On Modulo 2^n+1 Adder Design

Two architectures for modulo 2ⁿ+1 adders are introduced in this paper. The first one is built around a sparse carry computation unit that computes only some of the carries of the modulo 2ⁿ+1 addition. This sparse approach is enabled by the introduction of the inverted circular idempotency property of the parallel-prefix carry operator and its regularity and area efficiency are further enhanced by the introduction of a new prefix operator. The resulting diminished-1 adders can be implemented in smaller area and consume less power compared to all earlier proposals, while maintaining a high operation speed. The second architecture unifies the design of modulo 2ⁿ ± 1 adders. It is shown that modulo 2ⁿ+1 adders can be easily derived by straightforward modifications of modulo 2ⁿ-1 adders with minor hardware overhead.