Design of RNS Based Addition Subtraction and Multiplication Units

Residue number systems have gained significant importance in the field of high-speed digital signal processing due to their carry-free nature and speed-up provided by parallelism. The cynical aspect in the application of RNS is the selection of the moduli set and the design of the conversion units. 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 obtained in addition, subtraction and multiplication, which is usually time consuming. Thus, the comparison and division are more complicated and the fraction number computation is immured. In this paper, work is done by the residues of the number and performed Addition, Subtraction and Multiplication are performed which shows more advantages of Carry Free nature. Performance of RNS based Addition, subtraction and Multiplication Units has been implemented for modulo set {2 -1, 2 , 2+1} for n=2,3 with the targeted device of Spartan 3E using hardware description language called Verilog and synthesized in Xilinx ISE 13.2. Keywords—– Residue Number System (RNS), New Chinese Remainder Theorem (NCRT), Multioperand Modular Adder (MOMA), Mixed Radix Theorem (MRT), Chinese Remainder Theorem(CRT),Carry Save Adder(CSA).