An efficient VLSI design for a residue to binary converter for general balance moduli (2/sup n/-3,2/sup n/+1,2/sup n/-1,2/sup n/+3)

High-speed and High-efficient Modulo (2n-3) Multipliers

“…The multiplier in [5] is composed of a binary multiplier and a modular compressor (4:1) modulo (2 3) n  . The modular compressor (4:1) modulo (2 3) n  is very complex and consists of 4 n-bit binary adders, 1 (n+1)-bit binary adder, 2 n-bit (2:1) MUXs and 2 control logic modules, which contains two 2 ANDs and 2 (2:1) MUXs.…”

“…Also, the novel 2 2 {2 1, 2 , 2 1} n n n   [4] moduli set, with a dynamic range of 5n bit. Recently, a 4-modulus base set {2 1, 2 3, 2 1, 2 3} n n n n     has been proposed [5] as a hierarchical base composed by two pairs of moduli [6]. Even though several moduli sets have been proposed using modulo (2 3) n  operations, the design of the required modulo (2 3) n  multipliers is still a key challenge.…”

High-speed modulo (2<I><SUP>n</SUP></I>+3) multipliers

“…From Fig. 1, it can be obtained the critical path is the timing path that propagates through the used (n + 1) × (n + 1) binary multiplier, the used n-bit CSA, n-bit binary adder (1), 5-bit binary adder, n-bit binary adder (2) and n-bit binary adder (3).…”

“…The novel moduli set {2 2n − 1, 2 n , 2 2n + 1} is studied [2]. The 4-modulus base set {2 n − 1, 2 n + 3, 2 n + 1, 2 n − 3} has been proposed [3,4]. Even though several moduli sets have been proposed using modulo (2 n + 3) operations, the design of the required modulo (2 n + 3) multipliers is still a key challenge.…”

On equivalences and fair comparisons among residue number systems with special moduli

“…Other special moduli, such as those taking the forms 2 k ± c, where c is a small constant greater than 1, or 2 k ± 2 l ± 1, for 1 < l < k, are also of some interest [Hias03a], [Pate07], [Sheu04], but dealing with them is beyond the scope of this paper. Some special sets of moduli are listed in Table 1 as a small representative sample.…”