presented and a solution is suggested which is based upon a straightforward relation between the residues of a same integer X with respect to different moduli. The proposed solution proves fruitful in various applications, such as converting binary integers to residue notation and mod m addition or multiplication. Even if the most usual implementation approach for mod m processors is based on look-up tables, the use of a binary number system keeps its validity those situations, such as large-moduli residue arithmetic or conversion processes, where a memory approach is not viable. Moreover, VLSI area-time complexity aspects are considered for the presented applications and constructive proofs are given showing that the complexities of mod m and binary addition/multiplication structures coincide.
Subject Addition
Binary number system
Residue Number Systems
VLSI design
VLSI complexity

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