An Efficient Reverse Converter for the Three-Moduli Set ( $ 2^{n+1}-1, 2^{n}, 2^{n}-1$ )

The well-known three-moduli set (2
ⁿ
+1, 2
ⁿ
, 2
ⁿ
-1), where n is a positive integer, has received considerable attention over the last three decades. Many researchers have proposed residue-to-binary (reverse) converters for this moduli set. However, the problem of designing a reverse converter for the moduli set (2
ⁿ⁺¹
-1, 2
ⁿ
, 2
ⁿ
-1) did not receive significant attention. In this brief, we are proposing a reverse converter for this particular moduli set. When compared with the available similar converters, considerable reductions have been achieved. Using VLSI design tools, the area, time, and power reductions are in the range of (10.6 - 60.1)%, (13.8 - 25.2)%, and (7.7 - 52.1)%, respectively.