Deterministic BIST for RNS adders

Modulo 2ⁿ -1 adders as fast as n-bit 2´s complement adders have been recently proposed in the open literature. This makes a residue number system (RNS) adder with channels based on the moduli 2ⁿ, 2ⁿ - 1, and any other of the form 2^k - 1, with k < n, faster than RNS adders based on other moduli. We formally derive a parametric, with respect to the adder size, test set, for parallel testing of the channels of an RNS adder based on moduli of the form 2ⁿ, 2ⁿ - 1, 2^k - 1, 2^l - 1, ..., with l < k < n. The derived test set is reusable; it can be used for any value of n, k, l, ..., regardless of the implementation library used and is composed of n² + 2 test vectors. A test-per-clock BIST scheme is also proposed that applies the derived test vectors within n² + 2n cycles. Static CMOS implementations reveal that the proposed BIST offers 100 percent postcompaction fault coverage and an attractive combination of test time and implementation area compared to ROM and FSM-based deterministic BIST or LFSR-based pseudorandom BIST.