Abstract: The residue number system (RNS) is popular in high performance computation applications because of its carry-free nature. The challenges of RNS systems design lie in the moduli set selection and in the reverse conversion from residue representation to weighted representation. In this paper, we proposed a fully parallel reverse conversion algorithm for the moduli set {rn - 2, rn - 1, rn}, based on simple mathematical relationships. Also an efficient hardware realization of this algorithm is presented. Our proposed converter is very faster and results to hardware savings, compared to the other reverse converters.
Abstract: Efficient modulo 2n+1 adders are important for
several applications including residue number system, digital signal
processors and cryptography algorithms. In this paper we present a
novel modulo 2n+1 addition algorithm for a recently represented
number system. The proposed approach is introduced for the
reduction of the power dissipated. In a conventional modulo 2n+1
adder, all operands have (n+1)-bit length. To avoid using (n+1)-bit
circuits, the diminished-1 and carry save diminished-1 number
systems can be effectively used in applications. In the paper, we also
derive two new architectures for designing modulo 2n+1 adder, based
on n-bit ripple-carry adder. The first architecture is a faster design
whereas the second one uses less hardware. In the proposed method,
the special treatment required for zero operands in Diminished-1
number system is removed. In the fastest modulo 2n+1 adders in
normal binary system, there are 3-operand adders. This problem is
also resolved in this paper. The proposed architectures are compared
with some efficient adders based on ripple-carry adder and highspeed
adder. It is shown that the hardware overhead and power
consumption will be reduced. As well as power reduction, in some
cases, power-delay product will be also reduced.
Abstract: Residue Number System (RNS) is a modular representation and is proved to be an instrumental tool in many digital signal processing (DSP) applications which require high-speed computations. RNS is an integer and non weighted number system; it can support parallel, carry-free, high-speed and low power arithmetic. A very interesting correspondence exists between the concepts of Multiple Valued Logic (MVL) and Residue Number Arithmetic. If the number of levels used to represent MVL signals is chosen to be consistent with the moduli which create the finite rings in the RNS, MVL becomes a very natural representation for the RNS. There are two concerns related to the application of this Number System: reaching the most possible speed and the largest dynamic range. There is a conflict when one wants to resolve both these problem. That is augmenting the dynamic range results in reducing the speed in the same time. For achieving the most performance a method is considere named “One-Hot Residue Number System" in this implementation the propagation is only equal to one transistor delay. The problem with this method is the huge increase in the number of transistors they are increased in order m2 . In real application this is practically impossible. In this paper combining the Multiple Valued Logic and One-Hot Residue Number System we represent a new method to resolve both of these two problems. In this paper we represent a novel design of an OHRNS-based adder circuit. This circuit is useable for Multiple Valued Logic moduli, in comparison to other RNS design; this circuit has considerably improved the number of transistors and power consumption.
Abstract: In this paper, a new reverse converter for the moduli set {2n, 2n–1, 2n–1–1} is presented. We improved a previously introduced conversion algorithm for deriving an efficient hardware design for reverse converter. Hardware architecture of the proposed converter is based on carry-save adders and regular binary adders, without the requirement for modular adders. The presented design is faster than the latest introduced reverse converter for moduli set {2n, 2n–1, 2n–1–1}. Also, it has better performance than the reverse converters for the recently introduced moduli set {2n+1–1, 2n, 2n–1}
Abstract: In this paper we present two novel 1-bit full adder
cells in dynamic logic style. NP-CMOS (Zipper) and Multi-Output
structures are used to design the adder blocks. Characteristic of
dynamic logic leads to higher speeds than the other standard static
full adder cells. Using HSpice and 0.18┬Ám CMOS technology
exhibits a significant decrease in the cell delay which can result in a
considerable reduction in the power-delay product (PDP). The PDP
of Multi-Output design at 1.8v power supply is around 0.15 femto
joule that is 5% lower than conventional dynamic full adder cell and
at least 21% lower than other static full adders.