$(4+2\log n)\Delta G$ Parallel Prefix Modulo- $(2^n-3)$ Adder via Double Representation of Residues in [0, 2]

The most popular modulus in residue number systems (RNS), next to power-of-two modulus, are those of the form (2
ⁿ
-1). However, in RNS applications that require a larger dynamic range, without increasing the n parameter, modulus of the form (2
ⁿ
-3) are gaining popularity. Nevertheless, latency-balanced computational channels in RNS arithmetic systems are desirable. Ripple-carry modulo-(2
ⁿ
-1) adders are realized simply as one's complement adders, where (2
ⁿ
-1) serves as a second representation for 0. However, the same single n-bit adder realization is not possible for modulo (2
ⁿ
-3). Given that the efficient parallel prefix realization of modulo-(2
ⁿ
-1) adders exists, whose latency is compatible with similar modulo-2
ⁿ
adders, we are motivated to design latency-compatible parallel prefix modulo-(2
ⁿ
-3) adders. In this brief, we propose the fastest of such adders, where residues in {0, 1, 2} can be represented also as excess-(2
ⁿ
-3) encoding (i.e., {2
ⁿ
-3, 2
ⁿ
-2, 2
ⁿ
-1}, respectively) . The delay and area overhead of the proposed adder with respect to the base modulo-(2
ⁿ
-1) adder is only one extra gate in the critical delay path and, at most, 20% more area. In very rare cases that both operands are excess-(2
ⁿ
-3), augmenting the proposed adder with few extra gates leads to correct sum. The analytical results are confirmed by synthesis via Synopsys Design Compiler.