RNS-to-Binary Converters for Two Four-Moduli Sets $\{2^{n}-1,2^{n},2^{n}+1,2^{{n}+1}-1\}$ and $\{2^{n}-1,2^{n},2^{n}+1,2^{{n}+1}+1\}$

In this paper, reverse converters for two recently proposed four-moduli sets {2
ⁿ
- 1,2
ⁿ
,2
ⁿ
+ 1,2
ⁿ
+1 - 1} and {2
ⁿ
- 1, 2
ⁿ
, 2
ⁿ
+ 1, 2
ⁿ
+1 + 1} are described. The reverse conversion in the three-moduli set {2
ⁿ
- 1,2
ⁿ
,2
ⁿ
+ 1} has been optimized in literature. Hence, the proposed converters are based on two new moduli sets {(2
ⁿ
(2
²ⁿ
-1)),2
ⁿ⁺¹
-1} and {(2
ⁿ
(2
²ⁿ
-1)), 2
ⁿ⁺¹
+1} and use mixed radix conversion. The resulting designs do not require any ROM. Both are similar in their architecture except that the converter for the moduli set {2
ⁿ
- 1, 2
ⁿ
, 2
ⁿ
+ 1, 2
ⁿ
+1 + 1} is slightly complicated due to the difficulty in performing reduction modulo (2
ⁿ⁺¹
+1) as compared with modulo (2
ⁿ⁺¹
-1). The proposed conversion techniques are compared with earlier realizations described in literature with regard to conversion time as well as area requirements.