Residue number system (RNS)

In the residue number system, a set of moduli which are independent of each other is given. An integer is represented by the residue of each modulus and the arithmetic operations are based on the residues individually. The arithmetic operations based on residue number system can be performed on various moduli independently to avoid the carry in addition, subtraction and multiplication, which is usually time consuming. However, the comparison and division are more complicated and the fraction number computation is immatured. Due to this, a residue number system is not yet popular in general-purpose computers, though it is extremely useful for digital-signal-processing applications. This thesis deals with the design, simulation and microcontroller implementation of some (residue number system based) building blocks for applications in the field of digital signal processing. The building blocks which have been studied are binary to residue converter, residue to binary converter, residue adder and residue multiplier.